Introduction

Organic aerosols (OA) have become the predominant component of fine particulate matter (PM2.5) in many regions1,2. Despite their recognized importance in air quality, climate change, and human health, accurately simulating their formation in models remains a significant challenge due to gaps in understanding their formation mechanisms and accurate parameterization3,4. Semi-volatile organic compounds (SVOCs) play a crucial role in OA formation through the dynamic gas-particle partitioning (GPP) process. While many attempts have been made to comprehend the GPP of SVOCs, the focus has mainly been on hydrocarbon species such as polycyclic aromatic hydrocarbons (PAHs) and alkanes that are dominated by primary emissions, leaving knowledge gaps regarding oxygenated compounds due to a lack of effective instruments5,6,7,8. However, with the mitigation of primary SVOCs, oxygenated SVOCs have become increasingly important, emphasizing the necessity to understand the GPP for those oxygenated compounds.

Nitro–phenolic species (NPs), characterized by the presence of –NO2 and –OH substituents attached to a benzene ring, are considered as typical oxygenated SVOCs based on their physicochemical properties and volatility range. Many studies have confirmed their presence in both the gas and particle phases under ambient atmospheric conditions9,10,11. NPs can originate from primary emissions such as coal combustion, vehicle exhaust, and biomass burning, as well as from secondary formation via oxidation of aromatic precursors11,12,13,14,15. In addition to their phytotoxic effects, NPs are also recognized as key chromophores in brown carbon (BrC), with strong light absorption at wavelengths greater than 360 nm, thereby affecting solar radiative balance and modulating atmospheric oxidation capacity via photolysis9,10,16,17,18,19,20. Therefore, accurate characterization of their GPP is crucial for quantifying their roles in atmospheric chemistry and climate change. However, the current understanding of the GPP of NPs is limited to only variations in species, seasons, and locations11,15. Besides, inconsistencies between the field–derived GPP coefficient (Kep) and the theoretical estimations have been reported for NPs in previous studies5,10,21. For example, the particulate fraction (Fp), defined as the ratio of particulate concentration of one species to its total concentration in both gas and particle phases, for C6H5NO3 was underestimated by three orders of magnitude compared to ambient observations10. These phenomena underscore the urgency of comprehensively investigating the GPP of NPs.

Many theoretical methods have been established to estimate the GPP of SVOCs, among which Pankow’s absorption equilibrium theory (Eq. 1) as the foundation of many other theories, is the most used and has been used to estimate the GPP of NPs on aerosols in previous studies5,10,21. As shown in Eq. 1,

$${K}_{{ep}}=\frac{760\times {f}_{{om}}\times{R\times T}}{{10}^{6}\times {P}^{0}\times {{MW}}_{{om}}\times\zeta }$$
(1)

Kep (m3/μg) describes the ability of SVOCs to enter the particle phase and is determined by factors such as the fraction of organic matter in the particle phase (fom), temperature (T, K), the average molecular weight of organic matter (MWom, g/mol), activity coefficient (ζ), gas constant (R, 8.2 × 10−5 m3 atm mol−1 K−1), and the vapor pressure of the subcooled liquid (P0, Torr)22,23. In addition to the expression used in Eq. 1, which represents the classical form of the absorption equilibrium theory22,23, alternative formulations are also available (Eq. S2 and S3 in the Supporting Information), applying different standard units for calculating Kep24. Among these parameters, fom, T, and MWom can be directly measured or estimated, contributing minor uncertainty to Kep estimation. P0 for most oxygenated SVOCs can only be obtained from theoretical estimation, as has been widely used in previous studies. ζ accounts for the deviation from ideal behavior in a non-ideal mixture of chemical substances, and is influenced by the structure of SVOCs, aerosol composition, and interactions between SVOCs and aerosol components25. Previous studies have emphasized the species–specific nature of ζ in the real atmosphere, yet it is still commonly assumed to be 1 in many modeling efforts, as it is for pure substances, due to the difficulty of accurately determining activity coefficients in complex aerosol mixtures14,26. Though the estimated Kep with this assumption only differed by one to two orders of magnitude from the measurements for most alkanes and PAHs, the difference could be up to 106 times for oxygenated SVOCs, indicating significant uncertainties in the assumption for oxygenated species5,6,7,8,27,28,29. The Universal Quasi-Chemical Functional-group Activity Coefficients (UNIFAC) model was developed to estimate specific ζ values for organics, but challenges in obtaining comprehensive and accurate parameters for the estimation, along with its incomplete consideration of interactions between species, may introduce uncertainties and limit its broader application30,31. While a few studies have investigated the ζ value for several oxygenated SVOCs in laboratory experiments30,32,33, simplified aerosol components may result in different ζ values compared to the real atmosphere34,35. The unknown uncertainty in P0 estimation and challenges in obtaining ζ prevent us from accurately describing the GPP of oxygenated SVOCs. Recent advancements in instrumentation have enabled the simultaneous measurement of gaseous and particulate oxygenated SVOCs8,29, which motivate the idea of whether an apparent ζ can be derived from the field measurement for oxygenated SVOCs with theoretically estimated P0 to capture their GPP under real-world conditions.

Here, a field campaign was conducted to concurrently measure gaseous and particulate NPs at a coastal background site in Hong Kong using a Time–of–Flight Chemical Ionization Mass Spectroscopy (ToF–CIMS) coupled with a Filter Inlet for Gases and AEROsols (FIGAERO). The GPP of NPs was examined and compared with theoretical estimations. The observation-based ζ for each NP was determined and discussed. Benefiting from the high–time–resolution results, the evolutions of Fp of NPs were captured and further investigated by an observation–based box model (OBM) combined with the derived ζ.

Results and Discussion

Characteristics of NPs and comparison to theoretical estimation

A series of homologs of NPs including 14 types of mono–NPs (C6–9HxNO3, C6–9HxNO4, C6–8HxNO5, C7–9HxNO6) and 6 types of di–NPs (C6–9HxN2O5, C7–8HxN2O6) were identified and measured in the field campaign (Fig. 1a, S1, and Table S1)36. Gaseous NPs were measured by ToF–CIMS with gas inlet from 6 October to 24 November 2020 (Phase 1), and gaseous and particulate NPs were concurrently measured with the FIGAERO inlet from 26 November to 19 December 2020 (Phase 2).

Fig. 1: Overview of NPs partitioning observations.
figure 1

a The averaged concentration of measured gaseous and particulate NPs (mono–NPs and di–NPs); b The diurnal variation of concentration in the gas phase, particle phase and the fraction in the particle of C7H7NO3, C7H7NO4, and C7H6N2O5; c The measured and absorption equilibrium theory estimated Fp of NPs.

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Most of the measured NPs showed a good correlation between the gas and particle phases (Fig. S2a). Besides, individual NP strongly correlated with each other in the particle phase, and also with PM2.5 and BrC (Fig. S2b). The average concentration of total measured gaseous NPs during the whole campaign was 58.0 ± 36.6 ng/m3 with mono–NPs of 32.0 ± 25.7 ng/m3 and di–NPs of 26.1 ± 17.4 ng/m3, which were higher than the particulate concentrations of NPs (Fig. 1a and Table S1). The average and maximum concentrations of particulate NPs were 13.8 and 45.4 ng/m3, respectively, about one–fifth and one–third of the corresponding gas phase concentration in Phase 2 (67.8 and 227.5 ng/m3). Among the measured gaseous NPs, C6H4N2O5 was the most dominant species with an average concentration of 17.68 ± 12.4 ng/m3, followed by C6H5NO3 (11.18 ± 9.09 ng/m3), and C8H9NO4 (7.89 ± 8.51 ng/m3) in turn. Different from the gaseous NPs, C6H5NO3 showed the highest concentration (2.7 ± 2.0 ng/m3) in the particle phase, followed by C6H4N2O5 and C7H7NO3, with average concentrations of 1.4 ± 0.6 ng/m3 and 1.1 ± 0.92 ng/m3, respectively. The inconsistent trend of NPs concentrations in the gas and particle phases reflected the different GPP properties across species.

As shown in Fig. 1b and S3, the diurnal variations of gaseous NPs, particulate NPs, and Fp were captured. Unexpectedly, Fp showed three types of diurnal patterns, i.e., nighttime peaks, no diurnal variation, and daytime peaks, as summarized in Table 1. Gaseous mono–NPs with only one –OH substituted group (C6–9HxNO3) started to increase at around 8:00 and peaked at noon and afternoon, while the increase in particle phase began at 11:00 and reached the peak at around 17:00, resulting in a daytime Fp trough but higher nighttime value. NPs such as C6,7,9HxNO4, C6,7HxNO5, and C8,9HxNO6 presented similar diurnal variations in the gas and particle phases, leading to a stable diurnal of Fp. C6–8HxN2O5 and C7,8HxN2O6 showed daytime troughs in the gas phase, but a slight increase or stable trend in the particle phase, resulting in higher Fp in the daytime. The diversity of Fp diurnals suggests that there are essential yet complicated processes of GPP that need to be explored.

Table 1 The fitted activity coefficient ζ of studied compounds in this study
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The average Fp of NPs varied from 8.6% (C6H4N2O5) to 53% (C7H7NO5) (Fig. 1c), which was comparable to the Fp measured in previous studies at urban Jinan11, Mount Tai10, Beijing37, Rome9, and Iowa38 utilizing High-Performance Liquid Chromatography Mass Spectrometry (HPLC–MS), FIGAERO–CIMS, or Gas Chromatography Mass Spectrometry (GC–MS) method. The Fp of C6H5NO3 ranged from 4.6% to 39% with an average value of 20%, which is a little lower than the observed Fp of 4–nitrophenol at Mount Tai (27.8% to 77%) and at Jinan (about 30% and 55% in summer and spring, respectively)10,11. The measured Fp of C6H4N2O5 (3.2%–22%) was comparable to the reported Fp of 2,4–dinitrophenol at Mount Tai (1.4%–38%) and Jinan (about 5% and 35% in summer and spring, respectively)10,11. However, most of the estimated Fp of NPs from absorption equilibrium theory (with the assumption of ζ being 1) are located outside the observation range, showing discrepancies up to 4 orders of magnitude (Fig. 1c). In addition to the absorption equilibrium theory, several other theoretical methods were also used to estimate the Fp of NPs, including Junge–Pankow (J–P) adsorption model, Harner−Bidleman (H−B) Koa–based absorption model, steady–state approximation model (L−M−Y model), and Linear Solvation Energy Relationship (LSER) model. Detailed information is provided in the supporting information (SI). In light of the potential impact of compound structure on the GPP process, the calculation incorporated various possible NP structures. Large discrepancies were still found for most of the estimated values compared to the observations (Fig. S4 and S5). For example, the estimated Fp values of C6–9HxNO3 were 5.2 × 10–7 to 0.17, which was 2 to 105 times lower than the measurements. More results and detailed discussions are also given in the SI. The phenomenon was similar to the results reported in previous studies, showing the unmatchable results between estimated and measured Fp of NPs10,11,39. Although uncertainties arising from calibration, potential mixture of multiple structural isomers, and systematic errors may affect the accuracy of the measured Fp of NPs, the magnitude and consistency of the discrepancy, along with comparable results as reported in previous studies suggest that measurement uncertainties alone are unlikely to fully explain the observed differences between measured and estimated values9,10,11,37,38. Besides, observed Fp higher than theoretical estimations were also widely reported for other multifunctional compounds in addition to NPs in previous studies, suggesting some common and large uncertainties in accounting for the GPP of oxygenated SVOCs8,27,39.

Derivation of new empirical parameters

For the ideal solution/condition, the ζ in Pankow’s absorption equilibrium theory can be assumed as 1 in calculating the GPP of SVOCs22. However, the nonideal behavior of mixtures of organic aerosol components has been proved, which would lead to a deviation of ζ from 1 and thus bring errors to the estimation of Kep and Fp25,30.

The field measured Kep could be calculated from \(\frac{{C}_{p}}{{C}_{g}\times{PM}}\), where Cp (ng/m3), Cg (ng/m3), and PM (μg/m3) are the concentration of particulate NPs, gaseous NPs, and fine particulate matter. By integrating with Pankow’s theory, the relationship between ζ and other measured parameters could be derived as Eq.2, in which OA represents total organic matter in particles.

$${C}_{g}=\frac{{10}^{6}\times {C}_{p}\times{P}^{0}\times {{MW}}_{{om}}}{760\times{R\times T}\times {OA}}\times \zeta$$
(2)

As shown in Fig. S6, \({C}_{g}\) of most studied NP compounds showed good correlation with \(\frac{{{10}^{6}\times C}_{p}\times{{P}^{0}\times {MW}}_{{om}}}{760\times{R\times T}\times {OA}}\), implying that ζ kept relatively stable during the field campaign. Among the studied compounds, the scatter plots of C8H9NO5, C7H7NO6, C7H6N2O6, and C8H8N2O6 showed two branches, and good correlations between \({C}_{g}\) and \(\frac{{10}^{6}\times {C}_{p}\times{{P}^{0}\times {MW}}_{{om}}}{760\times{R\times T}\times {OA}}\) still existed in each branch, corresponding to daytime and nighttime data (Fig. S7). Then, an apparent effective value of ζ can be fitted. The derived ζ of studied NPs are summarized in Table 1 with most of the fitted values lower than 1. For example, the fitted ζ of C6–9HxNO3 ranged from 0.001 to 0.0041, which is 2 to 3 orders of magnitude lower than 1. It should be noted that the apparent parameter ζ may also encompass the potential uncertainties from P0 estimation with Estimation Programs Interface (EPI) suite40,41, which is a Windows-based suite of physical/chemical property and environmental fate estimation programs developed by EPA and Syracuse Research Corp. However, due to the lack of P0 measurement, theoretical estimations remain the only feasible approach and have been widely used in previous studies. More accurate ζ values can be refined as experimental P0 data become available in the future. More detailed discussion about P0 and the sensitivity of Fp towards the change of ζ for different species could be found in SI. The branching behavior of C8H9NO5, C7H7NO6, C7H6N2O6, and C8H8N2O6 suggests differences in GPP processes between day and night. The variability in the physicochemical properties (such as differences in acidity and viscosity) of organic aerosols influenced by air mass origin may influence the GPP process. However, the backward trajectory analysis showed no clear dependence of the pattern on air mass clusters. Then, it is speculated that the observed variations in ζ are likely caused by the different formation pathways and/or different molecular structures for them during day and night. Besides, disregarding uncertainties associated with P0 and other parameters, the high ζ values for C7H7NO6 and C7H6N2O6 observed at nighttime may suggest the occurrence of phase separation; however, further evidence and additional studies are required to substantiate this hypothesis.

In addition to the possible overestimation of P0, the low ζ of NPs might be contributed by the strong interactions between NPs and other components in the aerosol, such as hydrogen bond42. If the interaction between NPs and other aerosol components was stronger than the interaction of NPs in pure sub–cool liquid, the escape of NPs from aerosol would be harder than that from pure NPs, leading to a higher Fp and lower ζ of NPs in the real atmosphere than that in the ideal state. The NPs molecules contain –OH, –NO2, and benzene ring in their structures, which could act as hydrogen bond acceptors and donors at the same time. Highly oxygenated organic molecules generated from RO2 autoxidation and oligomers have been identified as dominant components contributing to secondary aerosol formation1,2. Many –OOH, –C(O)O–, and –OH functional groups in their structures can interact with NPs by hydrogen bond. If the interactions between aerosol components and NPs are higher than those between NPs themselves, more NPs would distribute in the aerosol phase than the ideal state, resulting in ζ lower than 143. Similar reasons could also explain the previously reported higher observed Fp than estimations for multifunctional compounds8,27,39.

Furthermore, it is found that for mono-NPs (CxHyNO3 and CxHyNO4) with the same oxygen content, an increase in the number of carbon atoms corresponds to a rise in their ζ values (Table 1 and Fig. S8). This trend is consistent with the findings of Donahue et al.44 and may be partly attributed to the reduced molecular polarity due to additional -CH3 groups. In contrast, no clear trend was observed for di-NPs. Although the addition of a second -NO2 group increases molecular polarity, di-NP often exhibited even higher apparent activity coefficients than their mono-NP counterparts. This result may reflect not only solute properties but also the interaction between solute and aerosol-phase solvent. According to the results of Donahue et al.44, a smaller difference in O:C ratio between them would yield a smaller deviation from ideal behavior. Therefore, it is plausible that the bulk aerosol composition is more chemically similar to the di-NPs than to mono-NPs, thereby minimizing solute-solvent mismatch and contributing to the higher apparent ζ values observed for di-NPs. While this interpretation is consistent with existing theoretical frameworks, we acknowledge that it remains speculative. Additional experimental studies are needed to quantify how functional group additions, molecular polarity, and bulk aerosol composition collectively influence activity coefficients under atmospherically relevant conditions.

Application of derived parameter in model mechanistic analysis

An OBM embedded with GPP module was used to simulate the formation and processing of NPs in both gas and particle phases. The derived ζ value instead of 1 was adopted in the OBM. Considering the availability of necessary pollutants and parameters for model input, NPs in period 1 (28 October to 8 November) and period 2 (3 December to 13 December) were simulated to represent Phase 1 and Phase 2, respectively. As shown in Fig. 2a and S9a, the OBM could well reproduce the temporal variations of gaseous C6H5NO3, C7H7NO3, and C8H9NO3 in period 1. Comparable gaseous C7H7NO3 and slightly lower concentrations of gaseous C6H5NO3 and C8H9NO3 than the observations were simulated in period 2. Regarding the particle phase, the simulated C7H7NO3 in period 2 was comparable to the measurement, while simulations were relatively lower than the observations for C6H5NO3 and C8H9NO3 (Fig. S9b). When gaseous mono-NPs concentrations were constrained in the model, the simulated particulate mono-NPs showed improved agreement with observations. These results demonstrate the applicability of the embedded GPP module and field-derived average ζ value. Particulate mono–NPs in Period 1 were also estimated based on the measured gaseous mono–NPs, with peak concentrations of C6H5NO3, C7H7NO3, and C8H9NO3 up to 23.1, 37.2, and 11.7 ng/m3, respectively. We further examined whether the derived ζ can be directly used to estimate the concentration of gaseous/particulate NPs from Eq. 2 by the known concentration in another phase. Unsurprisingly, the calculated Cg diurnal variations of compounds such as C6-9HxNO3 with nighttime Fp peaks were similar to their measurements (Fig. S10), indicating mathematical calculations from Eqs. 1 and 2 with the derived ζ can also estimate G-P partitioning of some species effectively.

Fig. 2: Observed and simulated C7H7NO3 during the campaign.
figure 2

a The simulated and measured C7H7NO3 in gas and particle phases; b The diurnal variation of measured gaseous C7H7NO3 during 28 October to 8 November (period 1) and 3 December to 13 December (period 2).

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It is worth noting that the observed peak time of gaseous C6–8HxNO3 in period 1 showed earlier than that in period 2 (Fig. 2b and S11), which presented bimodal peaks at around 12:00 and 16:00 in period 1, and respectively shifted two and one hours later in period 2. The consistency between the model simulation and observation implies that the peak shift is well captured by the photochemical mechanisms and embedded GPP process in the model. The budget analysis of C7H7NO3 is discussed as an example. As shown in Fig. 3a, b and Scheme S1, the gaseous C7H7NO3 formation was mainly from 3–methyl–phenoxy (MXYL1O), 4–methyl–phenoxy (PXYL1O) and 2–methyl–phenoxy (TOL1O) reacting with NO2, with average contributions of 2.5%, 4.0%, and 93.5% in period 1 and 1.7%, 2.7% and 95.6% in period 2, respectively. As the dominant precursor for gaseous C7H7NO3, TOL1O was generated from cresol oxidation by OH radical and NO3 radical, o–methylphenyl peroxide (OXYL1O2) reacting with NO, NO2, and RO2, and the photolysis of OXYL1OOH (Fig. S12a and S12b). The contribution of the photolysis of OXYL1OOH was negligible in the present study. Although OXYL1O2 reacting with NO could contribute to a large formation rate of TOL1O, the reaction between TOL1O and O3 could quickly recycle OXYL1O2 with similar rates, leading to a small net formation rate of TOL1O from OXYL1O2. The cresol oxidation by NO3 and OH dominated TOL1O formation, with a total rate up to 1.4 and 1.2 ppt/h during period 1 and period 2, respectively. Similar to our previous study, the contribution of NO3+cresol was more important than OH+cresol to the TOL1O formation, which can be explained by the comparable reaction rates, but a much higher yield of TOL1O from NO3 (39%) than OH (7.3%)36. Dominated by the photooxidation of toluene, the cresol concentration started to increase after sunrise and peaked at noontime. Attributed to the stronger and longer irradiation in period 1 than in period 2 (Fig. S12c), higher concentration of OH radicals with earlier peak time were observed in period 1 (Fig. 3c), resulting in the earlier cresol formation in period 1 than in period 2 (Fig. 3d). The combined effects of postponed cresol formation and lower OH concentrations in period 2, resulted in the late and less formation of TOL1O, PXYL1O, and MXYL1O, and thus the delayed formation of gaseous C7H7NO3 with a lower formation rate.

Fig. 3: Budget analysis of C7H7NO3 and diurnal variations of key species.
figure 3

The gaseous C7H7NO3 budget (a), phenoxy radical and NO2 diurnal (b), diurnal patterns of OH and NO3 radical (c), and diurnal of cresol (d) in period 1 and period 2.

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C7H7NO3 could be further photolyzed and oxidized by OH/NO3 radicals. The photolysis contributed over 80% of C7H7NO3 consumption during 9:00–15:00 in both periods, with the highest photolysis rate of 0.9 ppt/h at 13:00 for period 1 and 0.5 ppt/h at 14:00 for period 2, respectively. Further OH radical oxidation contributed 6.7% and 3.3% to daytime C7H7NO3 consumption in period 1 and period 2, respectively. NO3 radical oxidation was the dominant sink for C7H7NO3 at night and accounted for 67% and 53% of nocturnal consumption with the highest consumption rate of 1.3 and 0.7 ppt/h at 18:00 in period 1 and period 2, respectively. Besides the chemical sinks, dry deposition also contributed 28% and 42% of gaseous C7H7NO3 nighttime loss in period 1 and period 2, respectively. The GPP served as a daytime sink but a nighttime source for gaseous C7H7NO3. The rapid daytime secondary generation of gaseous C7H7NO3 drove the GPP equilibrium shift towards the particle phase, whereas fast consumption by NO3 oxidation during nighttime resulted in more particle–to–gas release of C7H7NO3. Offset by the consumption pathways, the net formation rate of gaseous C7H7NO3 (Pnet– C7H7NO3) showed positive values during 6:00–16:00 and 10:00–17:00 in period 1 and period 2, respectively, resulting in the diurnal peak shift of gaseous C7H7NO3 in two periods. Similar processes and reasons can also explain the observed diurnal peak shift of gaseous C6H5NO3 and C8H9NO3 in the two observation periods.

Unexpected complex GPP of di-NPs

The oxidation of gaseous mono-NPs by OH and NO3 radicals is a major formation pathway for gaseous di–NPs in the OBM. Compared to observation, the model simulated temporal trends of gaseous di–NPs are not as good as mono–NPs. Gaseous C7H6N2O5 and C8H8N2O5 showed almost consistent results as observations in period 2, but gaseous C6H4N2O5 was underestimated (Figure S13), suggesting the important role of the oxidation of gaseous mono–NPs on their formation, and also the existence of missing sources. Unlike the nighttime peaks observed in period 2 and previous studies, gaseous C6H4N2O5, C7H6N2O5 and C8H8N2O5 presented morning peaks around 6:00 to 10:00 in period 1 (Fig. S14), which could be explained by the physical transportation, resulting in the inconsistency between model simulation and observation. More discussions are presented in the SI.

Regarding the particulate di–NPs, their time series cannot be reproduced from the model simulation, even when the gaseous di–NPs were constrained in the model (Fig. S13b). It suggests that the simple GPP parameterization in the model cannot represent the complex gas–particle interaction of di–NPs. It is observed that measured particulate C6–8HxN2O5 showed daytime peaks during the field campaign, especially from 27 November to 3 December (Figs. 4a and S15a). The fast growth of gaseous C6–8HxN2O5 in the night, and the particulate C6–8HxN2O5 in the daytime might be attributed to the varied contributions of different formation mechanisms. It has been proposed that mono–NPs could react with the nitrite/nitrous acid (NO2–/HONO) in the aqueous phase under irradiation conditions and contribute to di–NPs formation45. The accompanied increase of particulate C6–8HxNO3 in the daytime provided the potential precursors for the formation of particulate C6–8HxN2O5. Thus, we examined the correlation between measured particulate C6–8HxN2O5 and particulate C6–8HxNO3×Solar Radiation (SR) in the daytime. The good correlation, as shown in Fig. 4a, b and S15, suggests that the photo–enhanced particulate reactions potentially contributed to particulate C6–8HxN2O5 formation in the daytime, which would further distribute to the gas phase. In contrast, the gaseous C6–8HxN2O5 formation at night was dominated by the NO3 oxidation of gaseous C6–8HxNO3, and then partitioning into the particle phase.

Fig. 4: Formation and phase partitioning of C7H6N2O5.
figure 4

a Time series of measured particulate C7H6N2O5 and the product of measured particulate C7H7NO3×SR; b Scatter plot of measured particulate C7H6N2O5 as a function of the product of measured particulate C7H7NO3×SR during the daytime; c Comparison of the calculated gaseous C7H6N2O5 from Eq.2 with fitted the lowest, highest, and averaged ζ and the measured gaseous C7H6N2O5.

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Under ideal conditions, the GPP coefficient should be the same no matter the phase from which the compounds originated. However, the results show that compounds in the real atmosphere tended to partition more into the phase they generated in compared to the ideal state, namely a hysteresis effect, which might reflect a non–equilibrium state of GPP, possibly influenced by kinetic limitations, delayed mixing, or phase-dependent transformation processes46,47,48. The daytime particulate formation and nighttime gaseous accumulation resulted in a lower ζ in the daytime and the daytime peak of Fp for C6–8HxN2O5. Because C6–9HxNO3 were dominated by gaseous oxidation, their time series could be better reproduced from OBM that only includes the gas phase reactions, and their Fp diurnal patterns could be well explained by Pankow’s theory with fitted ζ. However, for species like C6–8HxN2O5 that are involved in both gaseous and particulate formation pathways, the OBM model cannot reproduce their time series, especially in the particle phase. Additionally, for NPs such as C7H7NO6, which exhibit different fitted ζ values during daytime and nighttime (Table 1), a decrease in gas-phase concentrations and a slight increase in particle-phase concentrations were observed during the day (Fig. S3). This suggests that, in addition to significant gaseous formation occurring in the evening, photochemical reactions during the day may also contribute to the particulate formation of these NPs. These differences in formation pathways likely contribute to the differing ζ values obtained between daytime and nighttime. Given the complex particulate reactions, such as accretion and photochemical processes, that occur concurrently with gaseous reactions in the ambient atmosphere, it is likely that the compounds associated with these reactions undergo a more intricate GPP process than previously acknowledged49,50,51,52. The measurement of GPP with high time resolution is helpful to reveal the complex reaction mechanisms behind the apparent phenomena.

The mathematically calculated gaseous C6–8HxN2O5 from Eq. 2 also showed different diurnal variations from the measurements (Figs. 4c and S10). The field-derived maximum and minimum ζ were further fitted from the highest and lowest 20% ratio of Cg of di–NPs to \(\frac{{{10}^{6}\times C}_{p}\times{{P}^{0}\times {MW}}_{{om}}}{760\times{RT}\times {OA}}\), which were 0.5 to 2 times of the averaged ζ (Fig. S16). If the highest and lowest ζ values were used in the calculation, the calculated Cg would peak in the daytime, different from the observed daytime valley (Figs. 4c and S17). When dividing the diurnal into two parts, i.e., 9:00–16:00 and the remaining part, it is found that the value and trend of the calculated Cg from the lowest ζ in the noontime was closer to the measurement, while Cg more comparable to the measurement was observed during nighttime when using the averaged ζ. These phenomena are consistent with the analysis above that there is a lower ζ in the daytime for di-NPs. Besides, these results also suggest that more refined ζ corresponding to different chemical pathways is needed to describe the GPP of compounds generated from both gas and particle phases more precisely.

Atmospheric implications

By incorporating the derived ζ into the Pankow’s absorption equilibrium theory, we first recalculated the average Fp values for NPs observed in this study. As expected, these reconstructed values closely matched the measurement (Fig. 5a), serving to demonstrate the internal consistency of the approach. More importantly, the newly fitted ζ values were further utilized to estimate Fp in previous studies to evaluate their applicability in different situations (Fig. 5b). The estimated Fp values using the fitted ζ for 4–nitrophenol (4NP), 3–methyl–4–nitrophenol (3M4NP), 2–methyl–4–nitrophenol (2M4NP), 2,6–dimethyl–4–nitrophenol (2,6DM4NP), and 4–nitrocatechol (4NC) were found to align well with their observation ranges reported by Li et al.10. Similar results with improved estimation of Fp can also be obtained for I.M. Al–Naiema’s results38. The strong agreement of Fp with the measured values suggests that, although the fitted ζ values were obtained from a subtropical coastal site, they have great potential for broader application in other regions.

Fig. 5: Application of the derived ζ in measurements and modeling.
figure 5

The comparison of Fp between the observation and the estimation with ζ = 1 and ζ = fitted value in our (a) and previous studies (b); c Comparison of particulate NPs (ng/m3) between the observation and GEOS-Chem model simulation with derived apparent ζ, and d the derived ζ as a function of P0.

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To further explore the effectiveness of the apparent ζ and Pankow’s absorption equilibrium on GPP of NPs, a GEOS-Chem global 3-D chemical transport model (v12.9.3) with a resolution of 5° longitude ×4° latitude and 72 vertical layers was applied to simulate NPs formation worldwide. This model has been successfully used to assess the contributions of organic nitrogen aerosols to global atmospheric nitrogen deposition21. Field observation data reported in previous studies covering the locations of latitudes from 22.2° to 55.3° and longitudes from -118.12° to 136.92° were used for comparison (Table S2). As shown in Fig. 5c, the simulated particulate NPs were mostly within one order of magnitude of the measurement values, underscoring the practical applicability of the derived apparent ζ and Pankow’s theory in describing the GPP of NPs across different regions. Accurate simulation of particulate NPs is essential for estimating their contribution to aerosol formation and evaluating their roles in solar radiation. Additionally, the method for deriving apparent ζ from field measurement can be applied to other SVOCs, providing a promising approach to improve the model performance in simulating the GPP of SVOCs and further exploring their impacts on aerosol formation and air quality.

Besides, it was observed that the derived ζ decreased with the increase of P0, following a relationship of Log ζ = -0.91 × Log P0 −3.3 (Fig. 5d). This suggests that the ζ value for compounds with similar structures could be estimated accordingly, opening avenues for measuring and estimating the ζ value for other types of SVOCs. Ulteriorly, it is promising that utilizing their newly fitted or estimated ζ value could enhance the performance of regional models in simulating SVOCs distributions, investigating their contributions to OA formation and understanding their impacts on air quality. Nevertheless, some considerations are warranted. Uncertainties from the theoretical estimation of P0 were included in the apparent ζ due to a lack of accurate measurement values, however, systematic revisions can be made when accurate P0 is measured in the future. The obtained ζ values here represent an average value for isomeric compounds with different structures, and the specific structure variations may lead to higher or lower ζ values. Furthermore, different atmospheric conditions might introduce the unknown deviations in ζ. Given the wide application of GPP theory in estimating the distributions of SVOCs in various models, the potential underestimation of Fp for most oxygenated SVOCs caused by the oversimplified ζ assumption would underrate the significance of oxygenated SVOCs in global/regional climate and air quality. Therefore, a more quantitative understanding of ζ is necessary to accurately evaluate the role of SVOCs in atmospheric chemistry.

Methods

Measurement of NPs and other key precursors and parameters

Data presented here were collected at a regional background monitoring station (Cape D’Aguilar, 22.22°N, 114.25°E), which is located on the southeastern tip of Hong Kong Island, surrounded by sea on three sides and about 10 km from the nearest urban center53. The continuous field campaign was conducted in autumn to winter (from 6 October to 19 December) in 2020, which was the period with more frequent photochemical pollution in Hong Kong.

An Iodide–adduct ToF–CIMS was used to measure targeted NPs. Only the gas inlet was used from 6 October to 24 November (Phase 1), and FIGAERO was installed on 26 November (Phase 2) to concurrently measure gaseous and particulate NPs till the end of the field campaign. The primary reagent ion of I‒ was produced by passing the CH3I and humid carrier gas N2 through an inline ionizer (210Po). The relative humidity (RH) of the carrier gas was kept at around 50% to maintain a stable ratio between I‒ and I·H2O‒. The pressure of the IMR was set to 100 mbar, leading to a sample flow of 2.5 L/min. When the FIGAERO inlet was used, aerosols with a size smaller than 3 µm were pumped through a cyclone cutting head with a flow rate of 10 L/min and continuously collected on the Teflon filter for 25 min, meanwhile, the gaseous pollutants were analyzed by ToF–CIMS concurrently. Then, a thermal desorption program described in the SI was applied to analyze the NPs collected on the filter. During each cycle of sample collection and analysis (1 h), 25 min was used for the gaseous sample analysis, and a total of 35 min was used to analyze the particulate sample that was collected at the same time as the gaseous sample. The concentration of NPs was calibrated by the obtained calibration coefficients as described in SI. Briefly, NPs standards including 2–methyl–4–nitrophenol, 2,6–dimethyl–4–nitrophenol, and 3,6–dimethyl–2,4–dinitrophenol were added to the filter, and analyzed with the same thermal desorption program as ambient sample analysis, then calibration coefficients could be obtained. Detailed information on data analysis and other instruments can be found in the SI.

Calculation and theoretical estimation of Fp

The Fp of species i is defined as Eq. 3,

$${F}_{p}=\frac{{C}_{p}}{{C}_{g}+{C}_{p}}$$
(3)

where Cp (ng/m3) and Cg (ng/m3) are the concentrations of species i in the particle and gas phase, respectively. Kep could be calculated from Eq. 4, where PM represents the PM2.5 concentration (μg/m3), and could also be estimated from theory: Eq. 1.

$${K}_{{ep}}=\frac{{C}_{p}}{{C}_{g}\times{PM}}$$
(4)

Both adsorption and absorption are reported to be important pathways for gaseous SVOCs to enter the particle phase, while they are more significant for gaseous SVOCs partitioning on solid and liquid aerosol, respectively. Because of the most likely liquid state for most of the aerosol caused by high RH during the period (average RH: 71% and the frequency of RH larger than 60% was over 84%), the GPP of NPs in the gas and particle phase was assumed to be led by the absorption process54. The most typical theory of SVOC absorbed in particles is the absorption equilibrium theory developed by Pankow as shown in Eq. 122. Thus, the Fp could be described by Eq. 5 by incorporating the estimated Kep.

$${F}_{p}=\frac{{K}_{{ep}}\times{PM}}{1+{K}_{{ep}}\times{PM}}$$
(5)

Besides Pankow’s absorption equilibrium theory, several other theoretical methods have also been used to estimate the Fp of NPs5,55. Detailed discussions of these theoretical methods are presented in SI.

Model simulations

An OBM built on the Master Chemical Mechanism (MCM v3.3.1) (http://mcm.york.ac.uk)56,57 was employed to analyze the budget of the observed NPs15,36, which is described in detail in SI and our previous study36. Briefly, the OBM incorporates inorganic and organic reaction mechanisms from MCM 3.3.1, supplemented with additional processes including the photolysis of gaseous and particulate NPs, dry deposition, and the GPP of NPs. In the model, 1.4% and 3% of the photolysis rate of NO2 (JNO2) were respectively adopted as the photolysis rate for nitrophenol and other NPs in both gas and particle phases, based on our previous findings36. Dry deposition rates for NPs in both gas and particle phases and other reactive species were set within a range of (0.550~1)/HMIX (HMIX: height of mixing layer), following the approach used in previous work58. A GPP module, following Johnson et al.59, was embedded in the model by coupling with the derived ζ for targeted NPs. The dynamical process of GPP could be treated as a reversible reaction with an absorption process (kin) and a desorption process (kout)59. Detailed mechanisms for targeted NPs in the OBM are provided in the SI. The model simulations were conducted for two periods: 26 October to 8 November (period 1) and 3 to 12 December (period 2), during which the OBM was constrained with observational data including trace gases, key VOC species, N2O5, and meteorological parameters. Besides, a GEOS-Chem global 3-D chemical transport model (v12.9.3, http://geos-chem.org) embedded with the GPP module was used to simulate the NPs formation in different regions. Except for the updated parameters in the GPP module, the basic settings of the model were the same as before, which can be found in our previous study21.