The goal of this work is to investigate changes in NOx and O3 on the chemistry of isoprene nitrates in the afternoon period in Beijing. To do this, the models should demonstrate the favoured reaction pathways under different oxidant concentrations in the absence of other variables. This means that physical and photolytic processes should be held constant, i.e. the models will describe the chemistry occurring at a representative point in the day. Species must also be allowed to reach their steady-state concentrations in order to eliminate the role of the model spin-up period on resultant species concentrations. Comparison of the concentrations of species in these so-called steady-state models then allows for conclusions to be drawn as to the preferred oxidation products under various conditions.

All models described in this work were run using AtChem2, an open-source zero-dimensional box model (Sommariva et al., 2020). All models also made use of the isoprene mechanism published by Vereecken et al. (2021) (henceforth the FZJ mechanism) which aimed to improve the representation of NO3 chemistry of isoprene by building on chemistry from the Master Chemical Mechanism (MCM) and the review of isoprene chemistry published by Wennberg et al. (2018) (Jenkin et al., 2015; Wennberg et al., 2018; Vereecken et al., 2021; Carlsson et al., 2023). In order to make the species naming consistent between the MCM portion and the added chemistry of the FZJ mechanism, ISOPCNO3 was renamed to EISOP1N4OH as both identical species are present in the original FZJ mechanism.

The steady-state models are sets of models run at a range of fixed NOx and O3 mixing ratios. Models were run for NOx mixing ratios up to 45 ppb and O3 mixing ratios of 140 ppb, corresponding to the upper limit of measurements made in the Beijing 2017 campaign (Shi et al., 2019). In order to provide additional OH reactivity, a constant concentration of methane was added to all of the models to ensure that the modelled OH reactivity matched measured values under Beijing-like conditions; this is discussed further in the “Model Validation” section. The required mixing ratio corresponded to 82 ppm of methane in all of the models. The modelled concentration of species is taken as the final concentration after 5 model days, after all species had been allowed to reach steady-state concentrations. Each model was run at photolysis conditions corresponding to those calculated by AtChem2 for 16:00 LT in Beijing, China. This was around the time of peak daytime NO3 concentrations in Beijing, before concentrations rapidly increased during sunset. To ensure steady-state was reached in a reasonable time, and to provide loss routes for species without losses, species were removed from the model at a dilution rate of 2.31×10-5 s-1, corresponding to a dilution lifetime of 12 h. This value was selected based on a combination of the physical loss processes included in previous modelling work, and the impact of this decision is assessed in Sect. 3.1 (Mayhew et al., 2022; Edwards et al., 2014, 2013).

All models were run at a temperature of 298.15 K, a pressure of 1013 mbar, and a relative humidity of 50 %. The latitude, longitude, and date used for photolysis calculations were 39.909∘, 116.398∘, and 1 June 2022. NOx was constrained by adjusting the NO and NO2 concentrations at the beginning of each time step such that the total NOx matched the desired concentration, but the ratio of NO and NO2 remained constant.

Models were also run to simulate conditions in the Amazon region, with VOC concentrations adjusted to match observations of isoprene concentrations and OH reactivity in this region. These models were run at a higher-isoprene concentration of 5 ppb and methane concentrations of 100 ppm (Williams et al., 2016; Pfannerstill et al., 2021; Langford et al., 2022). The latitude and longitude values used corresponded to the city of Manaus and were -3.132 and -60.01∘, respectively. The time of day was kept at 16:00 LT.

These models are designed for comparison between one another to gain insight into the impact of changes in NOx and O3 on organonitrate concentration. The models show the concentrations at steady state for the provided photolysis conditions, chemistry, and dilution rate, which is in contrast to the constantly changing photolysis and dilution encountered under ambient conditions. This means that chemistry that would occur at other times (e.g. nighttime chemistry) does not contribute to the results of these models. Previous work has demonstrated not only the importance of nighttime chemistry for understanding organonitrates but also that many of the organonitrates produced overnight will decrease in concentrations over the early-morning period to reach low concentrations in the afternoon (Kenagy et al., 2020; Mayhew et al., 2022). The downstream chemistry of these nighttime organonitrates, and other nighttime species, will have some impacts on daytime chemistry that are not captured by the models presented here. However, Sect. 3.1 illustrates that the conclusions made in this paper are applicable to the Beijing afternoon conditions being investigated and that the conclusions are robust to changes in the modelling approach.

Throughout this paper, the model results are investigated through the use of isopleth plots. These plots consist of the steady-state concentration of a species (or another model output such as OH reactivity) in each of the models plotted as a coloured circle at the corresponding position on a set of NOx–O3 axes. The colour scale is indicated by a colour bar placed alongside each set of axes and will be a different scale for each plot. A continuous colour gradient is then overlaid on the axes by interpolation over a triangular grid of the model points. Ten contour lines are also drawn over the top of each plot to highlight the contour shape. These lines are equally spaced in the coloured dimension (e.g. species concentration), meaning close vertical lines would correspond to a strong sensitivity to changes in O3 and close horizontal lines would correspond to a strong sensitivity to changes in NOx.

Under real-world conditions, the O3 concentrations will be determined by the nonlinear interactions of NOx and VOCs, which is in contrast to the models where NOx, O3, and VOCs are all constrained. This means that some sections of the model isopleths will be inaccessible. For example, some amount of O3 will form in the presence of NOx and VOCs, so occupying the upper-left corner of the isopleths may not be possible outside of the constrained model scenario. Similarly, it may not be possible to map real-world changes to one dimension (such as a decrease in NOx) onto the isopleth plots without accounting for a change in the other dimension (such as a change in O3).

Section 3.6 makes use of the vapour pressure (often expressed as a log value to the base of 10) to investigate the potential contributions to SOA. The UManSysProp facility was used to do this (Topping et al., 2016); UManSysProp can estimate the vapour pressure of compounds represented as SMILES strings via a range of different group contribution methods (Barley and Mcfiggans, 2010; O'Meara et al., 2014). This work used predictions at 298 K throughout and used the “evaporation” technique, though sensitivity to all of the available prediction methods is described in Sect. 3.6.

As a test of the ability of the steady-state models to represent conditions present under ambient scenarios, the model results were compared to measurements collected in the summer of 2017 in Beijing (Shi et al., 2019; Hamilton et al., 2021; Whalley et al., 2021; Reeves et al., 2021; Newland et al., 2021; Mayhew et al., 2022). The NOx mixing ratios measured in the afternoon periods in Beijing ranged between 5 and 20 ppb, and O3 mixing ratios ranged from around 60 to 140 ppb. Isoprene mixing ratios ranged up to around 2 ppb in the afternoon period, hence a typical value of 1 ppb was chosen for the steady-state models. The concentration isopleths for inorganic species that were zoomed in to this representative range of O3 and NOx mixing ratios are provided in the Supplement (Sect. S1).

Measurements of OH reactivity (kOH) during the afternoon period were between around 10 and 30 s-1 (Whalley et al., 2021), which the models reproduced at the appropriate NOx and O3 mixing ratios by design due to the additional methane included in the model run for this purpose (Fig. 4a). The modelled NO3 reactivity (kNO3) is around 0.4–1.9 s-1 compared to the estimated value of around 0.5 s-1 presented in Hamilton et al. (2021) (Fig. 4b) (Hamilton et al., 2021). Values of kOH and kNO3 at a wider range of NOx and O3 mixing ratios are provided in Fig. S1.

In the NOx–O3 space corresponding to typical Beijing afternoon conditions, the models show NO mixing ratios of around 0.3–2.8 ppb (Figs. 5a, S2a), consistent with the low-NO observations in the afternoon period in Beijing with observed mixing ratios of around 0.25 and 3 ppb (Newland et al., 2021). The models show NO3 mixing ratios of 0.4 to 2 ppt (Figs. 6a, S3a), which are slightly below the measured NO3 mixing ratio in the afternoon of around 2 ppt (Hamilton et al., 2021). The modelled OH concentrations are between 2.5×106 and 6.5×106 molecules cm-3 (Figs. 6b, S3b), which are slightly below the measured concentrations of around 7.5×106 molecules cm-3. HO2 is generally overpredicted with a range between 4.2×108 and 9.1×108 molecules cm-3, compared to measurements of around 2.5×108 molecules cm-3 (Figs. 6c, S3c) (Whalley et al., 2021). This is consistent with previous modelling studies that indicate an overprediction of HO2 by models, particularly under the low-NO afternoon conditions being investigated here (Mayhew et al., 2022; Whalley et al., 2021). Furthermore, models that included an additional sink of HO2 to bring it in line with measurements resulted in an underprediction of OH due to the HOx removed from the system.

A series of sensitivity tests were carried out in order to assess the sensitivity of our conclusions to changes in model parameters. Four different parameters were adjusted: the concentration of isoprene, the concentration of methane, the dilution rate, and the time of day. These sensitivity tests were found to have little impact on the conclusions drawn in this work, and any potential impacts are discussed where required. Further details on tests are provided in the Supplement (Sect. S2).

The IHN concentration isopleth (Fig. 7a) shows a strong similarity to the OH isopleth (Fig. 6b), highlighting its rapid formation from the OH oxidation of isoprene and subsequent RO2+ NO reaction to form the nitrate group (Fig. 1). This means that at high-O3 mixing ratios, IHN shows a strong dependence on NOx, and the dependence on O3 becomes more significant at lower-O3 mixing ratios.

IPN shows increasing concentrations with increasing O3 and decreasing NOx (Fig. 7b). This reflects the requirement for low-NO concentrations to be present for two reasons. Firstly, high-NO3 concentrations are required to form the INO2 radical by the reaction of isoprene with NO3. Secondly, the RO2+ HO2 reaction is required to form the hydroperoxide group of IPN, and so lower-NO concentrations will reduce competition with the rapid RO2+ NO reaction. Additionally, HO2 concentrations are highest under low-NOx conditions (Fig. 6c), further favouring the RO2+ HO2 reaction.

In contrast to the other nitrated species investigated here, ICN shows two peaks in concentration, one at very low O3 and the other at very high O3 (Fig. 7c). This is because ICN can be formed from many different routes. These routes include the abstraction of an H atom from IHN which provides a formation route under lower-O3 conditions, when OH and IHN are both high in concentration. Alternatively, under higher-O3 conditions, ICN can form from the reaction of OH and IPN or the decomposition of nitrated alkoxy radicals (INO). The result of these multiple peaks is that under moderate NOx and O3 conditions, the concentration of ICN is relatively insensitive to changes in both NOx and O3. It is also important to note that the absolute concentrations of ICN predicted to form in these models are very low (the peaks in concentration corresponding to mixing ratios of just over 1 ppt) due to low production rates, which is consistent with low daytime ICN mixing ratios previously identified in Beijing (Reeves et al., 2021; Mayhew et al., 2022).

Recent work has highlighted species with the formula C4H7NO5 as potentially major oxidation products of isoprene (Tsiligiannis et al., 2022). Consistent with previous modelling studies (Mayhew et al., 2022), these models largely form C4H7NO5 from OH-initiated oxidation, meaning the concentration isopleth is similar to that of OH and IHN.

Both INHE and INPE show a similar pattern as IPN in the NOx–O3 isopleths (Fig. 8a, b), with the highest concentrations occurring at low NOx and very high O3. INPE is reliant on high NO3 and HO2 in a similar manner to IPN as the RO2+ HO2 step is still required to form INPE. While HO2 is not required to form INHE via the alkoxy-epoxidation pathway, the formation of INHE from IPN is the major formation route under lower-NOx conditions. Additionally, the alkoxy-epoxidation pathway to the formation of INHE relies on an RO2–RO2 cross reaction. This cross reaction will be favoured under low-NOx–high-O3 conditions, where NO concentrations will be the lowest, meaning that the competition with the rapid RO2–NO reaction is minimal. This requirement for very high O3 and low NOx means that we should expect very low concentrations of daytime INHE and INPE under typical urban conditions. This is consistent with modelling of Beijing which showed that while INHE may comprise a large fraction of nighttime C5H9NO5 compounds, the daytime contribution is very small (Mayhew et al., 2022).

In contrast, INCE shows reasonably high concentrations under high-O3 mixing ratios at a range of NOx mixing ratios. The profile of these concentrations is very similar to the NO3 isopleth (Fig. 6a) and stems from the main formation route to INCE requiring the NO3 oxidation of isoprene followed by an RO2+ NO reaction step. This formation route shares similarities with the dinitrates discussed in Sect. 3.4.

As previously noted for INCE, Fig. 9 shows that the steady-state concentrations of isoprene dinitrate (IDN) and isoprene dinitrooxyepoxide (IDNE) are very similar to the NO3 concentration isopleth (Fig. 6a). This is indicative of the formation route of IDN and IDNE, where an initial NO3 oxidation is followed by the reaction of the resulting RO2 with NO to form the second nitrate group (Figs. 1 and 3). At any daytime concentration of NOx where sufficient NO3 is present to perform the initial oxidation step, there will also be sufficient NO present to rapidly react with the resulting RO2. Although the high-O3 mixing ratios observed in Beijing result in low-NO concentrations compared to typical daytime concentrations in a polluted megacity, there is still ample NO present to react with peroxy radicals produced by the initial NO3 oxidation. Figure 9 shows that at each O3, there is a critical NOx concentration above which the concentration of IDN, IDNE, and INCE is almost exclusively controlled by O3 concentrations. This critical NOx mixing ratio is reasonably low compared to typical urban NOx mixing ratios, indicating that the concentration of dinitrates in urban environments may be largely controlled by the O3 mixing ratios present.

As discussed in Sect. S2, increasing the total VOC in the model leads to a broadening in the NOx axis of the transition between sensitive regimes of NOx and O3 for NO3; the same also applies to IDN, IDNE, and INCE. For a fixed ozone concentration, increasing the NOx from 0 will increase IDN, IDNE, or INCE concentrations due to the increased NO3 resulting from the increased availability of NO2 (Fig. 10). Then, once the threshold NOx concentration is reached and NO3 concentrations are not limited by the availability of NOx, the concentration becomes controlled by O3 and HO2 (Sect. S2), creating the “hump” in concentration which then stabilises as HO2 concentrations begin to decrease at high NOx and the NO2/NO ratio becomes increasingly controlled by the fixed O3 concentration. This means that with high-VOC concentrations, at a given O3 concentration, reductions in NOx will result in increased IDN, IDNE, or ICNE concentrations sooner than under lower-VOC conditions.

By summing the model concentrations for all organonitrates present in the mechanism, an isopleth of total organonitrates was obtained (Fig. 11). This shows a band of high-organonitrate concentrations at moderate NOx. At high O3, further changes to O3 have little effect on the total organonitrate concentration. Total organonitrates also become less sensitive to changes in NOx in this high-O3 region. This band is the result of organonitrates produced by OH and NO3 oxidation of isoprene. At low-O3 mixing ratios, the total organonitrates are dominated by OH-initiated species such as IHN (Fig. 7a). Conversely, at high-O3 mixing ratios, NO3-initiated species such as IDN comprise a larger fraction of total organonitrates (Fig. 9a). This is illustrated in the pie charts in Fig. 11 which show the organonitrate composition under different NOx–O3 regimes.

The composition breakdown also reveals that total isoprene organonitrates are dominated by IHN under most conditions, but this fraction decreases as ozone mixing ratios increase. At higher O3, a large fraction of the composition comes from IDN, IDNE, and INCE due to their higher concentrations under high-O3 conditions (Sect. 3.3 and 3.4). CH3NO3 comprises a substantial fraction of total organonitrates in these models. CH3NO3 can be formed by the OH oxidation of methane via the methylperoxy radical, and so its concentrations in these models are exaggerated due to the large amounts of methane added to the model. Formation from the OH oxidation of methane comprises the majority of all of the methylperoxy formation in all of the models, excluding formation from the reversible decomposition of methane peroxynitrate (CH3O2NO2) which is balanced by the opposing formation reaction. CH2NO2OOH is also listed in Fig. 11. CH2NO2OOH is formed from the products of isoprene ozonolysis, explaining the higher concentrations under high-O3 conditions. There are no chemical losses in the mechanism for CH2NO2OOH, which likely explains the high contribution to total organonitrates. The remaining portion of “other” organonitrates corresponds to a wide range of species, none of which contribute more than 6 % to the total organonitrate sum in any models.

As noted in Sect. S2, changing the VOC concentration affects the position in NOx–O3 space where the maximum organonitrate concentrations are observed. In the case of total organonitrates, decreasing the total VOC concentration results in the band of high concentrations moving to lower NOx. Figures S7 and S8 show that with lower-methane concentrations in the model, the peak organonitrate concentrations occur at around 12 ppb of NOx whereas this increases to around 25 ppb of NOx in the high-methane case. The peak organonitrate concentrations at each of these NOx concentrations are similar in each of these sets of model runs.

One of the major motivations for studying isoprene nitrates is their potential to contribute to secondary organic aerosol (SOA) by condensation or reactive uptake to existing particles. While the highest concentration species such as IHN and IDN may be most significant when considering the role of isoprene nitrates as NOx reservoirs, low-concentration species can be much more important for SOA formation if they are of a sufficiently low volatility. As an estimation of the impact of changing NOx and O3 on particle-phase processes, the log of the vapour pressure was estimated for each organonitrate in the mechanism based on the species' structure using UManSysProp (Topping et al., 2016). As a measure of a compound's volatility, a lower vapour pressure value corresponds to a less volatile compound which will more readily partition into existing particles. This volatility-based approach does not account for potential reactive uptake, which is likely to be important for the epoxide species previously discussed. Furthermore, the hydrolysis of organonitrates, particularly tertiary nitrates, may reduce particle-phase concentrations (Vasquez et al., 2020). This particle-phase hydrolysis may then have knock-on effects for the gas-phase organonitrates, particularly where the tertiary nitrate isomer comprises a large fraction of the composition, such as for IHN.

Figure 12 shows the total organonitrate plot normalised to the vapour pressure value for each compound, which gives an estimation of the contribution of organonitrate uptake to SOA at each NOx and O3 mixing ratio. Since the predicted vapour pressures range over 10 orders of magnitude, lower-volatility species can have a large effect on SOA formation despite their much lower concentration. The lowest vapour pressures predicted here are for the two MCM species NC524NO3 and NC524OOH. These two compounds comprise almost 100 % of the normalised concentration in Fig. 12 under all NOx and O3 conditions, and their individual concentration profiles can be seen in Fig. 13. The concentration isopleths for the 15 lowest volatility compounds are shown in Fig. S17. Many of these species show profiles similar to that of NC524OOH, with the highest concentrations occurring at low urban NOx concentrations.

According to Fig. 12, reductions in NOx from typical urban conditions would result in higher normalised concentrations of organonitrates, meaning the contribution of isoprene nitrates to SOA may increase with decreasing NOx until very low urban NOx conditions are met. However, it is important to note the difficulty in representing the lowest-volatility species in the isoprene oxidation mechanism. Many of these species are the product of multiple oxidation steps with large uncertainties surrounding their rates of formation. Additionally, many of the lowest-volatility species do not contain any chemical losses in the mechanism due to a lack of information on their reactions.

The low predicted volatilities of NC524NO3 and NC524OOH are the result of the many functional groups present in the molecules. Similarly, oxidised species could be described as highly oxidised molecules (HOMs) (Bianchi et al., 2019). The chemistry of HOMs is not currently well represented in many mechanisms due to their varied autoxidation formation pathways. For example, the profile of NC524OOH concentrations in Fig. 13b results from the requirement of HO2 to form the hydroperoxide group, hence the profile is similar to that of HO2. If an RO2 H-shift formation pathway to NC524OOH, or similar HOMs, were included in the mechanism, then this might alter the profile in Fig. 12 (Vereecken and Nozière, 2020). It should be expected that the formation of HOMs would be sensitive to changes in ozone as the lower-NO concentrations at higher ozone will reduce the competition of the RO2+ NO pathway with the RO2 autoxidation reactions that form HOMs. Inclusion of improved autoxidation chemistry in the mechanisms would also increase the number of low-volatility compounds produced from the oxidation of isoprene. There is also the potential for the oxidation products of nighttime species to be low-volatility compounds that would contribute to SOA but would not be captured by these models which represent the steady-state concentration of organonitrates at 16:00 LT, without the contribution of chemistry occurring at other times of the day.

Figure S16 shows that the results presented here are reasonably insensitive to the choice of vapour pressure and boiling point prediction methods selected within UManSysProp. Section S3 also outlines the results using an alternative volatility estimation method, making use of only the molecular formula of each compound.

In order to test the investigation of less polluted environments, a series of models were run at a range of lower-NOx and lower-O3 mixing ratios. Measurements collected in the Amazon rainforest were taken as an example of an unpolluted environment, and the model was adjusted to match typical isoprene mixing ratios and OH reactivity observed in this environment. The results from these models are presented in the supplementary information (Sect. S5).

The reduced NOx and O3 mixing ratios used in these models mean that, despite the changes to isoprene and methane concentrations, they correspond well to higher-resolution models of the low-NOx and low-O3 portions of the Beijing models. Figure S19 shows that the total organonitrates in the Amazon models are sensitive to changes in NOx, with increasing ozone slightly reducing total organonitrates.

As discussed in the introduction, IEPOX is one of the major precursors of isoprene SOA, particularly under low-NOx conditions where the IEPOX precursor, ISOPOOH, can form from oxidation by OH and further reaction with HO2. This dependence on HO2 means that the Amazon models predict increasing concentrations of IEPOX as NOx is increased from close to 0, regardless of the O3 concentration (Fig. 14b). This is in agreement with findings from Shrivastava et al. who found increases in isoprene SOA resulting from increases in NOx and O3 from an urban plume (Shrivastava et al., 2019). The increased SOA could be further explained by the increases in nitrated epoxides and dinitrated species predicted on increasing both NOx and O3 (Fig. S19).

Methyl vinyl ketone (MVK) and methacrolein (MACR) are also often of interest in isoprene oxidation, particularly in pristine environments such as the Amazon where the production of MVK and MACR relies on the presence of NO (Langford et al., 2022). This is illustrated in Fig. 14d, whereas Fig. 14c illustrates that the abundance of NO under typical urban conditions means that the MVK + MACR concentrations in the Beijing models are dependent on OH concentrations.