Organic peroxy radical chemistry in oxidation flow reactors and environmental chambers and their atmospheric relevance

Oxidation flow reactors (OFRs) are a promising complement to environmental chambers for investigating atmospheric oxidation processes and secondary aerosol formation. However, questions have been raised about how representative the chemistry within OFRs is of that in the troposphere. We investigate the fates of organic peroxy radicals (RO₂), which play a central role in atmospheric organic chemistry, in OFRs and environmental chambers by chemical kinetic modeling and compare to a variety of ambient conditions to help define a range of atmospherically relevant OFR operating conditions. For most types of RO₂, their bimolecular fates in OFRs are mainly RO₂+HO₂ and RO₂+NO, similar to chambers and atmospheric studies. For substituted primary RO₂ and acyl RO₂, RO₂+RO₂ can make a significant contribution to the fate of RO₂ in OFRs, chambers and the atmosphere, but RO₂+RO₂ in OFRs is in general somewhat less important than in the atmosphere. At high NO, RO₂+NO dominates RO₂ fate in OFRs, as in the atmosphere. At a high UV lamp setting in OFRs, RO₂+OH can be a major RO₂ fate and RO₂ isomerization can be negligible for common multifunctional RO₂, both of which deviate from common atmospheric conditions. In the OFR254 operation mode (for which OH is generated only from the photolysis of added O₃), we cannot identify any conditions that can simultaneously avoid significant organic photolysis at 254 nm and lead to RO₂ lifetimes long enough (∼ 10 s) to allow atmospherically relevant RO₂ isomerization. In the OFR185 mode (for which OH is generated from reactions initiated by 185 nm photons), high relative humidity, low UV intensity and low precursor concentrations are recommended for the atmospherically relevant gas-phase chemistry of both stable species and RO₂. These conditions ensure minor or negligible RO₂+OH and a relative importance of RO₂ isomerization in RO₂ fate in OFRs within $\sim \times \mathrm{2}$ of that in the atmosphere. Under these conditions, the photochemical age within OFR185 systems can reach a few equivalent days at most, encompassing the typical ages for maximum secondary organic aerosol (SOA) production. A small increase in OFR temperature may allow the relative importance of RO₂ isomerization to approach the ambient values. To study the heterogeneous oxidation of SOA formed under atmospherically relevant OFR conditions, a different UV source with higher intensity is needed after the SOA formation stage, which can be done with another reactor in series. Finally, we recommend evaluating the atmospheric relevance of RO₂ chemistry by always reporting measured and/or estimated OH, HO₂, NO, NO₂ and OH reactivity (or at least precursor composition and concentration) in all chamber and flow reactor experiments. An easy-to-use RO₂ fate estimator program is included with this paper to facilitate the investigation of this topic in future studies.

1 Introduction

Laboratory reactors are needed to isolate and study atmospheric chemical systems. Environmental chambers have been a major atmospheric chemistry research tool for decades (Cocker et al., 2001; Carter et al., 2005; Presto et al., 2005; Wang et al., 2011; Platt et al., 2013). Over the last few years, oxidation flow reactors (OFRs; see Appendix A for the meanings of the acronyms) (Kang et al., 2007) have emerged as a promising complement to chambers and are being used to investigate atmospheric oxidation processes, particularly volatile organic compound (VOC) oxidation and secondary organic aerosol (SOA) formation and aging (Kang et al., 2011; Lambe et al., 2015; Hu et al., 2016; Palm et al., 2016). These processes have air quality (Levy II, 1971), human health (Nel, 2005) and climate impacts (Stocker et al., 2014).

The most important advantage of OFRs is their ability to achieve relatively high photochemical ages (of the order of equivalent hours or days assuming an average ambient OH concentration of 1.5×10⁶ molecules cm⁻³; Mao et al., 2009) in minutes instead of hours in chambers (Lambe et al., 2011). Rapid aging is usually achieved by highly active HO_x radical chemistry initiated by low-pressure Hg lamp emissions (185 and 254 nm) (Li et al., 2015; Peng et al., 2015). This allows for shorter residence times in OFRs, thus reducing the relative importance of gas and particle losses to walls (Palm et al., 2016), which can be very important in Teflon chambers (Cocker et al., 2001; Matsunaga and Ziemann, 2010; Zhang et al., 2014; Krechmer et al., 2016). In addition, the lower costs and small size (volumes of the order of 10 L) of OFRs allow for better portability. These, together with the ability to rapidly achieve high photochemical ages, are advantageous for field applications. These advantages of OFRs have led a number of atmospheric chemistry research groups (Lambe and Jimenez, 2018) to deploy them in field (Hu et al., 2016; Ortega et al., 2016; Palm et al., 2016, 2017), source (Ortega et al., 2013; Tkacik et al., 2014; Karjalainen et al., 2016; Link et al., 2016) and laboratory studies (Kang et al., 2011; Lambe et al., 2013; Richards-Henderson et al., 2016; Lim et al., 2017).

While the use of oxidation flow reactors is growing rapidly in the atmospheric chemistry community, some researchers have raised two concerns with regard to OFRs: (1) the chemical regime of OFRs may be unrealistic compared to the atmosphere, and (2) OFRs are derivative of flow reactors with a long tradition in atmospheric chemistry, especially for chemical kinetic measurements, and thus there is not much new to be discussed or analyzed in their chemistry. While it is true that OFRs follow the tradition of flow tubes used in atmospheric chemistry, they attempt to simulate a much more complex system all at once and typically use much longer residence times, and thus many fundamental and practical issues arise that have not been addressed before. The need to achieve longer effective photochemical ages within a short residence time can, however, lead to the occurrence of undesirable oxidation pathways.

To clarify this issue, a series of chemical kinetic modeling studies have been performed: Li et al. (2015) and Peng et al. (2015) established a radical chemistry and oxidation model whose predictions compare well against laboratory experiments and found that OH can be substantially suppressed by external OH reactants (e.g., SO₂, NO_x and VOCs externally introduced into the reactor); Peng et al. (2016) identified a low water mixing ratio (H₂O) and/or high external OH reactivity (OHR_ext, i.e., first-order OH loss rate constant contributed by external OH reactants) as conditions that can cause significant non-tropospheric VOC reactions (e.g., through photolysis at 185 and/or 254 nm); Peng and Jimenez (2017) studied NO_y chemistry in OFRs and showed that high-NO conditions, under which organic peroxy radicals react more rapidly with NO than with HO₂, can only be realized by simple NO injection in a very narrow range of physical conditions, whose application to investigating intermediate- and high-NO environments (e.g., urban area) is limited; Peng et al. (2018) thus evaluated a few new techniques to maintain high-NO conditions in OFRs and found the injection of percent-level N₂O effective to achieve this goal.

While HO_x and NO_y chemistries have been extensively characterized in OFRs so far, organic peroxy radical (RO₂) chemistry has yet to be considered in detail, as previous studies have only considered the balance between RO₂+NO vs. RO₂+HO₂. There has been some speculation that due to high OH concentrations in OFRs, RO₂ concentration and lifetime might be significantly different from ambient values, leading to the dominance of RO₂ self- and cross-reactions and the elimination of RO₂ isomerization pathways (Crounse et al., 2013; Praske et al., 2018). Given the central role RO₂ plays in atmospheric chemistry (Orlando and Tyndall, 2012; Ziemann and Atkinson, 2012) and the rapidly increasing use of OFRs, RO₂ chemistry in OFRs needs to be studied in detail to characterize the similarities and differences between their reaction conditions and those in the ambient atmosphere and traditional atmospheric reaction chambers.

In this paper, we address this need via modeling. All major known fates of RO₂ in OFRs will be investigated and compared with those in typical chamber cases and in the atmosphere. This comparison will provide insights into the atmospheric relevance of RO₂ chemistry in atmospheric simulation reactors and allow for the selection of experimental conditions with atmospherically relevant RO₂ chemistry in experimental planning.

2 Methods

Due to a variety of loss pathways of RO₂ and a myriad of RO₂ types, RO₂ chemistry is of enormous complexity. We detail the RO₂ production and loss pathways of interest in this study, the approximations used to simplify this complex problem and the steps to investigate it methodically. We briefly introduce the base OFR design and the model, which are described in detail elsewhere (Kang et al., 2007; Peng et al., 2015, 2018).

2.1 Potential aerosol mass oxidation flow reactor (PAM OFR)

The concept of the base OFR design simulated in this study, the potential aerosol mass (PAM) reactor, was first introduced by Kang et al. (2007) The geometry of the most popular PAM OFR is a cylinder of ∼ 13 L volume. The PAM reactor we simulate is equipped with low-pressure Hg lamps (model no. 82-9304-03, BHK Inc.) emitting UV light at 185 and 254 nm. When both 185 and 254 nm photons are used to generate OH (termed “OFR185”), water vapor photolysis at 185 nm produces OH and HO₂. Recombination of O₂ and O(³P), formed by O₂ photolysis at 185 nm, generates O₃. O(¹D), formed through O₃ photolysis at 254 nm, reacts with water vapor and produces additional OH. 185 nm photons can be filtered by installing quartz sleeves around the lamps. This converts the reactor into “OFR254” mode, for which the photolysis of O₃, which must be initially injected, is the only OH production route. The notation “OFR254-X” is used to specify the initial amount of injected O₃ (X ppm) in OFR254. Lambe et al. (2017) and Peng et al. (2018) have shown that the initial injection of N₂O is able to maintain up to tens of ppb NO in both OFR185 and OFR254. These modes are denoted “OFR185-iN₂O” and “OFR254-X-iN₂O”, or more generally “OFR-iN₂O”. In OFR254-iN₂O, O(¹D) generated from O₃ photolysis reacts with N₂O to generate NO, while in OFR185-iN₂O, O(¹D) is mainly supplied by N₂O photolysis at 185 nm (Peng et al., 2018).

2.2 RO₂ production and loss pathways

A single generic RO₂ is adopted for modeling purposes to avoid the huge number of RO₂ types that would complicate effective modeling and analysis. In OH-initiated VOC oxidation, RO₂ is primarily produced via VOC + OH → R (+H₂O) followed by $\mathrm{R}+{\mathrm{O}}_{\mathrm{2}}\to {\mathrm{RO}}_{\mathrm{2}}$, where R is hydrocarbyl or oxygenated hydrocarbyl radical. Since the second step is extremely fast in air (Atkinson and Arey, 2003), the first step controls the RO₂ production rate, which depends on OH concentration and OHR_ext due to VOCs (OHR_VOC; see Appendix B for details). OHR_VOC also includes the contribution from oxidation intermediates of primary VOCs (e.g., methyl vinyl ketone and pinonic acid). When the information about oxidation intermediates is insufficient to calculate OHR_VOC, OHR due to primary VOCs is used instead as an approximant. RO₂ production through other pathways, e.g., VOC ozonolysis and photolysis, is not considered, since all non-OH pathways of VOC destruction only become significant at low H₂O and/or high OHR_ext (Peng et al., 2016). These conditions lead to significant non-tropospheric VOC photolysis and thus are of little experimental interest.

Table 1 lists all known RO₂ loss pathways. Among those, RO₂ photolysis, RO₂+NO₃ and RO₂+O₃ are not included in this study, since they are minor or negligible in OH-dominated atmospheres, chambers and OFRs for the following reasons.

Table 1 Rate constants (in cm³ molecule⁻¹ s⁻¹ except for isomerization; in s⁻¹), cross section (in cm²) and product(s) of RO₂ loss pathways. Only organic species are listed for product(s).

^a Ziemann and Atkinson (2012). ^b Orlando and Tyndall (2012); ^c typical value within the reported range in Orlando and Tyndall (2012); thermal decomposition rate constants of nitrates of acyl and non-acyl RO₂ are assumed to be 0.0004 and 3 s⁻¹, respectively, which are also typical values within the reported ranges in Orlando and Tyndall (2012). ^d Value used in the present work based on Bossolasco et al. (2014); Assaf et al. (2016, 2017a); Müller et al. (2016); Yan et al. (2016). ^e Müller et al. (2016); Yan et al. (2016); Assaf et al. (2017b, 2018). ^f Crounse et al. (2013). ^g Knap and Jørgensen (2017). ^h Burkholder et al. (2015). ⁱ Klems et al. (2015).

The first-order RO₂ photolysis rate constant is of the order of 10⁻² s⁻¹ at the highest lamp setting in OFRs (Kalafut-Pettibone et al., 2013) and of the order of 10⁻⁵ s⁻¹ in the troposphere under the assumption of unity quantum yield (Klems et al., 2015), while RO₂ reacts with HO₂ at > 1 s⁻¹ at the highest lamp setting in OFRs and at $\sim \mathrm{2}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹ in the troposphere. Note that in this study we assume an average ambient HO₂ concentration of 1.5×10⁸ molecules cm⁻³ (Mao et al., 2009; Stone et al., 2012) and RO₂+HO₂ rate constant of $\mathrm{1.5}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molecule⁻¹ s⁻¹ (Orlando and Tyndall, 2012).

When daytime photochemistry is active, NO₃ is negligible in the atmosphere. In OFR-iN₂O modes, RO₂+NO₃ is negligible unless at very low H₂O and high UV intensity (abbreviated UV hereafter), which result in high O₃ to oxidize NO₂ to NO₃ and keep HO₂ minimized. However, very low H₂O causes serious non-tropospheric organic photolysis (Peng et al., 2016) and thus these conditions are of no experimental interest.

In the atmosphere RO₂+O₃ is thought to play some role only at night (Orlando and Tyndall, 2012). Similar conditions may exist in some OFR254 cases if a very large amount of O₃ is injected and H₂O and UV are kept very low to limit HO_x production. These conditions are obviously not OH dominated and not further investigated in this study.

Of the RO₂ fates considered in this study, RO₂+HO₂, RO₂+NO and RO₂+RO₂ have long been known to play a role in the atmosphere (Orlando and Tyndall, 2012). Recommended general rate constants are available for RO₂+HO₂ and RO₂+NO (Ziemann and Atkinson, 2012; Table 1), albeit with some small dependencies on the type of RO₂ and a few deviations that are slightly larger but not important for the overall chemistry (e.g., CH₃O₂ and C₂H₅O₂ for RO₂+HO₂). We use these recommended values for generic RO₂ in this study. RO₂+NO has two main product channels, i.e., RO+NO₂ and RONO₂, whose branching ratios are RO₂ structure dependent (Ziemann and Atkinson, 2012). We do not include these product channels in this study, since they have negligible impacts on the chemical scheme described here. This feature results from two facts: (i) we focus on generic RO₂ and do not explicitly consider the chemistry of the products of different RO₂ loss pathways; and (ii) the channel producing RO and NO₂ contributes little to NO₂ production (Peng et al., 2018). However, RO₂ self- and cross-reaction rate constants are highly dependent on the specific RO₂ types and can vary over a very large range (10⁻¹⁷–10⁻¹⁰ cm³ molecule⁻¹ s⁻¹). Unsubstituted primary, secondary and tertiary RO₂ radicals self-react at $\sim {\mathrm{10}}^{-\mathrm{13}}$, $\sim {\mathrm{10}}^{-\mathrm{15}}$ and $\sim {\mathrm{10}}^{-\mathrm{17}}$ cm³ molecule⁻¹ s⁻¹, respectively (Ziemann and Atkinson, 2012). Rate constants of cross-reactions between these RO₂ types also span this range (Orlando and Tyndall, 2012). Substituted RO₂ types have higher self- and cross-reaction rate constants (Orlando and Tyndall, 2012). RO₂+RO₂ of highly substituted primary RO₂ can be as high as $\sim {\mathrm{10}}^{-\mathrm{11}}$ cm³ molecule⁻¹ s⁻¹ (Orlando and Tyndall, 2012). Very recently, a few highly oxidized 1,3,5-trimethylbenzene-derived RO₂s were reported to self- and cross-react at $\sim {\mathrm{10}}^{-\mathrm{10}}$ cm³ molecule⁻¹ s⁻¹ (Berndt et al., 2018). In the present work, we make a simplification to adapt to the generic RO₂ treatment by assuming a single self- and cross-reaction rate constant for generic RO₂ in each case. Three levels of RO₂+RO₂ rate constants, i.e., $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{13}}$, $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{11}}$ and $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{10}}$ cm³ molecule⁻¹ s⁻¹, are studied in this paper. The first level is referred to as “medium RO₂+RO₂” as many other RO₂ types can have self- and cross-reaction rate constants as low as 10⁻¹⁷ cm³ molecule⁻¹ s⁻¹; the second level is defined as “fast RO₂+RO₂”; and the last level is called “very fast RO₂+RO₂”. No RO₂+RO₂ rate constant lower than the medium level is investigated in the current work, although there are still a large variety of RO₂ types whose self- and cross-reactions are at lower rate constants, since at the medium level, RO₂+RO₂ is already negligible in all the environments studied in this work, i.e., OFRs, chambers and the atmosphere (see Sect. 3.1.1). Since there are only a few very specific examples for very fast RO₂+RO₂ reported to date, we will not systematically explore this category but compare very fast RO₂+RO₂ as a sensitivity case with the other two types of RO₂+RO₂ reactions.

Acyl RO₂ is considered as a separate RO₂ type (neither medium nor fast RO₂+RO₂) in this study since its reaction with NO₂ can be a major sink of RO₂ in OFR (Peng and Jimenez, 2017). Thermal decomposition lifetimes of the product of RO₂+NO₂, i.e., acylperoxy nitrates, can be hours at laboratory temperatures (Orlando and Tyndall, 2012; also taken into account in the current work; see Table 1), while OFR residence times are typically minutes. Besides, acyl RO₂ reacts with many RO₂ types at $\sim {\mathrm{10}}^{-\mathrm{11}}$ cm³ molecule⁻¹ s⁻¹ (Orlando and Tyndall, 2012), similar to that of fast RO₂+RO₂. We thus assume the acyl RO₂ self- and cross-reaction rate constant to also be $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molecule⁻¹ s⁻¹ to facilitate comparison with fast RO₂+RO₂ results.

In OFRs operated at room temperature, acylperoxy nitrates barely decompose, as their thermal decomposition lifetime is typically ∼ 1 h (Orlando and Tyndall, 2012), while OFR residence time is usually a few minutes. In contrast, peroxy nitrates of non-acyl RO₂ do decompose on a timescale of 0.1 s (Orlando and Tyndall, 2012; Table 1). As a consequence, the production and decomposition of peroxy nitrates of non-acyl RO₂ reach a steady state in OFRs, which can be greatly shifted toward the peroxy nitrate side in cases with very high NO₂ (Peng and Jimenez, 2017; Peng et al., 2018).

RO₂+OH (Fittschen et al., 2014) and RO₂ isomerization (Crounse et al., 2013) have recently been identified as possible significant RO₂ fates in the atmosphere. Reactions of the former type, according to several recent experimental and theoretical studies (Bossolasco et al., 2014; Assaf et al., 2016, 2017a, b; Müller et al., 2016; Yan et al., 2016), have similar rate constants ($\sim \mathrm{1}\times {\mathrm{10}}^{-\mathrm{10}}$ cm³ molecule⁻¹ s⁻¹) regardless of RO₂ type. Therefore, the reaction rate constant of generic RO₂ with OH is assigned as $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{10}}$ cm³ molecule⁻¹ s⁻¹. RO₂ isomerization reactivity is highly structure dependent (Crounse et al., 2013; Praske et al., 2018) and rate constant measurements are still scarce, preventing us from assigning a generic RO₂ isomerization rate constant. However, for generic RO₂, isomerization is generally not a sink but a conversion between two RO₂ radicals (both encompassed by the generic one in this study), as RO₂ isomerization usually generates an oxygenated hydrocarbyl radical, which rapidly recombines with O₂ and forms another RO₂. Therefore, RO₂ isomerization is not explicitly taken into account in the modeling, but is considered in the RO₂ fate analysis.

In summary, six pathways are included in the RO₂ fate analysis of this study. The need to explore these six pathways for a high number of OFR, chamber and atmospheric conditions makes the presentation of results challenging. For clarity, we present the results in two steps. In the first step, only well-known RO₂ fates (reaction with NO₂, HO₂, NO and RO₂) will be included in the model. In the second step, the results of the first step will be used to guide the modeling and analysis of a more comprehensive set of significant RO₂ fates.

2.3 Model description

The model used in the present work is a standard chemical kinetic box model implemented in the KinSim 3.4 solver in Igor Pro 7 (WaveMetrics, Lake Oswego, Oregon, USA) and has been described in detail elsewhere (Peng et al., 2015, 2018). Plug flow in the reactor with a residence time of 180 s is assumed, since the effects of non-plug flow are major only in a narrow range of conditions of little experimental interest, and the implementation of laminar flow or measured residence time distribution substantially increases computational cost (Peng et al., 2015; Peng and Jimenez, 2017). The reactions of RO₂ discussed in Sect. 2.2 are added to the chemical mechanism. A generic slow-reacting VOC (with the same OH rate constant as SO₂) is used as the external OH reactant. Its initial concentration is determined by the initial OHR_ext in each model case. Then as this proxy external OH reactant slowly reacts, OHR_ext slowly decays. This slow change in OHR_ext represents not only the decay of the initial reactant but also the generation and consumption of later-generation products that continue to react with OH. The reason for this approximation has been discussed in detail in previous OFR modeling papers (Peng and Jimenez, 2017; Peng et al., 2018). We exclude NO_y species, which are explicitly modeled, from the calculation of OHR_ext; thus, OHR_ext only includes non-NO_y OHR_ext hereafter. As OHR_ext is dominated by OHR_VOC in most OFR experiments, we use OHR_ext to denote OHR_VOC in OFRs (while for ambient and chamber cases OHR_VOC is still used to exclude the contribution of CO, etc.). The outputs of our model (e.g., species concentrations and exposures) were estimated to be accurate to within a factor of 2–3 when compared with field OFR experiments; better agreement can generally be obtained for laboratory OFR experiments (Li et al., 2015; Peng et al., 2015).

Another key parameter in the model is the HO_x recycling ratio (β), defined in this study as the number of HO₂ molecule(s) produced per OH molecule destroyed by external OH reactants (Peng et al., 2015). This ratio depends on the products of RO₂ loss pathways. The main product of RO₂+HO₂ is usually ROOH (Table 1), yielding no recycled HO₂, while the main products of RO₂+NO are RO and NO₂, the former of which can often undergo extremely fast H abstraction by O₂ to form a carbonyl and HO₂. We used the fully chemically explicit (automated chemical mechanism generation based on available knowledge) box model GECKO-A (Aumont et al., 2005) to simulate OH oxidation of several simple VOCs (e.g., propane and decane) under various OFR conditions with zero NO. We consistently find that β∼ 0.3. At the other extreme, when RO₂ is solely consumed by RO₂+NO, the product RO yields HO₂ at a branching ratio close to 1, β∼ 1. For intermediate cases, we assume that β may be interpolated as a linear function of $\mathrm{r}({\mathrm{RO}}_{\mathrm{2}}+\mathrm{NO})/\left[\mathrm{r}\right({\mathrm{RO}}_{\mathrm{2}}+\mathrm{NO})+\mathrm{r}({\mathrm{RO}}_{\mathrm{2}}+{\mathrm{HO}}_{\mathrm{2}}\left)\right]$, where r(RO₂+NO) and r(RO₂+HO₂) are the local reactive fluxes of RO₂+NO and RO₂+HO₂.

In the present work, we model OFR185, OFR254-70 and OFR254-7 (including their iN₂O variants). We specify the same temperature and atmospheric pressure (295 K and 835 mbar, typical values in Boulder, Colorado, USA) as our previous OFR modeling studies (Li et al., 2015; Peng et al., 2015, 2016, 2018; Peng and Jimenez, 2017). The explored physical condition space follows that of our previous OFR-iN₂O modeling work (Peng et al., 2018). The only differences are that in this study we also include cases without any N₂O injected (OFR185 and OFR254 only) and exclude OHR_ext=0 conditions, which produce no RO₂. In detail, the explored physical condition space covers the following: H₂O of 0.07 %–2.3 % (relative humidity of 2 %–71 % at 295 K); UV photon flux at 185 nm (abbreviated F185) of 1.0×10¹¹–1.0×10¹⁴ photons cm⁻² s⁻¹ (corresponding photon flux at 254 nm (F254) of 4.2×10¹³–8.5×10¹⁵ photons cm⁻² s⁻¹); OHR_ext of 1–1000 s⁻¹; and N₂O mixing ratio (abbreviated N₂O hereafter) of 0 and 0.02 %–20 %. All model cases are logarithmically evenly distributed except for N₂O =0 and F254. The latter is calculated based on the F185–F254 relationship for the lamps simulated here (Li et al., 2015).

For the classification of conditions, the same criteria as in the OFR-iN₂O modeling study (Peng et al., 2018) are adopted. In detail, high- and low-NO conditions are classified by $\mathrm{r}({\mathrm{RO}}_{\mathrm{2}}+\mathrm{NO})/\mathrm{r}({\mathrm{RO}}_{\mathrm{2}}+{\mathrm{HO}}_{\mathrm{2}})$. In the current work, these reactive fluxes are explicitly tracked in the modeling instead of approximated as in previous studies (Peng and Jimenez, 2017; Peng et al., 2018). The terms “good,” “risky” and “bad” are used to describe OFR operating conditions in terms of non-tropospheric organic photolysis and are defined based on the ratios of F185 and F254 exposure (F185_exp and F254_exp, i.e., integrated photon fluxes over residence time) to OH exposure (OH_exp), as presented previously (Peng and Jimenez, 2017; Peng et al., 2018). Briefly, under a given condition non-tropospheric photolysis is of different relative importance in the fate of each specific organic species: under good conditions, photolysis at 185 and/or 254 nm is unimportant for almost all VOCs; under bad conditions, non-tropospheric photolysis is problematic for most VOC precursors, since significant photolysis of their oxidation intermediates at 185 and/or 254 nm is almost inevitable; and risky conditions can be problematic for some but not all VOCs. Note that good, risky or bad conditions refer only to non-tropospheric organic photolysis and not to whether RO₂ chemistry is atmospherically relevant. Table S1 summarizes our condition classification criteria.

3 Results and discussion

In this section, the results are presented in two parts, i.e., first for the simulations with well-known pathways only and secondly with all significant pathways, as proposed in Sect. 2.2. Then based on the results and their comparison with the atmosphere and chamber experiments, we propose guidelines for OFR operation to ensure atmospherically relevant RO₂ chemistry, as well as other chemistries already discussed in the previous studies (Peng et al., 2016, 2018), in OFRs.

3.1 Simulations with well-known pathways (RO₂+HO₂, RO₂+RO₂, RO₂+NO and RO₂+NO₂)

Due to the significantly different reactivities of non-acyl and acyl RO₂, the results of these two types of RO₂ are shown separately.

3.1.1 Non-acyl RO₂

In this case non-acyl RO₂ radicals have only three fates, i.e., RO₂+HO₂, RO₂+NO and RO₂+RO₂. The relative importance of these three fates can be shown in a triangle plot (Fig. 1). The figure includes data points of OFR185 (including OFR185-iN₂O) and OFR254-70 (including OFR254-70-iN₂O), as well as several typical ambient and chamber studies, including two pristine remote area cases (P₁ and P₂) from the ATom-1 study (Wofsy et al., 2018), two forested area cases (F₁ and F₂) from the BEACHON-RoMBAS and GoAmazon campaigns, respectively (Ortega et al., 2014; Martin et al., 2016, 2017), an urban area case (U) from the CalNex-LA campaign (Ryerson et al., 2013), and five typical chamber experiment cases (C₁–C₅) from the FIXCIT study (Nguyen et al., 2014). These typical cases shown in Fig. 1 bring to light several interesting points.

• In all ambient and chamber cases, medium and slower RO₂+RO₂ contribute negligibly to the RO₂ fate. This confirms a common impression that self- and cross-reactions of many RO₂ radicals do not significantly affect RO₂ fates.

• However, if RO₂ self- and cross-reacts rapidly, RO₂+RO₂ can be the most important loss pathway among RO₂+RO₂, RO₂+HO₂ and RO₂+NO even in pristine regions with higher VOC (e.g., P₁ in Fig. 1) compared to an average pristine region case (P₂). Note that the P₁ case is still very clean compared to typical forested and urban areas (Table 2).

• Forested areas located in the same region as pollution sources are not as “low NO” as one may expect (points F₁ and F₂ in Fig. 1). RO₂+NO contributes ∼ 20 %–50 % to RO₂ loss, as NO and HO₂ concentrations are of the same order of magnitude in these cases.

• RO₂+NO dominates over RO₂+RO₂ and RO₂+HO₂ in almost all urban areas. Even in relatively clean urban areas such as Los Angeles during CalNex-LA in 2010 (point U in Fig. 1), average NO is ∼ 1 ppb, still sufficiently high to ensure the dominance of RO₂+NO among the three pathways.

• Various chamber cases in the FIXCIT campaign (low to high OHR_ext; low to high NO; points C_x in Fig. 1) are able to represent specific RO₂ fates that appear in different regions in the atmosphere.

On these plots, points for bad conditions (in terms of non-tropospheric photolysis) are not shown because of the lack of experimental interest. The triangle plots for OFR254-7 (including OFR254-7-iN₂O) in the same form (Supplement Fig. S1a, b) show no qualitative differences from the results of OFR254-70, implying that initial O₃ in OFR254 modes has only minor impacts on RO₂ fate. We see this result not only for well-known non-acyl RO₂ fate, but also for the aspects discussed in the following sections. The similarity between OFR254 modes can be explained by the minor effects of a lower O₃ on HO_x at relatively low OHR_ext (Peng et al., 2015). Cases at higher OHR_ext often have stronger non-tropospheric photolysis (Peng et al., 2016) and hence are more likely to be under bad conditions and are not shown in Figs. 1 and S1a, b. For simplicity, this similarity is not discussed further.

Figure 1 Triangle plots of RO₂ fate by RO₂+HO₂, RO₂+RO₂ and RO₂+NO (without RO₂+OH and RO₂ isomerization considered in the model) for RO₂ with the medium self- and cross-reaction rate constant ($\mathrm{1}\times {\mathrm{10}}^{-\mathrm{13}}$ cm⁻³ molecule⁻¹ s⁻¹) in (a) OFR185 (including OFR185-iN₂O) and (c) OFR254-70 (including OFR254-70-iN₂O) and for RO2 with the fast self- and cross-reaction rate constant ($\mathrm{1}\times {\mathrm{10}}^{-\mathrm{11}}$ cm⁻³ molecule⁻¹ s⁻¹) in (b) OFR185 (including OFR185-iN₂O) and (d) OFR254-70 (including OFR254-70-iN₂O). Inclined tick values on an axis indicate the grid lines that should be followed (in parallel to the inclination) to read the corresponding values on this axis. The OFR data points are colored by the logarithm of the exposure ratio between 254 nm photon flux and OH, a measure of badness of OFR conditions in terms of 254 nm organic photolysis. Several typical ambient and chamber cases (see Table 2 for details on these cases) are also shown for comparison.

Table 2 Several typical ambient and chamber (the FIXCIT campaign) cases that are compared to OFR cases.

^a Wofsy et al. (2018) for the Atom-1 campaign. ^b Fry et al. (2013) for the BEACHON-RoMBAS campaign. ^c RO₂ concentration was given in Fry et al. (2013) (50 ppt) so that OHR_VOC is not needed for RO₂ fate estimation. ^d Daun Jeong and Saewung Kim, personal communication (2018), for the GoAmazon campaign (Martin et al., 2016, 2017). ^e Typical case in the CalNex-LA campaign (Ryerson et al., 2013). ^f Estimated (Peng et al., 2016). ^g Typical ambient value (Mao et al., 2009; Stone et al., 2012). ^h Data from Nguyen et al. (2014). ⁱ Initial value.

An important feature confirmed in Fig. 1 is that OFR-iN₂O modes effectively realize conditions of experimental interest with variable relative importance of RO₂+NO in RO₂ fate (Lambe et al., 2017; Peng et al., 2018). Tuning initially injected N₂O can achieve this goal (Fig. 2). While it is possible to reduce RO₂+HO₂ in OFR185-iN₂O to negligible compared to RO₂+NO by increasing N₂O, this is not possible in OFR254-70-iN₂O due to fast NO oxidation by the large amounts of O₃ added in the reactor. Nevertheless, OFR254-70-iN₂O can still make RO₂+NO dominate over RO₂+HO₂ in RO₂ fate. OFR and chamber cases span a range of ∼ 0 %–∼ 100 % in relative importance of RO₂+NO in RO₂ fate (Fig. 2), suggesting that both chambers and OFRs are able to ensure the atmospheric relevance of RO₂+NO in RO₂ fate.

Figure 2 Frequency distributions of the relative importance of RO₂+NO in the fate of RO₂ (with medium self- and cross-reaction rate constant and without RO₂+OH and RO₂ isomerization considered) for OFR185 (including OFR185-iN₂O) and OFR254-70 (including OFR254-70-iN₂O). Distributions for several different N₂O levels are shown. Only good and risky conditions (in terms of non-tropospheric organic photolysis) are included in the distributions. Also shown is the relative importance of RO₂+NO for several typical ambient and chamber cases (see Table 2 for details on these cases).

Another important feature that can be easily seen in Fig. 1 is that medium-rate RO₂+RO₂ (and hence also RO₂+RO₂ slower than 10⁻¹³ cm³ molecule⁻¹ s⁻¹) is of negligible importance in the fate of RO₂ (Fig. 1a, c) in OFR185 (including OFR185-iN₂O), OFR254-70 (under most conditions, including OFR254-70-iN₂O), chambers and the atmosphere. Thus, a very large subset of RO₂ types have only a minor or negligible contribution from RO₂+RO₂ to their fate. This is already known for ambient RO₂ fate (Ziemann and Atkinson, 2012). The reason why this is also true in OFRs is that while OH is much higher than ambient levels, HO₂ and NO (high-NO conditions only) are also higher. One can easily verify that steady-state RO₂ concentrations (see Appendix B for details) would not deviate from ambient levels by orders of magnitude. The reactive fluxes of RO₂+RO₂ in OFRs are thus not substantially different than in the atmosphere, while RO₂+HO₂ and RO₂+NO (high-NO conditions only) are both faster in OFRs because of higher HO₂ and NO. The combined effect is a reduced relative importance of RO₂+RO₂ in RO₂ fate in OFRs compared to the atmosphere. The only exception in OFRs occurs at very high VOC precursor concentrations (OHR_ext significantly > 100 s⁻¹) in OFR254 (Fig. S2), in which OH levels are not substantially suppressed due to large amounts of O₃ (Peng et al., 2015). As a result, RO₂ concentration is remarkably increased by strong production, and RO₂+RO₂ relative importance increases roughly quadratically and becomes significant.

The generally lower relative importance of RO₂+RO₂ in OFRs than in the atmosphere is more obvious for the fate of RO₂ with fast RO₂+RO₂ rate constants (Figs. 1b, d and 3). Although OFRs can reasonably reproduce RO₂ fates in typical low- and moderate-OHR_ext ambient environments (e.g., typical pristine and forested areas; Figs. 1b, d and 3) and low-OHR_ext chambers, OFR185 cannot achieve a relative importance of RO₂+RO₂ significantly larger than 50 %, such as found in remote environments with higher VOC (e.g., P₁ in Fig. 1) and high-OHR_ext chamber experiments (e.g., C₂ and C₅ in Fig. 1; the distribution for C₂ is also shown in Fig. 3). In OFR254-70, a relative importance of RO₂+RO₂ as high as ∼ 90 % may be attained (Fig. S3). However, this requires very high OHR_ext, which leads to medium (and slower) RO₂+RO₂ showing higher-than-ambient relative importance. In reality, fast RO₂+RO₂ reactions all involve substituted RO₂, which almost certainly arises from and coexists with unsubstituted RO₂ (with slower self- and cross-reactions). Therefore, very high OHR_ext in OFR254 is not really suitable for attaining dominant RO₂+RO₂ conditions. In OFR185, a higher OHR_ext generally also results in a higher RO₂+RO₂ relative importance because of higher RO₂ production (Fig. S3). Nevertheless, higher OHR_ext is more likely to lead to risky or bad conditions (Fig. 3; Peng et al., 2016). It should be noted that although it is difficult to reliably achieve RO₂+RO₂ with a relative importance larger than 50% in RO₂ fate in OFRs, the distributions of RO₂+RO₂ relative importance in OFRs seem to be within a factor of 2 of those of field and aircraft campaigns (Fig. 3).

Figure 3 Frequency distributions of the relative importance of RO₂+RO₂ in the fate of RO₂ (with fast self- and cross-reaction rate constant and without RO₂+OH and RO₂ isomerization considered) for OFR185 (including OFR185-iN₂O), OFR254-70 (including OFR254-70-iN₂O), and a chamber experiment and in the atmosphere (a couple of different environments). The OFR distributions for good and risky conditions (in terms of 254 nm organic photolysis; see Table S1 for the definitions of these conditions) are shown separately. Also shown is the relative importance of RO₂+RO₂ for several typical chamber cases (see Table 2 for details on these cases). The range of the RO₂+RO₂ relative importance for most high-NO conditions is highlighted in cyan.

In the case of very fast RO₂+RO₂, all features for fast RO₂+RO₂ discussed above are still present (Fig. S1c, d). The only major difference between the results for fast RO₂+RO₂ and very fast RO₂+RO₂ is the significantly higher relative importance of RO₂+RO₂ in RO₂ fate in the latter case, which is expected. In summary, fast RO₂+RO₂ is not perfectly reproduced in OFRs in terms of relative importance in RO₂ fate, but it is significant when this pathway is also important in the atmosphere.

The HO_x recycling ratio β (see Sect. 2.3) is one of the key factors determining HO₂ in the OFR model, yet it is not well constrained. Although we make reasonable assumptions for it in the model input (see Sect. 2.3 for details), a sensitivity study to explore its effects is also performed here. For RO₂ with the fast self- and cross-reaction rate constant, we perform simulations with the HO_x recycling ratios fixed to a number of values from 0 (radical termination) to 2 (radical proliferation) in lieu of those calculated under the assumptions described in Sect. 2.3. As expected, the contribution of RO₂+RO₂ to RO₂ fate increases monotonically between β=2 and β=0 (Fig. S4) as the recycling of the competing reactant HO₂ decreases. Nevertheless, the change in the average RO₂+RO₂ relative importance from β=0 to β=2 is generally within a factor of 2. Thus, it still holds that the RO₂+RO₂ relative importance in OFRs is generally lower than in the atmosphere. Only at β∼ 0 may OFR185 theoretically attain a relative importance of RO₂+RO₂ of ∼ 70 %, as in the P₁ case (pristine, but relatively high VOC; Fig. S5). Note that β=0 for all VOC oxidation (including oxidation of intermediates) is extremely unlikely. In OFR254, even if RO₂+RO₂ may contribute up to ∼ 100 % to RO₂ fate at very high OHR_ext at β=0, these conditions still also lead to significant RO₂+RO₂ in the fate of RO₂ that self- and cross-reacts more slowly, which is not atmospherically relevant.

3.1.2 Acyl RO₂

As described in Sect. 2.1, the generic acyl RO₂ modeled in this study has the same loss pathways as RO₂ with the fast self- and cross-reaction rate constant, except for RO₂+NO₂, which can be a significant acyl RO₂ loss pathway in OFRs as well as both chambers and the atmosphere. When this reaction is included in the simulations of acyl RO₂, it is a minor or negligible loss pathway of RO₂ at low N₂O, while it can be the dominant fate of acyl RO₂ at high N₂O (Fig. 4). In general, the RO₂+NO₂ relative importance increases with initial N₂O. This is always true in OFR254-70-iN₂O between N₂O = 0.02 % and N₂O = 20 %, while in OFR185-iN₂O, the average relative contribution of RO₂+NO₂ to RO₂ fate starts to decrease at N₂O ∼ 10 % because RO₂+NO regains some importance. This results from the HO_x suppression caused by high NO_y and strong NO production at high N₂O. Strong NO production increases its concentration and suppresses HO_x under these conditions, limiting the conversion of NO to NO₂. Because of the strong OH suppression by high NO_y at N₂O ≥10 %, these conditions are not desirable (Peng et al., 2018).

Figure 4 Average relative importance of RO₂+NO₂ in acyl RO₂ fate (RO₂+OH and RO₂ isomerization not considered) in OFR185 (including OFR185-iN₂O) and OFR254-70 (including OFR254-70-iN₂O). The averages are calculated based on good and risky conditions (in terms of non-tropospheric organic photolysis) only.

The only difference between the simulations of acyl RO₂ and of the fast self- and cross-reacting non-acyl RO₂ is the quasi-irreversible reaction ${\mathrm{RO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{2}}\to {\mathrm{RO}}_{\mathrm{2}}{\mathrm{NO}}_{\mathrm{2}}$ at room temperature, whose effects are revealed by a comparison of the triangle plots of the RO₂ fates in each case (Figs. 1b, d and S6). RO₂+NO₂ is clearly dominant in acyl RO₂ fate in OFRs as long as RO₂+NO plays some role (not necessarily under high-NO conditions). In OFR185-iN₂O, the relative importance of RO₂+RO₂ in the sum of the HO₂, NO and RO₂ pathways is reduced (Fig.  S6a) compared to that of non-acyl RO₂ with fast RO₂+RO₂ (Fig. 1b) because RO₂+NO₂ decreases acyl RO₂ concentration. Such a decrease is not significant in OFR254-70-iN₂O (Fig. S6b, compared to Fig. 1d), since for non-acyl RO₂, it is already stored in the form of RO₂NO₂ as an RO₂ reservoir. In other words, the high initial O₃ greatly accelerates NO-to-NO₂ oxidation and shifts the equilibrium ${\mathrm{RO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{2}}\leftrightarrow {\mathrm{RO}}_{\mathrm{2}}{\mathrm{NO}}_{\mathrm{2}}$ far to the right even for non-acyl RO₂.

RO₂+NO₂ is an inevitable and dominant sink of most acyl RO₂ in high-NO_x OFRs, though the extent of this dominance differs substantially among the different OFR operation modes. In OFR254-70-iN₂O, RO₂+NO makes a minor or negligible contribution to acyl RO₂ fate because the required high O₃ very rapidly oxidizes NO to NO₂ and leads to very low NO-to-NO₂ ratios (e.g., ∼ 0.003–0.03; see Fig. S7). In OFR185-iN₂O, the contribution of RO₂+NO can be somewhat significant, with typical NO-to-NO₂ of ∼ 0.03–0.4. (Fig. S7). Urban NO-to-NO₂ ratios vary widely, for example (roughly, and excluding significant tails in the frequency distributions) 0.02–1 for Barcelona and 0.007–0.7 for Los Angeles and Pittsburgh (see Fig. S7). Given these variations among different urban areas, RO₂+NO and RO₂+NO₂ for acyl RO₂ in OFR185-iN₂O can be regarded as relevant to urban atmospheres. Exceptions to the relevance of OFR185-iN₂O occur during morning rush hours (e.g., see the high NO-to-NO₂ tail for the Pittsburgh case in Fig. S7), near major NO sources and/or in urban atmospheres with stronger NO emission intensity (e.g., Beijing, especially in winter; Fig. S7). In these cases, NO-to-NO₂ ratios may significantly exceed 1, and RO₂+NO may be the dominant acyl RO₂ loss pathway. Such high-NO conditions appear difficult to simulate in OFRs with the current range of techniques.

Acyl RO₂ is not the dominant type among RO₂ types under most conditions in OFRs, chambers and the atmosphere, since their formation usually requires multistep (at least 2 steps) oxidation via specific pathways leading to an oxidized end group (i.e., aldehyde and then acylperoxy). However, simulations using the GECKO-A model in urban (Mexico City) and forested (Rocky Mountains) atmospheres (Fig. S8) show that acyl RO₂ can still be a major (very roughly 1∕3) component of RO₂ at ages of several hours or more. Therefore, acyl RO₂ chemistry in a high-NO OFR can significantly deviate from that in an urban atmosphere with NO dominating NO_x and can be relevant to an urban atmosphere with NO₂ dominating NO_x. On the other hand, a few theoretical studies suggested that H abstraction by the acylperoxy radical site from hydroperoxy groups close to the acylperoxy site in multifunctional acyl RO₂ may be extremely fast (Jørgensen et al., 2016; Knap and Jørgensen, 2017). If these theoretical predictions are sufficiently accurate, these acyl RO₂ types may exclusively undergo an intramolecular H shift to form non-acyl RO₂ or other radicals and prevent RO₂+NO₂ from occurring even at very high (ppm level) NO₂. However, this type of RO₂ is structurally specific and may not have strong impacts on the overall acyl RO₂ chemistry.

3.2 Simulations with all significant pathways

Since RO₂ isomerization does not significantly affect the generic RO₂ concentration, the two RO₂ fates that were recently found to be potentially important, i.e., RO₂+OH and RO₂ isomerization, can be discussed separately.

3.2.1 RO₂+OH

In the troposphere, RO₂+OH is a minor (at low NO) or negligible (at high NO) RO₂ loss pathway (Fittschen et al., 2014; Assaf et al., 2016; Müller et al., 2016), as its rate constant is roughly an order of magnitude higher than that of RO₂+HO₂ (Table 1), while the ambient OH concentration is on average 2 orders of magnitude lower than that of HO₂ (Mao et al., 2009; Stone et al., 2012; Fig. 5). We will not discuss RO₂+OH in the high-NO cases in detail. Simply put, the relative importance of RO₂+OH is generally negatively correlated with input N₂O in OFR-iN₂O, as NO_x suppresses OH and the relative importance of RO₂+NO increases. Below, we focus on low-NO (actually, for simplicity, zero-NO) conditions.

Figure 5 Frequency distributions of (a) the HO₂-to-OH ratio and (b) the relative importance of RO₂+OH in the fate of RO₂ (with medium self- and cross-reaction rate constant) for OFR185 (including OFR185-iN₂O), OFR254-70 (including OFR254-70-iN₂O), and a chamber experiment and in the atmosphere (a couple of different environments). The OFR distributions for lower (F185 < 3.16×10¹² photons cm⁻² s⁻¹; F254 < 5.95×10¹⁴ photons cm⁻² s⁻¹) and higher UV (F185 $\ge \mathrm{3.16}\times {\mathrm{10}}^{\mathrm{12}}$ photons cm⁻² s⁻¹; F254 $\ge \mathrm{5.95}\times {\mathrm{10}}^{\mathrm{14}}$ photons cm⁻² s⁻¹) are shown separately. Only good and risky conditions (in terms of non-tropospheric organic photolysis) are included in the distributions for OFRs. Also shown are the HO₂-to-OH ratio and the relative importance of RO₂+OH for an OFR experiment with ambient air input in a field study (BEACHON-RoMBAS; Palm et al., 2016).

At N₂O =0, it would be ideal if an HO₂-to-OH ratio identical to the ambient values was realized in OFRs. In OFR185 cases with medium RO₂+RO₂, an HO₂-to-OH ratio around 100 occurs at a combination of low H₂O (of the order of 0.1%), low F185 (of the order of 10¹¹ photons cm⁻² s⁻¹) and medium OHR_ext (10–100 s⁻¹) and also at medium F185 (∼ 10¹² photons cm⁻² s⁻¹) combined with very high OHR_ext (∼ 1000 s⁻¹, Fig. S9). Under both sets of conditions, relatively high external OH reactants suppress OH, whose production is relatively weak, and convert some OH into HO₂ through HO_x recycling in organic oxidation (e.g., via alkoxy radical chemistry). The reason why such an OH-to-HO₂ conversion is needed to attain an ambient-like HO₂-to-OH ratio is that OFR185 is unable to achieve this via the internal (mainly assisted by O₃) interconversion of HO_x. This inability is most evident when F185 (10¹³–10¹⁴ photons cm⁻² s⁻¹) and H₂O (of the order of 1 %) are high and OHR_ext is low (< ∼ 10 s⁻¹; Fig. S9). Under these conditions, OH production by H₂O photolysis is so strong that the HO₂-to-OH ratio is lowered to ∼ 1, since OH and H (which recombines with O₂ to form HO₂) are produced in equal amounts from H₂O photolysis. As the RO₂+OH rate constant is only roughly 1 order of magnitude higher than that for RO₂+HO₂, slightly lower HO₂-to-OH ratios (e.g., ∼ 30) suffice to keep RO₂+OH minor in this case. A combination of UV and H₂O that are not very high and a moderate OHR_ext that is able to convert some OH to HO₂ and somewhat elevate the HO₂-to-OH ratio results in minor relative importance for RO₂+OH (Figs. S9 and S10).

In OFR254-70, it is more difficult to reach an HO₂-to-OH ratio of ∼ 100, which can only be realized at a combination of very low H₂O and F254 (∼ 0.07 % and $\sim \mathrm{5}\times {\mathrm{10}}^{\mathrm{13}}$ photons cm⁻² s⁻¹, respectively) and very high OHR_ext (∼ 1000 s⁻¹). This is mainly due to high O₃ in OFR254-70, which controls the HO_x interconversion through ${\mathrm{HO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}\to \mathrm{OH}+\mathrm{2}{\mathrm{O}}_{\mathrm{2}}$ and $\mathrm{OH}+{\mathrm{O}}_{\mathrm{3}}\to {\mathrm{HO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}$ and makes both OH and HO₂ more resilient to changes due to OHR_ext (Peng et al., 2015). Even without H₂O photolysis at 185 nm as a major HO₂ source, the HO_x interconversion controlled by O₃ in OFR254-70 still brings the HO₂-to-OH ratio to ∼ 1 in the case of minimal external perturbation (see the region at the highest H₂O and UV and OHR_ext=0 in the OFR254-70 part of Fig. S9). This ratio cannot be easily elevated in OFR254-70 because of the resilience of OH to suppression for this mode (Peng et al., 2015). Thus, this ratio is relatively low (< 30) under most conditions (Fig.  S9), and consequently (and undesirably) RO₂+OH is a major RO₂ fate in OFR254-70. There is an exception at relatively low H₂O and UV with very high OHR_ext (Fig. S10); however, these conditions are undesirable in terms of non-tropospheric organic photolysis (Peng et al., 2016).

Only the results of RO₂ with medium RO₂+RO₂ are discussed in this section. Those of RO₂ with the fast RO₂+RO₂ are not shown as they are not qualitatively different. In OFR185, for the fast self- and cross-reacting RO₂, RO₂+RO₂ is relatively important at high OHR_ext (> ∼ 100 s⁻¹; Fig. S3), while RO₂+OH is a major RO₂ fate at low OHR_ext (generally of the order of 10 s⁻¹ or lower) and relatively high H₂O and UV (Fig. S10). These two ranges of conditions are relatively far away from each other, and hence there is no condition under which RO₂+RO₂ and RO₂+OH are both major pathways that compete, which simplifies understanding RO₂ fate. However, in OFR254-70, some conditions may lead to both significant RO₂+RO₂ (for the fast self- and cross-reacting RO₂) and RO₂+OH (e.g., H₂O ∼ 0.5 %, F254 $\sim \mathrm{1}\times {\mathrm{10}}^{\mathrm{15}}$ photons cm⁻² s⁻¹ and OHR_ext∼ 100 s⁻¹). Nevertheless, as long as RO₂+OH plays a major role, these conditions do not bear much experimental interest and thus do not need to be discussed in detail.

3.2.2 RO₂ isomerization

RO₂ isomerization is a first-order reaction. For this type of reaction to occur, RO₂ does not need any other species but only a sufficiently long lifetime against all other reactants combined, as most RO₂ isomerization rate constants are < 10 s⁻¹. Radical (OH, HO₂, NO, etc.) concentrations in OFRs are much higher than ambient levels and may shorten RO₂ lifetimes compared to those in the troposphere. Possibly reduced RO₂ lifetimes naturally raise concerns over the potentially diminished importance of RO₂ isomerization in OFRs.

In this section we examine generic RO₂ lifetimes against all reactions (calculated without RO₂ isomerization taken into account) in OFR (including OFR-iN₂O) cases (for the medium RO₂+RO₂ case) and compare them with the RO₂ lifetimes in recent major field and aircraft campaigns in relatively clean environments and a field campaign in an urban area (CalNex-LA), as well as a low-NO chamber experiment (Fig. 6). Indeed, RO₂ lifetimes in clean ambient cases and in chambers with near-ambient radical levels are generally much longer than those in OFRs. The RO₂ lifetime distribution of the explored good and risky cases in OFR254-70 (including OFR254-70-iN₂O) barely overlaps the ambient and chamber cases, while in OFR185 (including OFR185-iN₂O), the RO₂ lifetime can be as long as ∼ 10 s, which is longer than in urban areas and roughly at the lower end of the range of ambient RO₂ lifetimes in clean environments (Fig. 6). The longest RO₂ lifetime in OFR185 occurs at very low F185 (of the order of 10¹¹ photons cm⁻² s⁻¹) and H₂O (∼ 0.1 %; Fig. S11) when HO_x is low. In OFR254-70, for RO₂ to survive for ∼ 10 s, in addition to very low UV and H₂O, high OHR_ext is also needed (Fig. S11). High-OHR_ext conditions in OFR254-70 cause OH suppression and a decrease in HO_x concentration and hence result in relatively long RO₂ lifetimes. However, the strong OH suppression is likely to create bad conditions (high contribution of non-tropospheric photolysis) (Peng et al., 2016). Low-OHR_ext conditions do not lead to long RO₂ lifetimes in OFR254-70 even at very low F254 and H₂O, since O₃-assisted HO_x recycling prevents a very low HO_x level even if HO_x primary production is low (Peng et al., 2015)

Figure 6 (a) Same format as Fig. 5, but for RO₂ lifetime (RO₂ isomerization included in the model but excluded from lifetime calculation). (b) Relative contribution of isomerization to RO₂ fate as a function of RO₂ isomerization rate constant in several model cases for OFR experiments in the BEACHON-RoMBAS campaign (Palm et al., 2016), in a chamber experiment and in two ambient cases. Isomerization rate constants of several RO₂ types (Crounse et al., 2013; Praske et al., 2018) are also shown.

An RO₂ lifetime (without RO₂ isomerization included) of 10 s leads to a relative importance of isomerization of 50 % in the total fate (including all loss pathways) of RO₂ with an isomerization rate constant of 0.1 s⁻¹, which is a typical order of magnitude for isomerization rate constants of multifunctional RO₂ with hydroxyl and hydroperoxy substituents (Fig. 6; Crounse et al., 2013; D'Ambro et al., 2017; Praske et al., 2018). Although a 50 % relative importance of isomerization under some OFR conditions is still lower than those in relatively low-NO ambient environments and low-NO chambers, this relative importance should certainly be deemed major and far from negligible as some have speculated (Crounse et al., 2013). Other monofunctional RO₂ (with peroxy radical site only) and bifunctional RO₂ with a peroxy radical site and a carbonyl group isomerize so slowly (∼ 0.001–0.01 s⁻¹) that their isomerizations are minor or negligible loss pathways in the atmosphere, chambers and OFRs with RO₂ lifetimes around 10 s (Fig. 6). Isomerizations of other types of multifunctional RO₂ (e.g., multifunctional acyl RO₂ with hydroxyl and hydroperoxy substituents at favorable positions) are extremely fast (rate constants up to 10⁶ s⁻¹; Jørgensen et al., 2016; Knap and Jørgensen, 2017) and always dominate in their fates in the relatively low-NO atmosphere as well as in chambers and OFRs with RO₂ lifetimes around 10 s.

In the discussion about RO₂ isomerization above (as in the RO₂+OH exploration in Sect. 3.2.1), we only examine low-NO (or zero-NO for simplicity) conditions with medium RO₂+RO₂. In high-NO environments, e.g., polluted urban atmospheres with NO of at least ∼ 10 ppb and high-NO OFRs in the iN₂O modes, the RO₂ lifetime is so short that isomerization is no longer a major fate for any but the most rapidly isomerizing multifunctional RO₂ types discussed above. NO measured in Los Angeles during the CalNex-LA campaign (Ortega et al., 2016) was only ∼ 1 ppb, which would to allow RO₂ to survive for a few seconds and isomerize (Fig. 6), even in an urban area.

The OFR simulations for the discussions about RO₂ isomerization are the same as those conducted to study RO₂+OH, i.e., the ones with medium RO₂+RO₂ and RO₂+OH included. For fast RO₂ self- and cross-reaction cases, RO₂ lifetimes may be significantly shorter than for RO₂ with the medium self- and cross-reaction rate constant at high OHR_ext (> ∼ 100 s⁻¹) in OFR185 (Fig. S3). These high-OHR_ext conditions are likely to be risky or bad (of little experimental interest) (Peng et al., 2016) and thus do not need to be discussed further in detail. OFR254-70 (a zero-NO mode) does not generate good or risky (of at least some experimental interest in terms of non-tropospheric organic photolysis) conditions, also leading to low-NO-atmosphere-relevant RO₂ lifetimes (Fig. 6). RO₂ types with faster self- and cross-reaction rate constants have even shorter lifetimes in OFR254-70 and will not be discussed further.

3.3 Guidelines for OFR operation

In this section we discuss OFR operation guidelines for atmospherically relevant RO₂ chemistry, with a focus on OFR185 and OFR254 (zero-NO modes). Since RO₂+HO₂ and RO₂+NO both can vary from negligible to dominant RO₂ fate in OFRs, chambers and the atmosphere (Figs. 1 and 2), these two pathways are not a concern in OFR atmospheric relevance considerations, and neither is RO₂+RO₂. Medium or slower RO₂+RO₂ is minor or negligible in the atmosphere and chambers, as well as in OFRs, as long as high OHR_ext is avoided in OFR254 (Fig. S2). Fast RO₂+RO₂ is somewhat less important in OFRs than in the atmosphere (Figs. 1b, d and 3), but is still qualitatively atmospherically relevant, given the uncertainties associated with the HO_x recycling ratios of various reactive systems and the huge variety of RO₂ types (and hence RO₂+RO₂ rate constants).

Accordingly, we focus on the atmospheric relevance of RO₂+OH and RO₂ isomerization, i.e., their relative contributions close to ambient values. Under typical high-NO conditions, RO₂+NO dominates RO₂ fate and RO₂+OH is negligible. High NO also shortens the RO₂ lifetime enough to effectively inhibit RO₂ isomerization. Both the dominance of RO₂+NO and the inhibition of RO₂ isomerization also occur in the atmosphere and in chambers, so high-NO OFR operation (typically NO > 10 ppb) represents these pathways realistically. Some care is, however, required with the RO₂+OH and RO₂ isomerization pathways at low NO. Since RO₂+HO₂ in OFRs is always a major RO₂ fate at low NO and RO₂+RO₂ is generally not problematic, RO₂+OH and RO₂+HO₂ can be kept atmospherically relevant as long as the HO₂-to-OH ratio is close to 100 (the ambient average). In addition, the RO₂ lifetime (calculated without RO₂ isomerization taken into account) should be at least around 10 s.

Practically, OH production should be limited to achieve this goal. Too-strong OH production at high H₂O and UV can elevate OH and HO₂ concentrations, which shortens RO₂ lifetime and decreases the HO₂-to-OH ratio to ∼ 1 (see Sect. 3.2.1). OH production is roughly proportional to both H₂O and UV (Peng et al., 2015), so it can be limited by reducing either or both. However, H₂O and UV have different effects on non-tropospheric organic photolysis. At a certain OHR_ext, the OH production rate roughly determines the OH concentration in OFRs. Reducing UV decreases both OH and UV roughly proportionally (Peng et al., 2015), and hence changes in F185_exp ∕ OH_exp and F254_exp ∕ OH_exp are small (Peng et al., 2016); i.e., non-tropospheric organic photolysis does not become significantly worse if UV is reduced. By contrast, if H₂O is reduced without also decreasing UV, F185_exp ∕ OH_exp and F254_exp ∕ OH_exp both increase, signifying a stronger relative importance of non-tropospheric photolysis. Therefore, reducing UV is strongly preferred as an OH production limitation method and is effective in making both RO₂+OH and RO₂ isomerization more atmospherically relevant.

To further explore the effects of UV reduction on the RO₂+OH (Fig. 5) and RO₂ isomerization (Fig. 6) pathways, we divide our OFR case distributions into higher UV and lower UV classes, with the boundary being the midlevel (in logarithmic scale) UV in the explored range. The distributions for lower UV conditions (solid lines in Figs. 5 and 6) are clearly closer to the ambient cases (i.e., HO₂-to-OH ratio closer to 100, smaller RO₂+OH relative importance and longer RO₂ lifetime).

Since OFR254 is unable to achieve both conditions with at least some experimental interest (i.e., with sufficiently low non-tropospheric photolysis) and an atmospherically relevant RO₂ lifetime, we now discuss preferable conditions for OFR185 only. As F185 close to or lower than 10¹² photons cm⁻² s⁻¹ is needed for the RO₂ lifetime to be around 10 s or longer (Fig. S11), the OH concentration under preferable conditions for atmospherically relevant RO₂ chemistry (∼ 10⁹ molecules cm⁻³ or lower) is much lower than the maximum that OFR185 can physically reach (∼ 10¹⁰–10¹¹ molecules cm⁻³). Furthermore, lower OH production leads to higher susceptibility to OH suppression by external OH reactants (Peng et al., 2015), which can create non-tropospheric photolysis problems (Peng et al., 2016). We thus recommend H₂O as high as possible to maintain practically high OH while allowing lower UV to limit the importance of non-tropospheric organic photolysis.

Figure 7 (a) RO₂ lifetime in the absence of isomerization, (b) relative importance of RO₂+OH in RO₂ fate, and (c) logarithm of the exposure ratio between 254 nm photon flux and OH as a function of 185 nm photon flux and external OH reactivity for OFR185 at N₂O =0 and H₂O =2.3 %. Three lines denoting conditions leading to OH of 3.16×10⁸, 1×10⁹ and 3.16×10⁹ molecules cm⁻³ are added in each panel. The thick and thin parts of these lines correspond to good and risky conditions (in terms of 254 nm organic photolysis, which is usually worse than 185 nm organic photolysis; Peng et al., 2016), respectively.

The performance of various OFR185 conditions at high H₂O (2.3 %) is illustrated in Fig. 7 as a function of F185 and OHR_ext. The three criteria for the performance, i.e., RO₂ lifetime (calculated without RO₂ isomerization considered), relative importance of RO₂+OH and log(F254_exp ∕ OH_exp) (a measure of 254 nm non-tropospheric photolysis, which is usually worse than that at 185 nm; Peng et al., 2016), are shown. At F185 of ∼ 10¹¹–10¹² photons cm⁻² s⁻¹ and OHR_ext around or lower than 10 s⁻¹, all three criteria are satisfied. Since UV (and hence OH production) is relatively low, a low OHR_ext (∼ 10 s⁻¹) is required to avoid heavy OH suppression and keep conditions good (green area in Fig. 7c). Nevertheless, risky conditions (log(F254_exp ∕ OH_exp) < 7; light red area in Fig. 7c) may also bear some experimental conditions depending on the type of VOC precursors (specifically on their reactivity toward OH, their photolability at 185 and 254 nm, and the same quantities for their oxidation intermediates; Peng et al., 2016; Peng and Jimenez, 2017). Thus, higher OHR_ext (up to ∼ 100 s⁻¹) may also be considered in OFR experiments with some precursors (e.g., alkanes). In practice, the preferred conditions may require F185 even lower than that our lowest simulated lamp setting (Li et al., 2015). Such a low F185 may be realized, e.g., by partially blocking 185 nm photons using nontransparent lamp sleeves with evenly placed holes that allow for some 185 nm transmission.

Under these preferred conditions, OH concentration in OFR185 is ∼ 10⁹ molecules cm⁻³, equivalent to a photochemical age of ∼ 1 eq. days for a typical residence time of 180 s. This is much shorter than ages corresponding to the maximal oxidation capacity of OFRs (usually eq. weeks or months; Peng et al., 2015), but it is similar to the ages of the maximal organic aerosol formation in OFRs processing ambient air (Tkacik et al., 2014; Ortega et al., 2016; Palm et al., 2016). We show the maximal SOA formation case in the OFR185 experiments in the BEACHON-RoMBAS campaign in the Rocky Mountains (Palm et al., 2016) as an example (Figs. 5 and 6). During the campaign, relative humidity was high (> 60 % in most of the period), OHR_ext was estimated to be relatively low (∼ 15 s⁻¹) in this forested area and UV in the OFR was limited in the case of the maximal SOA formation age (∼ 0.7 eq. days). All these physical conditions were favorable for atmospherically relevant RO₂ fate (Figs. 5 and 6). RO₂+OH was minor in this case and the relative importance of RO₂ isomerization in RO₂ fate in the OFR was within a factor of ∼ 2 of that in the atmosphere for all RO₂ (regardless of the isomerization rate constant) during the BEACHON-RoMBAS campaign (Fig. 6). The effect of UV on the relative importance of RO₂ isomerization for this example is also illustrated in Fig. 6. In the sensitivity case with a lower age, lower UV results in a larger contribution of isomerization to RO₂ fate, while the relative importance of RO₂ isomerization is lower in a sensitivity case with an age 3 times that of the maximal SOA formation. In an extreme sensitivity case with the highest UV in the range of this study (with an age of 4 eq. months), RO₂ isomerization becomes minor or negligible for all RO₂ except extremely rapidly isomerizing ones.

The discussions above indicate that the atmospheric relevance of gas-phase RO₂ chemistry in OFRs deteriorates as the photochemical age over the whole residence time (180 s) increases. To reach longer ages, longer residence times (with UV still being low) can be adopted. However, OFR residence times > 10 min tend to be limited by the increasing importance of wall losses (Palm et al., 2016). As a result, longer residence times can only increase photochemical age in OFRs up to about a week. This implies that in OFR cases with ages much higher than that of maximal SOA formation (corresponding to the heterogeneous oxidation stage of SOA), the atmospheric relevance of gas-phase RO₂ chemistry in the SOA formation stage (before the age of maximal SOA formation) often cannot be ensured. However, under those conditions new SOA formation is typically not observed, and the dominant process affecting OA is heterogeneous oxidation of the preexisting OA (Palm et al., 2016). If the heterogeneous oxidation of newly formed SOA is of interest, a two-stage solution may be required. Lower UV can be used in the SOA formation stage to keep the atmospheric relevance of the gas-phase chemistry, while high UV can be used in the heterogeneous aging stage to reach a high equivalent age. The latter approach is viable since heterogeneous oxidation of SOA by OH is slow and particle-phase chemistry is not strongly affected by gas-phase species except OH when OH is very high (Richards-Henderson et al., 2015, 2016; Hu et al., 2016). This two-stage solution may be realized through a cascade-OFR system or UV sources at different intensities within an OFR (e.g., spliced lamps).

Praske et al. (2018) measured RO₂ isomerization rate constants at 296 and 318 K and observed an increase in the rate constants by a factor of ∼ 5 on average. A 15 K temperature increase in OFRs would lead to RO₂ isomerization being accelerated by a factor of ∼ 3, while other major gas-phase radical reactions have weak or no temperature dependence (e.g., ∼ 7 %, ∼ 5 %, ∼ 6 % and ∼ 19 % slowdowns for isoprene+OH, toluene + OH, typical RO₂+NO and RO₂+HO₂, respectively; Atkinson and Arey, 2003; Ziemann and Atkinson, 2012). As a consequence, the relative importance of RO₂ isomerization in RO₂ fate in OFRs can be elevated and closer to atmospheric values (Fig. 6). Nevertheless, a 15 K increase in temperature may also result in some OA evaporation (Huffman et al., 2009; Nault et al., 2018). Besides, the reduction of acylperoxy nitrate formation in OFRs, which may be useful to mimic some urban environments where NO plays a larger role in acyl RO₂ fate (see Sect. 3.1.2), is unlikely to be achieved by increasing OFR temperature. The O–N bond energy of acylperoxy nitrates is ∼ 28 kcal mol⁻¹ (Orlando and Tyndall, 2012), which can be taken as an approximate reaction energy of their decomposition. Then a 20 K temperature increase results in the equilibrium constant of acyl ${\mathrm{RO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{2}}\leftrightarrow$ acyl RO₂NO₂ being shifted toward RO₂+NO₂ by a factor of ∼ 20. However, this shift is still too small relative to the equilibrium constant itself. It can be deduced by a simple calculation that for the generic acyl RO₂ in this study in an OFR at 318 K (20 K higher than room temperature) with NO₂ of 10¹² molecules cm⁻³ (a relatively low level in typical OFR-iN₂O experiments; Peng et al., 2018), ∼ 0.1 % of the total amount of acyl RO₂+ acyl RO₂NO₂ will be present in the form of acyl RO₂. Even if acylperoxy nitrate decomposition is 20 times faster than at room temperature and the formed acyl RO₂ can irreversibly react with NO and decrease the acylperoxy nitrate concentration, this effect is small: typically up to an approximate 20 % decrease in acylperoxy nitrate and usually negligible changes in NO and NO₂. The minor effect is due to (i) an acylperoxy concentration that is still very low, (ii) an NO concentration that is much lower than NO₂ and (iii) an acylperoxy nitrate decomposition lifetime that is still of the order of minutes.

As discussed above, high H₂O, low UV and low OHR_ext are recommended for keeping the atmospheric relevance of RO₂ chemistry in OFRs. These three requirements are also part of the requirements for attaining good high-NO conditions in OFR185-iNO (the OFR185 mode with initial NO injection; Peng and Jimenez, 2017). In addition to these three, an initial NO of several tens of ppb is also needed to obtain a good high-NO condition in OFR185-iNO. Under these conditions, RO₂+NO dominates over RO₂+HO₂ and hence RO₂+OH; UV is low, the photochemical age is typically ∼ 1 eq. days and the RO₂ lifetime can be a few seconds. Therefore, these conditions are a good fit for studying the environments in relatively clean urban areas, such as Los Angeles during CalNex-LA (Ortega et al., 2016), where NO is high enough that the dominant bimolecular fate of RO₂ is RO₂+NO but low enough to maintain RO₂ lifetimes that allow for the most common RO₂ isomerizations.

As RO₂ fate in OFRs is a highly complex problem and it can be tricky to find suitable physical conditions to simultaneously achieve experimental goals and keep the atmospheric relevance of the chemistry in OFRs, we provide here an OFR RO₂ Fate Estimator (in the Supplement) to qualitatively aid experimental planning. The OFR RO₂ Fate Estimator couples the OFR Exposure Estimator (Peng et al., 2016, 2018) to a general RO₂ fate estimator (also in the Supplement; see Fig. S12 for a screenshot of its layout). The OFR Exposure Estimator updated in this study also contains estimation equations for the HO₂-to-OH ratio in OFR185 (in OFR254, RO₂ fate is always atmospherically irrelevant at low NO, while at high NO, RO₂+NO dominates and a detailed RO₂ fate analysis is no longer needed). In the general RO₂ fate estimator, all RO₂ reactant concentrations and all RO₂ loss pathway rate constants can be specified. Thus, the general RO₂ fate estimator can also be applied to the atmosphere and chamber experiments, in addition to OFRs. When applied to OFRs, the general RO₂ fate estimator is provided by the OFR RO₂ Fate Estimator with quantities estimated in the OFR Exposure Estimator (e.g., OH and NO). RO₂ concentration and fate are calculated according to Appendix B in the RO₂ fate estimators.

4 Conclusions

We investigated RO₂ chemistry in OFRs with an emphasis on its atmospheric relevance. All potentially major loss pathways of RO₂, i.e., reactions of RO₂ with HO₂, NO and OH, of acyl RO₂ with NO₂, and self- and cross-reactions of RO₂ and RO₂ isomerization, were studied and their relative importances in RO₂ fate were compared to those in the atmosphere and chamber experiments. OFRs were shown to be able to tune the relative importance of RO₂+HO₂ vs. RO₂+NO by injecting different amounts of N₂O. For many RO₂ types (including all unsubstituted non-acyl RO₂ and substituted secondary and tertiary RO₂), their self-reactions and the cross-reaction between them are minor or negligible in the atmosphere and chambers. This is also the case in OFR185 (including OFR185-iN₂O) and OFR254-iN₂O; however, those RO₂ self- and cross-reactions can be important at high precursor concentrations (OHR_ext> 100 s⁻¹) in OFR254. For substituted primary RO₂ and acyl RO₂, their self- and cross-reactions (including the ones with RO₂ whose self-reaction rate constants are slower) can play an important role in RO₂ fate in the atmosphere and chambers and may also be major RO₂ loss pathways in OFRs, although they are somewhat less important in OFRs than in the atmosphere. Acylperoxy nitrates are the dominant sink of acyl RO₂ at high NO_x in OFRs (particularly in OFR254-iN₂O for which RO₂+NO is negligible for acylperoxy loss), while there is only a minor reservoir of acyl RO₂ in the atmosphere under most conditions except in urban atmospheres, where RO₂+NO and RO₂+NO₂ can both be the dominant acylperoxy loss pathway depending on conditions. In chambers, most acyl RO₂ can be stored in the form of acylperoxy nitrates if NO₂ is very high (hundreds of ppb to ppm level).

Besides the abovementioned well-known pathways, RO₂+OH and RO₂ isomerization may also play an important role in RO₂ fate and sometimes results in atmospherically irrelevant RO₂ chemistry in OFRs. Here we summarize the main findings about all the pathways and the related guidelines for OFR operation.

• Under typical high-NO conditions, RO₂+NO dominates RO₂ fate and the RO₂ lifetime is too short to allow for most RO₂ isomerizations, regardless of whether in the atmosphere, chambers or OFRs, thus raising no concern about the atmospheric relevance of the OFR RO₂ chemistry.

• Under low-NO conditions, OFR254 cannot yield any physical conditions leading to a sufficiently long RO₂ lifetime for its isomerization because of the high radical levels and their resilience to external perturbations in OFR254.

• In OFR185 with strong OH production (and hence high OH), RO₂+OH and RO₂ isomerization may strongly deviate from that in the atmosphere (becoming important and negligible, respectively, for relatively rapidly isomerizing RO₂; rate constants of the order of 0.1 s⁻¹).

• To attain both atmospherically relevant VOC and RO₂ chemistries, OFR185 requires high H₂O, low UV and low OHR_ext. These conditions ensure minor or negligible RO₂+OH and a relative importance of RO₂ isomerization in RO₂ fate in OFRs within a factor of ∼ 2 of that in the atmosphere.

• Under conditions allowing both VOC and RO₂ chemistries to be atmospherically relevant, the maximal photochemical age that can be reached is limited to a few eq. days. This age roughly covers the period required for maximum SOA formation in ambient air.

• To most realistically study much higher ages for SOA functionalization and fragmentation by heterogeneous oxidation, a sequence of low-UV SOA formation followed by a high UV condition (in the same reactor or in cascade reactors) may be needed.

• High H₂O, low UV and low OHR_ext in the OFR185-iNO mode can achieve conditions relevant to clean urban atmosphere, i.e., high NO but not sufficiently high to inhibit common RO₂ isomerization.

Finally, RO₂ chemistry is not only highly complex but also plays a central and instrumental role in atmospheric chemistry, in particular VOC oxidation and SOA formation. For all experiments conducted with an atmospheric chemistry simulation apparatus (chamber, flow reactor, etc.), an atmospherically relevant RO₂ chemistry is crucial to meaningful experimental results. However, most literature studies have not published experimental data that are sufficient for estimating RO₂ fate. The FIXCIT chamber experiment campaign is one of the few exceptions for which comprehensive data were reported (Nguyen et al., 2014) and used for the RO₂ fate analysis in the present work. We recommend measuring and/or estimating and reporting OH, HO₂, NO, NO₂ and OHR_VOC (or initial precursor composition at least) whenever possible for all future atmospheric laboratory and field experiments for organic oxidation to facilitate the analysis of RO₂ fate and the evaluation of its atmospheric relevance.

Appendix A: Glossary of the acronyms (except field campaign names) used in the paper.

OFR	oxidation flow reactor
VOC	volatile organic compound
SOA	secondary organic aerosol
H2O	water vapor mixing ratio
OHRext	external OH reactivity (due to CO, SO2, VOCs, etc.)
PAM	potential aerosol mass, a specific type of OFR
OFR185	oxidation flow reactor using both 185 and 254 nm light
OFR254	oxidation flow reactor using 254 nm light only
OFR254-X	OFR254 with X ppm O3 initially injected
OFR-iN2O	OFR with N2O initially injected
OFR185-iN2O	OFR185 with N2O initially injected
OFR254-iN2O	OFR254 with N2O initially injected
OFR254-X-iN2O	OFR254-X with N2O initially injected
OHRVOC	OH reactivity due to VOCs
F185, F254, etc.	UV photon flux at 185 nm, 254 nm, etc.
N2O	N2O mixing ratio
OHexp, F185exp, etc.	exposure (integral over time) to OH, F185, etc.

Steady-state approximation for generic RO₂

The production rate of a generic RO₂ is almost identical to the VOC consumption rate, since the second step of the conversion chain VOC $\to \mathrm{R}\to {\mathrm{RO}}_{\mathrm{2}}$ is extremely fast. Therefore, the generic RO₂ production rate, P, can be expressed as follows:

$$\begin{array}{}\text{(B1)}& P={\sum }_i{k}_i{c}_i\cdot \mathrm{OH}={\mathrm{OHR}}_{\mathrm{VOC}}\cdot \mathrm{OH},\end{array}$$

where OH is OH concentration and c_i and k_i are respectively the concentration and the reaction rate constant with OH of the ith VOC. OHR_VOC is the total OHR due to VOC and equal to Σ_ik_ic_i by definition.

For the generic RO₂ loss rate, the reactions of RO₂ with HO₂, NO, RO₂, NO₂ (for acyl RO₂ only) and OH are considered. Isomerization generally does not lead to a total RO₂ concentration decrease and is thus not included in its loss rate. Then the RO₂ loss rate is

$$\begin{array}{ll}{\displaystyle }& {\displaystyle }L=k_{{\mathrm{HO}}_{\mathrm{2}}}{\mathrm{RO}}_{\mathrm{2}}\cdot {\mathrm{HO}}_{\mathrm{2}}+k_{\mathrm{NO}}{\mathrm{RO}}_{\mathrm{2}}\cdot \mathrm{NO}+\mathrm{2}{k}_{{\mathrm{RO}}_{\mathrm{2}}}{\mathrm{RO}}_{\mathrm{2}}\cdot {\mathrm{RO}}_{\mathrm{2}}\\ \text{(B2)}& {\displaystyle }& {\displaystyle }+k_{{\mathrm{NO}}_{\mathrm{2}}}{\mathrm{RO}}_{\mathrm{2}}\cdot {\mathrm{NO}}_{\mathrm{2}}+k_{\mathrm{OH}}{\mathrm{RO}}_{\mathrm{2}}\cdot \mathrm{OH},\end{array}$$

where RO₂, HO₂, NO, NO₂ and OH are the concentrations of corresponding species and k_A (A= RO₂, HO₂, NO, NO₂ and OH) is the reaction rate constant of RO₂ with A. For non-acyl RO₂, the term $k_{{\mathrm{NO}}_{\mathrm{2}}}{\mathrm{RO}}_{\mathrm{2}}\cdot {\mathrm{NO}}_{\mathrm{2}}$ is not included; for cases with well-known pathways only (RO₂+HO₂, RO₂+RO₂, RO₂+NO and RO₂+NO₂; see Sect. 3.1), the term k_OHRO₂⋅OH is excluded. $k_{{\mathrm{RO}}_{\mathrm{2}}}$ needs to be given a value (which may be the main levels of RO₂ self- and cross-reaction rate constants in this study, $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{13}}$ and $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molecule⁻¹ s⁻¹, or other values depending on the RO₂ type).

At the steady state, P and L are equal. For an ambient and/or chamber setting, OH, HO₂, NO, NO₂ and OHR_VOC are often measured or known. In this case, simultaneously considering Eqs. (B1) and (B2) yields a quadratic equation of RO₂ concentration (the only unknown). Then the generic RO₂ concentration can be easily obtained by solving this equation:

$$\begin{array}{}\text{(B3)}& {\displaystyle }{\mathrm{RO}}_{\mathrm{2}}=\left(-K+\sqrt{K^{\mathrm{2}}+\mathrm{8}{k}_{{\mathrm{RO}}_{\mathrm{2}}}\cdot {\mathrm{OHR}}_{\mathrm{VOC}}\cdot \mathrm{OH}}\right)/\left(\mathrm{4}{k}_{{\mathrm{RO}}_{\mathrm{2}}}\right)\end{array}$$

where $K=k_{{\mathrm{HO}}_{\mathrm{2}}}{\mathrm{HO}}_{\mathrm{2}}+k_{\mathrm{NO}}\mathrm{NO}+k_{{\mathrm{NO}}_{\mathrm{2}}}{\mathrm{NO}}_{\mathrm{2}}+k_{\mathrm{OH}}\mathrm{OH}$.