Modeling of the chemistry in oxidation flow reactors with high initial NO

Oxidation flow reactors (OFRs) are increasingly employed in atmospheric chemistry research because of their high efficiency of OH radical production from low-pressure Hg lamp emissions at both 185 and 254 nm (OFR185) or 254 nm only (OFR254). OFRs have been thought to be limited to studying low-NO chemistry (in which peroxy radicals (RO2) react preferentially with HO2) because NO is very rapidly oxidized by the high concentrations of O3, HO2, and OH in OFRs. However, many groups are performing experiments by aging combustion exhaust with high NO levels or adding NO in the hopes of simulating high-NO chemistry (in which RO2+NO dominates). This work systematically explores the chemistry in OFRs with high initial NO. Using box modeling, we investigate the interconversion of Ncontaining species and the uncertainties due to kinetic parameters. Simple initial injection of NO in OFR185 can result in more RO2 reacted with NO than with HO2 and minor non-tropospheric photolysis, but only under a very narrow set of conditions (high water mixing ratio, low UV intensity, low external OH reactivity (OHRext), and initial NO concentration (NOin) of tens to hundreds of ppb) that account for a very small fraction of the input parameter space. These conditions are generally far away from experimental conditions of published OFR studies with high initial NO. In particular, studies of aerosol formation from vehicle emissions in OFRs often used OHRext and NOin several orders of magnitude higher. Due to extremely high OHRext and NOin, some studies may have resulted in substantial non-tropospheric photolysis, strong delay to RO2 chemistry due to peroxynitrate formation, VOC reactions with NO3 dominating over those with OH, and faster reactions of OH–aromatic adducts with NO2 than those with O2, all of which are irrelevant to ambient VOC photooxidation chemistry. Some of the negative effects are the worst for alkene and aromatic precursors. To avoid undesired chemistry, vehicle emissions generally need to be diluted by a factor of > 100 before being injected into an OFR. However, sufficiently diluted vehicle emissions generally do not lead to high-NO chemistry in OFRs but are rather dominated by the low-NO RO2+HO2 pathway. To ensure high-NO conditions without substantial atmospherically irrelevant chemistry in a more controlled fashion, new techniques are needed.


Introduction
The oxidation of gases that are emitted into the atmosphere, in particular volatile organic compounds (VOCs), is one of the most important atmospheric chemistry processes (Haagen-Smit, 1952;Chameides et al., 1988). VOC oxidation is closely related to radical production and consumption (Levy II, 1971), O 3 production, and the formation of secondary aerosols (Odum et al., 1996;Hoffmann et al., 1997;Volkamer et al., 2006;Hallquist et al., 2009), which have impacts on air quality and climate (Lippmann, 1991;Nel, 2005;Stocker et al., 2014).
Chemical reactors are critical tools for research of VOC oxidation. Oxidation reactions of interest often have typical timescales of hours to weeks. Studying these processes in ambient air can be confounded by dispersion and changes in ambient conditions, which often occur on similar timescales. Chemical reactors allow for the decoupling of these two types of processes. Also, they should be able to simulate the different regimes of reactions occurring in the atmosphere, e.g., VOC oxidation under the low-and high-NO conditions (peroxy radical fate dominated by reaction with HO 2 or NO) representing remote and urban areas, respectively (Orlando and Tyndall, 2012).
Large environmental chambers are a commonly used reactor type (Carter et al., 2005;Wang et al., 2011). They typically employ actinic wavelength (> 300 nm) light sources (e.g., outdoor solar radiation and UV black lights) to produce oxidants and radicals and have large volumes (on the order of several cubic meters or larger). However, the capability of generating sustained elevated levels of OH, the most important tropospheric oxidant, is usually limited in chambers, resulting in OH concentrations similar to those in the atmosphere (10 6 -10 7 molecules cm −3 ; Mao et al., 2009;Ng et al., 2010) and consequently long simulation times (typically hours) to reach OH equivalent ages of atmospheric relevance (George et al., 2007;Kang et al., 2007;Carlton et al., 2009;Seakins, 2010;Wang et al., 2011). The partitioning of gases and aerosols to chamber walls (usually made of Teflon) in timescales of tens of minutes to hours makes it difficult to conduct very long experiments that simulate high atmospherically relevant photochemical ages (Cocker et al., 2001;Matsunaga and Ziemann, 2010;Zhang et al., 2014;. In addition, the long simulation times and large size of chambers and auxiliary equipment are logistically difficult for field deployment, and their cost limits the number of laboratories equipped with them. Given the limitations of environmental chambers, a growing number of experimenters have instead employed oxidation flow reactors (OFRs). OFRs have a much smaller size (on the order of 10 L), efficiently generate OH via photolysis of H 2 O and/or O 3 by more energetic 185 and 254 nm photons from low-pressure Hg lamps, and overcome the abovementioned shortcomings of chambers due to a much shorter residence time (George et al., 2007;Kang et al., 2007Kang et al., , 2011Lambe et al., 2011). Moreover, OFRs are able to rapidly explore a wide range of OH equivalent ages within a short period (∼ 2 h) during which significant changes in ambient conditions can usually be avoided in the case of field deployment Palm et al., 2016Palm et al., , 2017. Because of these advantages, OFRs have recently been widely used to study atmospheric chemistry, in particular secondary organic aerosol (SOA) formation and aging, in both the laboratory and the field (Kang et al., 2011;Li et al., 2013;Ortega et al., 2013Tkacik et al., 2014;Palm et al., 2016).
In addition to experimental studies using OFRs, there has also been some progress in the characterization of OFR chemistry by modeling. Li et al. (2015) and Peng et al. (2015) developed a box model for OFR HO x chemistry that predicts measurable quantities (e.g., OH exposure, OH exp , in molecules cm −3 s and O 3 concentration, abbr. O 3 hereinafter, in ppm) in good agreement with experiments. This model has been used to characterize HO x chemistry as a function of H 2 O mixing ratio (abbr. H 2 O hereinafter, unitless), UV light intensity (abbr. UV hereinafter, in photons cm −2 s −1 ), and external OH reactivity (in s −1 , OHR ext = , k i c i , i.e., the sum of the products of concentrations of externally introduced OH-consuming species, c i , and rate constants of their reactions with OH, k i ). Based on this characterization, Peng et al. (2015) found that OH suppression, i.e., the reduction of OH concentration caused by OHR ext , is a common feature under many typical OFR operation conditions.  systematically examined the relative importance of non-OH (including non-tropospheric) reactants in the fate of VOCs over a wide range of conditions and provided guidelines for OFR operation to avoid non-tropospheric VOC photolysis, i.e., VOC photolysis at 185 and 254 nm.
In previous OFR modeling studies, NO x chemistry was not investigated in detail since in such in typical OFR experiments with large amounts of oxidants (e.g., OH, HO 2 , and O 3 ) NO would be very rapidly oxidized and thus unable to compete with HO 2 for reaction with peroxy radicals (RO 2 ). Li et al. (2015) estimated an NO (NO 2 ) lifetime of ∼ 0.5 (∼ 1.5) s under a typical OFR condition. From these estimates, OFRs processing ambient air or laboratory air without a large addition of NO x were assumed to not be suitable for studying oxidation mechanisms relevant to polluted conditions under higher NO concentrations. OFRs have recently been used to conduct laboratory experiments with very high initial NO x levels (Liu et al., 2015) and deployed to an urban tunnel where NO x was high enough to be a major OH reactant (Tkacik et al., 2014). The former study reported evidence for the incorporation of nitrogen into SOA. OFRs have also been increasingly employed to process emissions of vehicles, biomass burning, and other combustion sources (Table 1) in which NO can often be hundreds of ppm Martinsson et al., 2015;Karjalainen et al., 2016;Link et al., 2016;Schill et al., 2016;Alanen et al., 2017;Simonen et al., 2017). It can be expected that such a high NO input together with very high VOC concentrations would cause a substantial deviation from the good OFR operation conditions identified in Peng et al. (2016). Very recently, N 2 O injection has been proposed by  as a way to study the oxidation of VOCs under high NO conditions in an OFR. As more OFR studies at high NO x levels are conducted, there is a growing need to understand the chemistry of N-containing species in OFRs and whether it proceeds along atmospherically relevant channels.
In this study, we present the first comprehensive model of OFR NO y chemistry. We extend the model of Li et al. (2015) and Peng et al. (2015) by including a scheme for NO y species. Then this model is used to investigate (i) whether an OFR with initial NO injection results in NO significantly reacting with RO 2 under any conditions, (ii) whether previously published OFR experiments with high initial NO concentrations led to RO 2 +NO being dominant in VOC oxidation without negative side effects (e.g., non-tropospheric reactions), and iii) how to avoid undesired chemistry in future studies. The results can provide insights into the design and interpretation of future OH-oxidation OFR experiments with large amounts of NO x injection.

Methods
The physical design of the OFR modeled in the present work, the chemical kinetics box model, and the method of propagating and analyzing the parametric uncertainties on the model have already been introduced previously (Kang et al., 2007;Li et al., 2015;Peng et al., 2015). We only provide brief descriptions for them below.

Potential aerosol mass flow reactor
The OFR modeled in this study is the potential aerosol mass (PAM) flow reactor first introduced by Kang et al. (2007)  , we adopt the notation OFR254-X to denote OFR254 experiments with X ppm initial O 3 (O 3,in ). In this study, we investigate OFR experiments with NO injected and thus utilize "OFR185-iNO" to describe the OFR185 mode of operation with initially (at the reactor entrance) injected NO.
The same terminology is used for the OFR254 mode. For instance, the initial NO injection into OFR254-7 is denoted as OFR254-7-iNO.

Model description
The basic framework of the box model used in this study, a standard chemical kinetics model, is the same as in Peng et al. (2015). Plug flow is assumed in the model, since approximately taking residence time distribution into account leads to similar results under most conditions but at much higher computational expense . In addition to the reactions in the model of Peng et al. (2015) including all HO x reactions available in the JPL Chemical Kinetic Data Evaluation (Sander et al., 2011), all gas-phase NO y reactions available in the JPL database except those of organic nitrates and peroxynitrates are also considered in the current reaction scheme. An updated JPL evaluation was published recently (Burkholder et al., 2015) with slightly different (∼ 20 %) rate constants for NO 2 + HO 2 + M → HO 2 NO 2 + M and NO 2 + NO 3 → N 2 O 5 . The updated rate constants only result in changes of ∼ 10-20 % in the concentrations of the species directly consumed or produced by these reactions. These changes are smaller than the parametric uncertainties of the model (see Sect. 3.1.3). For other species, concentration changes are negligible. HO 2 NO 2 + M → HO 2 + NO 2 + M and N 2 O 5 + M → NO 2 + NO 3 + M, are also included in the scheme with kinetic parameters from the IUPAC Task Group on Atmospheric Chemical Kinetic Data Evaluation (Ammann et al., 2016). As in Peng et al. (2015Peng et al. ( , 2016, SO 2 is used as a surrogate for external OH reactants (e.g., VOCs). NO y species, although also external OH reactants, are explicitly treated in the model and not counted in OHR ext in this work. Therefore, OHR ext stands for non-NO y OHR ext only hereinafter unless otherwise stated. Also, particle-phase chemistry and physical and chemical interactions of gas-phase species with particles are not considered in this study. We have made this assumption because of the following.

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Z. Peng and J. L. Jimenez: Modeling of the chemistry in oxidation flow reactors with high initial NO i. The presence of aerosols has typically negligible impacts on the gas-phase chemistry of radicals, NO y , and the OH reactants studied here. The condensational sink (CS) of ambient aerosols can rarely exceed 1 s −1 even in polluted areas and is usually 1-3 orders of magnitude lower (Donahue et al., 2016;Palm et al., 2016). Thus, even under the assumption of unity uptake coefficient, CS cannot compete with OHR ext (usually on the order of 10 s −1 or higher) in OH loss. Uptake of NO onto aerosols only occurs through the reaction with RO 2 on the particle surface (Richards-Henderson et al., 2015), which is formed very slowly (see below) compared to gas-phase HO x and NO x chemistry. Uptake of HO 2 , O 3 , NO 3 , etc. is even more unlikely to be of importance due to lower uptake coefficients Hearn and Smith, 2004;Lakey et al., 2015). Combustion exhausts can have high aerosol loadings with condensational sinks on the order of 10 2 -10 3 s −1 (Matti Maricq, 2007). Even if these exhausts are directly injected into the reactor without any pretreatment, uptake onto the particles still cannot play a major role in the fate of gas-phase radical and NO x species since VOCs and NO x in raw exhausts, which are proportionally orders of magnitude higher, still dominate the fate of oxidants. Dilution of combustion emissions simultaneously lowers condensational sinks and the sinks of oxidants due to chemical reactions with their relative importance remaining the same as in undiluted emissions.
ii. Gas-phase radical and NO y species only has limited impacts on OA chemistry in this study. The heterogeneous oxidation of OA by OH is generally slow. Significant OA loss due to heterogeneous oxidation can only be seen at photochemical ages as high as weeks . The enhancement of heterogeneous oxidation due to NO is remarkable only at OH concentrations close to the ambient values but not at typical values in an OFR (Richards-Henderson et al., 2015).
It is well known that the aerosol concentration can have a major impact on the physical uptake of semivolatile and lowvolatility gas-phase species. However, this process is not explicitly modeled in this study.
As OHR ext plays a major and even dominant role in OH loss, it is an important approximation that the real OHR ext decay (due to primary VOC oxidation and subsequent oxidation of higher-generation products) is surrogated by that of SO 2 (see Fig. S2 of Peng et al., 2015). Gas-phase measurements in the literature on laboratory studies revealed that there is large variability in the evolution of total OHR ext during the oxidation of primary VOCs and subsequent oxidation of their intermediate products depending on the type of precursors (Nehr et al., 2014;Schwantes et al., 2017). This variability is clearly mainly due to the formation of different types and amounts of oxidation intermediates and products contributing to OHR ext . This variation is highly complex due to the large number of possible oxidation intermediates and the limited knowledge of detailed higher-generation mechanisms, and thus it is difficult to accurately capture even if modeling with a mechanism as explicit as the Master Chemical Mechanism (Schwantes et al., 2017). Therefore, it is justified to use a lumped surrogate to model the OHR ext decay for simplicity and efficiency. This approximation is a substantial contributor to the uncertainty in our model. The uncertainties due to the types of oxidation intermediates and products are very likely larger than those due to mass transfer processes between gas and particle phases, wall losses, etc., which are not considered in this study.
A residence time of 180 s and the typical temperature (295 K) and atmospheric pressure (835 mbar) in Boulder, CO, USA are assumed for all model cases. The lower-thansea-level pressure only leads to minor differences in the outputs . We explore physical input cases evenly spaced in a logarithmic scale over very wide ranges: H 2 O of 0.07-2.3 %, i.e., relative humidity (RH) of 2-71 % at 295 K; 185 nm UV of 1.0 × 10 11 -1.0 × 10 14 and 254 nm UV of 4.2 × 10 13 -8.5 × 10 15 photons cm −2 s −1 ; OHR ext of 1-16000 s −1 ; O 3,in of 2.2-70 ppm for OFR254; and initial NO mixing ratio (NO in ) from 10 ppt to 40 ppm. Conditions with OHR ext = 0 are also explored. UV at 254 nm is estimated from that at 185 nm according to the relationship determined by Li et al. (2015). Several typical cases within this range and their corresponding four-or two-character labels (e.g., MM0V and HL) are defined in Table 2. Literature studies are modeled by adopting all reported parameters (e.g., residence time, H 2 O, and O 3,in ) and estimating any others that may be needed (e.g., UV) from the information provided in the papers.
In this study, OH equivalent ages are calculated under the assumption of an ambient OH concentration of 1.5 × 10 6 molecules cm −3 (Mao et al., 2009). Conditions leading to a ratio of RO 2 reacted with NO over the entire residence time [r(RO 2 + NO)] to that with HO 2 [r(RO 2 + HO 2 )] larger than 1 are regarded as "high NO" (under the assumption of constant OHR ext from VOCs; see Sect. S1 for more details), where [r(X)] is the total reactive flux for reaction X over the entire residence time. F185 exp /OH exp and F254 exp /OH exp are used as measures of the relative importance of VOC photolysis at 185 and 254 nm to their reactions with OH, respectively; F185 exp (F254 exp ) are 185 (254) nm photon flux exposure, i.e., the product of 185 (254) nm photon flux and time. Readers may refer to Figs. 1 and 2 of Peng et al. (2016) for the determination of the relative importance of nontropospheric (185 and 254 nm) photolysis of individual VOCs. Although the relative importance of non-tropospheric photolysis depends on individual VOCs, in the present work, we set criteria on F185 exp /OH exp < 3 × 10 3 cm s −1 and F254 exp /OH exp < 4 × 10 5 cm s −1 to define "good" conditions and F185 exp /OH exp < 1 × 10 5 cm s −1 and Table 2. Code of the labels of typical cases. A case label can be composed of four characters denoting the water mixing ratio, the photon flux, the external OH reactivity excluding N-containing species, and the initial NO mixing ratio. A case label can also be composed of two characters denoting the water mixing ratio and the photon flux.  Table 3. Definition of condition types in this study (good/risky/bad high-/low-NO conditions).
F254 exp /OH exp < 1 × 10 7 cm s −1 (excluding good conditions) to define "risky" conditions. Conditions with higher F185 exp /OH exp or F254 exp /OH exp are defined as "bad". Under good conditions, the photolysis of most VOCs has a relative contribution < 20 % to their fate; under bad conditions, non-tropospheric photolysis is likely to be significant in all OFR experiments since it can hardly be avoided for oxidation intermediates, even if the precursor(s) does not photolyze at all. Under risky conditions, some species photolyzing slowly and/or reacting with OH rapidly (e.g., alkanes, aldehydes, and most biogenics) still have a relative photolysis contribution of < 20 % to their fates, while species photolyzing more rapidly and/or reacting with OH more slowly (e.g., aromatics and other highly conjugated species and some saturated carbonyls) will undergo substantial non-tropospheric photolysis. Note that these definitions are slightly different than in Peng et al. (2016). All definitions of the types of conditions are summarized in Table 3.

Uncertainty analysis
We apply the same method as in Peng et al. (2014Peng et al. ( , 2015 to calculate and analyze the output uncertainties due to uncertain kinetic parameters in the model. Random samples following lognormal distributions are generated for all rate constants and photoabsorption cross sections in the model using uncertainty data available in the JPL database (Sander et al., 2011) or estimated based on IUPAC data (Ammann et al., 2016). Then, Monte Carlo uncertainty propagation (BIPM et al., 2008) is performed for these samples through the model to obtain the distributions of outputs. Finally, we compute squared correlation coefficients between corresponding input and output samples and apportion the relative contributions of individual kinetic parameters to the output uncertainties based on these coefficients (Saltelli et al., 2005).

Results and discussion
In this section, we study the NO y chemistry in an OFR while considering relevant experimental issues. Based on these results, we propose some guidelines for OFR operation for high-NO OH oxidation of VOCs.
3.1 NO y chemistry in typical OFR cases with initial NO injection NO was thought to be unimportant (i.e., unable to significantly react with RO 2 ) in OFRs with initial NO injection (OFR-iNO) based on the argument that its lifetime is too short due to large amounts of O 3 OH, and HO 2 to compete with RO 2 + HO 2 . We evaluate this issue below by calculating NO effective lifetime (τ NO ; in s), defined as NO exposure (NO exp , in molecules cm −3 s) divided by initial NO concentration, under various conditions. This definition cannot effectively capture the true NO average lifetime if it is close to or longer than the residence time. In this case, τ NO close to the residence time will be obtained, which is still long enough for our characterization purposes.

OFR185-iNO
In OFR185-iNO, NO is not oxidized extremely quickly under all conditions. For instance, under a typical condition in the midrange of the phase space shown in Fig. 1a, τ NO ∼ 13 s. This lifetime is much shorter than the residence time but long enough for OH exp to reach ∼ 3 × 10 10 molecules cm −3 s, which is equivalent to an OH equivalent age of ∼ 6 h. Such an OH equivalent age is already sufficient to allow some VOC processing and even SOA formation to occur (Lambe et al., 2011;. Within τ NO , NO suppresses HO 2 through the reaction NO + HO 2 → NO 2 + OH, leading to NO exp /HO 2exp of ∼ 700 during this period, which is high enough for RO 2 to dominantly react with NO. Meanwhile, NO + HO 2 → NO 2 + OH enhances OH production, which helps OH exp build up in a relatively short period. In addition, non-tropospheric photolysis of VOCs at 185 and 254 nm is minor (F185 exp /OH exp ∼ 600 cm s −1 , Fig. 1a) because of enhanced OH production and moderate UV. Therefore, such an OFR condition may be of some interest for high-NO VOC oxidation. We thus analyze the NO y chemistry in OFR185-iNO in more detail below by taking the case shown in Fig. 1a as a representative example. In OFR185-iNO, HO x concentrations are orders of magnitude higher than in the atmosphere, while the amount of O 3 produced is relatively small during the first several seconds after the flow enters the reactor. As a result, NO is not oxidized almost exclusively by O 3 as in the troposphere, but also by OH and HO 2 to form HONO and NO 2 , respectively (Fig. 1a). The large concentration of OH present then oxidizes HONO to NO 2 and NO 2 to HNO 3 . Photolysis only plays a negligible role in the fate of HONO and NO 2 in OFRs in contrast to the troposphere where it is the main fate of these species. This is because the reactions of HONO and NO 2 with OH are greatly accelerated in OFR compared to those in the troposphere, while photolysis not . The interconversion between NO 2 and HO 2 NO 2 is also greatly accelerated (Fig. 1a) since a large amount of HO 2 promotes the formation of HO 2 NO 2 , the reaction with OH and thermal decomposition of which in turn enhance the recycling of NO 2 . Though not explicitly modeled in this study, RO 2 is expected to undergo similar reactions with NO 2 to form reservoir species, i.e., peroxynitrates (Orlando and Tyndall, 2012). Peroxynitrates that decompose on timescales considerably longer than OFR residence times may serve as effectively permanent NO y sinks in OFRs (see Sect. 3.4.1).
Interestingly but not surprisingly, the NO y chemistry shown in Fig. 1a is far from temporally uniform during the OFR residence time (Fig. S1a in the Supplement). Within τ NO , NO undergoes an e-fold decay as it is rapidly converted into NO 2 and HONO with concentrations that reach maxima around that time. After most NO is consumed, HONO and NO 2 also start to decrease, but significantly more slowly than NO, since they do not have as many or efficient loss pathways as NO. The reaction of OH with HONO, the dominant fate of HONO, is slower than that with NO (Fig. 1a). The net rate of the NO 2 -to-HO 2 NO 2 conversion becomes low because of the relatively fast reverse reaction (Fig. 1a). The total loss of NO 2 is also partially offset by the production from HONO. The generally stable concentrations of HONO and NO 2 (Fig. S1a) result in their respective reaction rates with OH that are comparable during and after τ NO (Fig. 1a), as OH variation is also relatively small during the entire residence time (Fig. S1b). However, the NO 2 -to-HO 2 NO 2 conversion after τ NO is much faster than during it (Fig. 1a) as a result of substantially decreased NO and HO 2 concomitantly increasing by > 1 order of magnitude after τ NO ( Fig. S1a and b). HNO 3 and HO 2 NO 2 , which are substantially produced only after NO 2 is built up, have much higher concentrations later than within τ NO .
Under other OFR185-iNO conditions than in Fig. 1a, the major reactions interconverting NO y species are generally the same, although their relative importance may vary. At lower NO in , the perturbation of HO x chemistry caused by NO y species is smaller. The effects of NO in less than 1 ppb (e.g., typical non-urban ambient concentrations) are generally negligible regarding HO x chemistry. Regarding NO y species, the pathways in Fig. 1a are still important under those conditions. At higher NO in (e.g., > 1 ppm), one might expect NO 3 and N 2 O 5 to play a role (as in OFR254-iNO; see Sect. 3.1.2 below) since high NO y concentrations might enhance self-or cross-reactions of NO y . However, this would not occur unless OH production is high since relatively low O 3 concentrations in OFR185-iNO cannot oxidize NO 2 to NO 3 rapidly. Also, a large amount of NO y can lead to significant OH suppression. That would in turn slow down the NO 3 production from HNO 3 by OH. This is especially true when an OFR is used to oxidize the output of highly concentrated sources (e.g., from vehicle exhausts). When sources corresponding to OHR ext of thousands of s −1 and NO in of tens of ppm are injected into OFR185 (Fig. 1b), they essentially inhibit active chemistry except NO consumption, as all subsequent products are much less abundant compared to remaining NO (Fig. S1c).  Table 2 for the typical case label code) in OFR185-iNO. Relative variances are shown in linear scales (left axis), while corresponding relative uncertainties equal to relative variances' square roots are indicated by the nonlinear right axis. Only the reactions with a contribution of no less than 0.04 to at least one relative variance are shown.

OFR254-iNO
The ppm level O 3,in used in the OFR254-iNO mode of operation has a strong impact on its NO y chemistry. An O 3,in of 2.2 ppm (lowest in this study) is already enough to shorten τ NO to ∼ 1 s, preventing NO from playing a role in the chemistry under most explored conditions. The reaction fluxes under a typical O 3,in of 7 ppm are shown in Fig. 1c. A reactive flux from NO + O 3 → NO 2 makes the reaction of NO with other oxidants (OH, HO 2 , etc.) negligible. The HNO 3 production pathway from NO 2 is similar to that in OFR185-iNO. The interconversion between NO 2 and HO 2 NO 2 is also fast over the residence time and even faster than in OFR185-iNO during τ NO since a high concentration of O 3 also controls the OH-HO 2 interconversion and makes HO 2 more resilient against suppression due to high NO ( Fig. S1f; Peng et al., 2015). A major difference in the NO y chemistry in OFR254-iNO (Fig. 1c) compared to OFR185-iNO (Fig. 1a) is significant NO 3 /N 2 O 5 chemistry due to high O 3 in OFR254-iNO, which accelerates the oxidation of NO 2 to NO 3 . Interconversion between NO 2 + NO 3 and N 2 O 5 also occurs to a significant extent because of high NO 2 . Under the conditions of Fig. 1c, NO 3 can also be significantly consumed by HO 2 . Unlike OFR185-iNO, OFR254-iNO can substantially form NO 3 from HNO 3 under conditions that are not on the extremes of the explored physical condition space, e.g., at higher UV and lower NO in (e.g., Fig. S2). In the case of very high NO in (equal to or higher than O 3,in ), all O 3 can be rapidly destroyed by NO. As a consequence, OH production is shut down and these cases are of little practical interest (Fig. S3h).

Uncertainty analysis
The results of uncertainty propagation confirm that the output uncertainties due to uncertain kinetic parameters are relatively low compared to other factors (e.g., non-plug flow in OFR; Peng et al., 2015) and the overall model accuracy compared to experimental data (a factor of 2-3; Li et al., 2015). For OFR185-iNO, NO, NO 3 , and OH exposures have relative uncertainties of ∼ 0-20, ∼ 40-70, and ∼ 15-40 %, respectively. The uncertainties in OH exposure are very similar to those in the cases without NO x . The contribution of NO y reactions to OH exp uncertainty is negligible, except for some contribution of OH + NO → HONO in a few cases with high NO in (Fig. 2). The uncertainties in NO exp are dominated by the reactions producing HO x and O 3 , i.e., the major consumers of NO. For NO 3 exposure, a few major production and loss pathways (e.g., NO 2 + NO 3 → N 2 O 5 , N 2 O 5 → NO 2 + NO 3 , and HO 2 + NO 3 → OH + NO 2 + O 2 ) dominate its uncertainties. OFR254-iNO has a simpler picture of parametric uncertainties in terms of composition. O 3 controls the NO oxidation under most conditions and this reaction contributes most of the output uncertainties for NO exposures. HO 2 + NO 3 → OH + NO 2 + O 2 dominates the uncertainty in NO 3 exposure. The levels of those uncertain-ties are lower than in OFR185-iNO (< 2 % for NO exposure, < 60 % in all cases, and < 25 % in most cases for NO 3 exposure). Thus, model uncertainties in OFR254-iNO are not shown in detail.

Different conditions types
Having illustrated the main NO y chemical pathways for typical cases, we present the results of the exploration of the entire physical parameter space (see Sect. 2.2). Note that the explored space is indeed very large and gridded logarithmically uniformly in every dimension. Therefore, the statistics of the exploration results can be useful to determine the relative importance of the condition types defined in Sect. 2.2 and Table 3.
It has been shown that during τ NO , RO 2 can react dominantly with NO (Sect. 3.1.1), while the entire residence time is considered to determine if a condition is high-NO (see Table 3). This is done because for VOC oxidation systems of interest, there will be significant oxidation of the initial VOC and its products under low-NO conditions if τ NO is shorter than the reactor residence time. After most NO is consumed, the longer the remaining residence time, the more RO 2 will react with HO 2 and the more likely that an input condition is classified as low NO. For a condition to be high NO, a significantly long τ NO is required. Figure 3 shows the fractional occurrence distribution of good, risky, and bad conditions in the entire explored condition space over logarithm of r(RO 2 +NO)/r(RO 2 + HO 2 ), which distinguishes high-and low-NO conditions. In OFR254-iNO, τ NO is so short that no good high-NO condition is found in the explored range in this study (Fig. 3a). A fraction of explored conditions are bad high-NO. These conditions result from a full consumption of O 3 by NO. Then very little HO x is produced (right panels in Fig. S3h), but the fate of any RO 2 formed is dominated by RO 2 + NO (right panels in Fig. S3i). However, also due to negligibly low OH concentration, little RO 2 is produced and non-tropospheric photolysis of VOCs is also substantial compared to their reaction with OH under these conditions, classifying all of them as "bad" (Fig. 3a).
In OFR185-iNO, in addition to the typical case shown in Fig. 1a, many other cases have a τ NO of ∼ 10 s or longer (Figs. S3b and S4), which allows for the possibility of high-NO conditions. Indeed, ∼ 1/3 of explored conditions in OFR185-iNO with a residence time of 3 min are high NO (Fig. 3b). Most of these high-NO conditions are also classified as bad, similar to those in OFR254-iNO. More importantly, in contrast to OFR254-iNO, good and risky high-NO conditions also comprise an appreciable fraction of the OFR185-iNO conditions. It is easily expected that very high OHR ext and NO in lead to bad high-NO conditions (all panels in Fig. 4) since they strongly suppress HO x , which yields bad conditions and in turn keeps NO destruction relatively low. The occurrence of bad high-NO conditions is reduced at high UV (bottom panels in Fig. 4), which can be explained by  Table 3) over logarithm of the ratio between RO 2 reacted with NO and with HO 2 (see Sect. S1 for more detail) for (a) OFR254-iNO (only the case with a residence time of 180 s) and (b) OFR185-iNO (including two cases with residence times of 180 and 30 s). Low-and high-NO regions (see Table 3) are colored in light blue and gray, respectively. lowered NO due to high O 3 production and fast OH reactant loss due to high OH production. Good high-NO conditions are rare in the explored space. They are only 1.1 % of total explored conditions (Fig. 3b) and present under very specific conditions, i.e., higher H 2 O, lower UV, lower OHR ext , and NO in of tens to hundreds of ppb (Figs. 4 and S5). Since a very high NO can suppress OH, to obtain both a significant NO level and good conditions, NO in can only be tens to hundreds of ppb. As NO in is lower and OH is higher than under bad high-NO conditions, UV should be lower than bad high-NO conditions to keep a sufficiently long presence of NO. Thus, UV levels at 185 nm for good high-NO conditions are generally lower than 10 12 photons cm −2 s −1 (Fig. S5). In addition, a low OHR ext (generally < 50 s −1 ) and a higher H 2 O (the higher the better, although there is no apparent threshold) are also required for good high-NO conditions (Fig. S5), as Peng et al. (2016) pointed out. Risky high-NO conditions often occur between good and bad high-NO conditions, e.g., at lower NO in than bad conditions (e.g., Cases ML, MM, HL, and HM in Fig. 4; see Table 2 for the typical case label code), at higher OHR ext and/or NO in than good conditions (e.g., Cases ML and MM), and at lower H 2 O than good conditions (e.g., Case LL).  Table 3 vs. external OH reactivity (excluding N-containing species) and initial NO for several typical cases in OFR185-iNO (see Table 2 for the case label code).
The trend in the distributions of good, risky, and bad low-NO conditions is generally in line with the analysis in Peng et al. (2016). For low-NO conditions, NO y species can be simply regarded as external OH reactants, as in Peng et al. (2016). As H 2 O decreases and/or OHR ext or NO in increases, a low-NO condition becomes worse (good → risky → bad; Figs. 4 and 5). In OFR185-iNO, increasing UV generally makes a low-NO condition better because of an OH production enhancement (Fig. 4), while in OFR254-iNO, increasing UV generally makes a low-NO condition worse (Fig. 5) since at a higher UV more O 3 is destroyed and the resilience of OH to suppression is reduced.
As discussed above, the fraction of high-NO conditions also depends on OFR residence time. A shorter residence time is expected to generally lead to a larger fraction of high-NO conditions since the time spent in the reaction for t > τ NO is significantly smaller. Thus, we also investigate an OFR185-iNO case with a residence time of 30 s. In Fig. 3b, compared to the case with a residence time of 3 min, the distributions of all condition types (good, risky, and bad) of the 30 s residence time case shift toward higher r(RO 2 + NO)/r(RO 2 + HO 2 ). Nevertheless, shortening the residence time also removes the period when the condition is better (i.e., less non-tropospheric photolysis), when external OH reactants have been partially consumed, and OH suppression due to OHR ext has been reduced later in the residence time. As a result, the fractions of good and risky conditions decrease (Fig. 3b). With the two effects (higher r(RO 2 + NO)/r(RO 2 + HO 2 ) and more significant non-tropospheric photolysis) combined, the fraction of good high-NO conditions increases by a factor of ∼ 3. An even shorter residence time does not result in a larger good high-NO fraction since the effect of enhancing non-tropospheric photolysis is even more apparent.

Effect of non-plug flow
We performed model runs in which the only change with respect to our box model introduced in Sect. 2.2 is that the plug flow assumption is replaced by the residence time distribution (RTD) measured by Lambe et al. (2011;see also Fig. S8 of Peng et al., 2015). The chemistry of different air parcels with different residence times is simulated by our box model and outputs are averaged over the RTD. Lateral diffusion between different air parcels is neglected in these simulations.
OH exp calculated from the mode with RTD (OH exp,RTD ) is higher than that calculated from the plug flow model (OH exp,PF ) in both OFR185-iNO and OFR254-iNO (Table 4 and Fig. S6). Under most explored conditions deviations are relatively small, which leads to an overall posi-  Figure 5. Same format as Fig. 4 but for OFR254-22-iNO.
tive deviation of OH exp,RTD from OH exp,PF by ∼ × 2 (within the uncertainties of the model and its application to real experimental systems). For OFR185-iNO, most conditions (∼ 90 %) in the explored space lead to < × 3 differences between OH exp,PF and OH exp,RTD , while for a small fraction of cases the differences can be larger (Fig. S6). The larger deviations are mainly present at high UV, OHR ext , and NO in in which conditions are generally bad and in which experiments are of little atmospheric relevance. Under these specific conditions, external OH reactants and NO y can be substantially destroyed for the air parcels with residence times longer than the average, while this is not the case for the average residence time. This feature was already described by see Fig. S10 of that study). Although only non-NO y external OH reactants were considered in that study, the results are the same. In the present study, a higher upper limit of the explored OHR ext range (compared to Peng et al., 2015, due to trying to simulate the extremely high OHR ext used in some recent literature studies) leads to large amounts of NO y and causes somewhat larger deviations. In OFR254-iNO, OH is less suppressed at high OHR ext and NO in than in OFR185-iNO because of high O 3 ; OH exp,RTD deviations from OH exp,PF are also smaller (Table 4). Based on the outputs of the model with RTD, a similar mapping of the physical input space as in Figs. 4 and 5 can be done (Figs. S7 and S8). Overall, the mapping of the RTD model results is very similar to that of the plug flow model. The conditions appear to be only slightly better in a few places of the explored space than those from the plug flow model, which can be easily explained by the discussions above. The mapping in Figs. S7 and S8 also appear to be slightly more low NO for the same reasons discussed above. After NO is destroyed at long residence times, HO 2 suppressed by NO also recovers as OH, and r(RO 2 + NO)/r(RO 2 + HO 2 ) is clearly expected to be smaller than in the plug flow model in general.
Z. Peng and J. L. Jimenez: Modeling of the chemistry in oxidation flow reactors with high initial NO Note that most conditions that appear to be better in the RTD model results are already identified as bad by the plug flow model. Those conditions look slightly better only because of their better RTD-averaged F185 exp /OH exp and F254 exp /OH exp . However, each of those cases is actually composed of both a better part at longer residence times and also a worse part at shorter residence times. Under those conditions, the reactor simultaneously works in two distinct regimes, one of which is bad due to heavy OH suppression. Such conditions are clearly not desirable for OFR operation.

Possible issues related to high NO x levels
In the discussion above, we focused on obtaining high-NO conditions and considered only one experimental issue (nontropospheric photolysis) that had been previously investigated in Peng et al. (2016) and is not specific for experiments with high NO injection. We discuss additional potential reasons why the OFR-iNO chemistry can deviate strongly from tropospheric conditions as specifically related to high NO x levels in this subsection.

NO 2
NO 2 reacts with RO 2 to form peroxynitrates, which are generally regarded as reservoir species in the atmosphere as most of them thermally decompose very quickly compared to atmospheric timescales. However, in OFRs with residence times on the order of minutes, some peroxynitrates may no longer be considered as fast decomposing. This is especially true for acylperoxy nitrates with lifetimes that can be hours at room temperature (Orlando and Tyndall, 2012). Acylperoxy nitrates are essentially sinks instead of reservoirs in OFRs for both NO 2 and RO 2 . RO 2 is estimated to be as high as several ppb in OFRs by our model (e.g., ∼ 6 ppb RO 2 in OFR185 at H 2 O = 1 %, UV at 185 nm = 1 × 10 13 photons cm −2 s −1 , OHR ext = 1000 s −1 , and NO in = 0), while high-NO experiments can yield far higher NO 2 . If all RO 2 were acylperoxy, the RO 2 chemistry could be rapidly shut down by NO 2 , as rate constants of these RO 2 + NO 2 reactions are around 10 −11 cm 3 molecule −1 s −1 (Orlando and Tyndall, 2012). Nevertheless, acyl peroxynitrates are not expected to typically be the dominant component of peroxynitrates since acyl radicals are not a direct oxidation product of most common VOCs and can only be formed after several steps of oxidation (Atkinson and Arey, 2003;Ziemann and Atkinson, 2012). Most alkylperoxy nitrates retain their short-lived reservoir characteristics in OFRs due to their relatively short thermal decomposition timescales (on the order of 0.1 s; Orlando and Tyndall, 2012). Even so, OFR experiments can be seriously hampered at extremely high NO 2 . If NO 2 reaches ppm levels, the equilibrium between RO 2 + NO 2 and alkylperoxy nitrate (RO 2 +NO 2 ↔RO 2 NO 2 ) is greatly shifted toward the alkylperoxy nitrate side, as the forward and reverse rate con-stants are on the order of 10 −12 cm 3 molecule −1 s −1 and 1 s −1 , respectively (Orlando and Tyndall, 2012). This results in a substantial decrease in effective RO 2 concentration, or in other words, a substantial slowdown of RO 2 chemistry.
Parts per million levels of NO 2 may impose an additional experimental artifact in the oxidation chemistry of aromatic precursors. OH-aromatic adducts, i.e., the immediate products of aromatic oxidation by OH, undergo the addition of O 2 and NO 2 at comparable rates under ppm levels of NO 2 (rate constants of the additions of O 2 and NO 2 are on the order of 10 −16 and 10 −11 molecules cm −3 s −1 , respectively; Atkinson and Arey, 2003). However, only the former addition is atmospherically relevant (Calvert et al., 2002). Liu et al. (2015) performed OFR254-iNO experiments with toluene over a range of NO in of 2.5-10 ppm, encompassing the NO concentration range at which the reactions of OH-toluene adduct with O 2 and with NO 2 are of equal importance (∼ 5 ppm; Atkinson and Arey, 2003). This suggests that nitroaromatics, the formation of which was reported in the study of Liu et al. (2015), might have been formed in substantial amounts in that study through the addition of NO 2 to the OH-toluene adduct.

NO 3
As discussed in Sect. 3.1, NO 3 can be formed in significant amounts in OFRs with high NO injection. Although NO 3 is also present in the atmosphere, especially during nighttime, significant VOC oxidation by both OH and NO 3 results in more complex chemistry that may complicate the interpretation of experimental results. NO 3 oxidation-only OFRs have been previously realized experimentally via the thermal dissociation of injected N 2 O 5 (Palm et al., 2017). We discuss below how to avoid significant VOC oxidation by NO 3 and achieve OH-dominated VOC oxidation in OFRs with high NO injection.
If NO 3exp /OH exp > 0.1, NO 3 can be a competitive reactant for biogenic alkenes and dihydrofurans, which have a C-C bond for NO 3 addition, and phenols, which have activated hydroxyl for fast hydrogen abstraction by NO 3 (Atkinson and Arey, 2003). For lower NO 3exp /OH exp , OH is expected to dominate the oxidation of all VOCs, as shown in Fig. 6. Oxidation for VOCs without alkene C-C bonds and phenol hydroxyl (such as alkanes and (alkyl)benzenes) is dominated by OH unless NO 3exp /OH exp > 1000. Despite its double bond, ethene reacts as slowly with NO 3 as alkanes, likely due to lack of alkyl groups enriching the electron density on the C-C bond, which slows NO 3 addition. We calculate NO 3exp /OH exp for OFR185-iNO and OFR254-iNO and plot histograms of this ratio in Fig. 6. Many experimental conditions lead to high enough NO 3exp /OH exp that NO 3 is a competitive sink for alkenes, while only under very extreme conditions can NO 3 be a competitive sink for species without C-C bonds. High-NO conditions in OFR185-iNO have lower NO 3exp /OH exp (∼ 10 −2 -10 2 ) than in OFR254- Figure 6. Fractional importance of the reaction rate of several species of interest with NO 3 vs. that with OH as a function of the ratio of exposure to NO 3 and OH. The curves of biogenics and phenols are highlighted by solid dots and squares, respectively. The turquoise and orange markers show the ranges of modeled exposure ratios between NO 3 and OH of a source study in an urban tunnel (Tkacik et al., 2014) and a laboratory study (Liu et al., 2015), respectively, using an OFR. In the upper part of the figure, the modeled frequency distributions of ratios of NO 3 exposure to OH exposure under good/risky/bad high-/low-NO conditions for OFR185-iNO and OFR254-iNO are also shown. See Table 3 for the definitions of the three types of conditions. All curves, markers, and histograms in this figure share the same abscissa.
iNO (∼ 10 1 -10 5 ) (Figs. 6 and S3d,g,j). This difference in NO 3exp /OH exp is due to the different levels of O 3 in the two modes, as high O 3 promotes NO 2 -to-NO 3 oxidation. Note that low-NO conditions in both OFR185-iNO and OFR254-iNO can also reach high NO 3exp /OH exp as some high-NO conditions have. This is because in OFR185-iNO a large part of NO 3 is formed by OH oxidation, resulting in NO 3exp /OH exp being largely influenced by NO in but not by other factors mainly governing OH (Fig. S3d); under low-NO conditions in OFR254-iNO, NO 3 can form rapidly from NO 2 + O 3 , while OH can be heavily suppressed by high OHR ext (Fig. S3g and j).
Most of the species shown in Fig. 6 are primary VOCs, except phenols and a dihydrofuran, which can be intermediates of the atmospheric oxidation of (alkyl)benzenes (Atkinson and Arey, 2003) and long-chain alkanes (Aimanant and Ziemann, 2013;Strollo and Ziemann, 2013;Ranney and Ziemann, 2016), respectively. Nevertheless, only the phenol production may occur in high-NO OFRs, as the particle-phase reaction in the photochemical formation of dihydrofurans from alkanes is too slow compared to typical OFR residence times (Ranney and Ziemann, 2016). Therefore, the impact of NO 3 oxidation on VOC fate needs to be considered only if the OFR input flow contains high NO mixed with biogenics and/or aromatics, e.g., (alkyl)benzenes and/or phenols.
However, (alkyl)benzenes were likely to be major SOA precursors in, to our knowledge, the only literature OFR studies with high NO levels Tkacik et al., 2014;Liu et al., 2015). In the study of the air in a traffic tunnel (OFR185-iNO mode; Tkacik et al., 2014), where toluene is usually a major anthropogenic SOA precursor as in other urban environments (Dzepina et al., 2009;Borbon et al., 2013;Hayes et al., 2015;Jathar et al., 2015), NO x was several hundred ppb. This resulted in an estimated NO 3exp /OH exp range of ∼ 0.1-1 in which up to ∼ 30 % of cresols (intermediates of toluene oxidation) may have been consumed by NO 3 . Dihydrofurans may also have formed in the tunnel air (but outside the OFR) in the presence of NO x (Aimanant and Ziemann, 2013;Strollo and Ziemann, 2013), and after entering the OFR they would have been substantially (up to ∼ 50 %) consumed by NO 3 . In the laboratory experiment of Liu et al. (2015) with toluene, the injection of as much as 10 ppm of NO elevated NO 3exp /OH exp to ∼ 100, at which cresols from toluene oxidation reacted almost exclusively with NO 3 in addition to being photolyzed.

A case study
We use a case study of an OFR254-13-iNO laboratory experiment with a large amount of toluene (5 ppm) and NO in Up to ~80% ~70% Up to ~50% ~5% Scheme 1. Possible major reactions in an OFR254-13-iNO with 5 ppm toluene and 10 ppm initial NO. Branching ratios in red are estimated by the model and/or according to Calvert et al. (2002), Atkinson and Arey (2003), Ziemann and Atkinson (2012), and Peng et al. (2016). Note that addition or substitution on the aromatic ring may occur at other positions. Intermediates and products shown here are the isomers that are most likely to form. Branching ratios shown in red are not overall but from immediate reactant.
(10 ppm) to illustrate how very high VOC and NO concentrations cause multiple types of atmospherically irrelevant reactions in an OFR. Due to very high OHR ext and NO in , the photolysis of toluene at 254 nm may have been important . In the case of a high (close to 1) quantum yield, up to ∼ 80 % of the consumed toluene in their experiments could have been photolyzed (Scheme 1). Of the rest of reacted toluene, ∼ 10 % undergoes H abstraction by OH from the methyl group in the model, leading to an RO 2 similar to alkyl RO 2 and likely proceeding with normal RO 2 chemistry. Approximately 90 % of the toluene formed an OH adduct (Calvert et al., 2002). As discussed above, 70 % of this adduct (depending on NO in ) is predicted to recombine with NO 2 , producing nitroaromatics because of the ppm level NO x . The adduct could also react with O 2 via two types of pathways, one of which was addition forming a special category of RO 2 (OH-toluene-O 2 adducts) potentially undergoing ring-opening (Atkinson and Arey, 2003;Orlando and Tyndall, 2012;Ziemann and Atkinson, 2012). The other was H elimination by O 2 , producing cresols. Again, like toluene, cresols may have been substantially photolyzed. As a result of NO 3exp /OH exp ∼ 100, only a minor portion of cresol could have undergone OH addition and then H elimination again. This pathway leads to the formation of methyldihydroxybenzenes and other OH-oxidation products (Atkinson and Arey, 2003). The rest of the cresols may have formed methylphenoxy radicals but nevertheless dominantly via H abstraction by NO 3 , since H abstraction by OH was a minor pathway compared to the OH-addition one (Atkinson et al., 1992). In summary, the model results suggest that there were two possible routes leading to nitroaromatic formation. However, one of them (recombination of OH-aromatic adducts with NO 2 ) is likely of little atmospheric relevance due to very high NO x needed, and the other (H abstraction from cresol) occurs in the atmosphere but is not a major fate of aromatics (Calvert et al., 2002).

Implications for OFR experiments with combustion emissions as input
Emissions from combustion sources, e.g., vehicles and biomass burning, usually contain VOCs and NO x at very high concentrations (Table 1). An injection of this type of emissions (typically with OHR ext of thousands of s −1 or larger and NO in of tens of ppm or larger) in OFRs without any pretreatment is likely to cause all experimental issues discussed in Peng et al. (2016) and this paper, i.e., strong OH suppression, substantial non-tropospheric photolysis, strong RO 2 suppression by NO 2 whether RO 2 is acyl RO 2 or not, fast reactions of NO 2 with OH-aromatic hydrocarbon adducts, substantial NO 3 contribution to VOC fate,  Karjalainen et al. (2016) in the cases of no dilution, dilution by a factor of 12 (as actually done in that study), and dilution by a factor of 100. Different periods of time are colored according to corresponding emissions (i.e., input conditions for OFR) classified as good/risky/bad high-/low-NO emissions. (b) OH exposure and percentage of remaining OH after suppression, relative importance of non-OH fate of benzene, exposure ratio of NO 3 to OH, NO effective lifetime, and relative importance of reaction of OH-toluene adduct with NO 2 in the fate of this adduct in the OFR of Karjalainen et al. (2016) during the first 200 s of their test in the cases of no dilution, dilution by a factor of 12, and dilution by a factor of 100. Horizontal orange and red dashed lines in the middle right panel denote "risky" and "bad" regions for exposure ratio of NO 3 to OH, respectively. Above the orange (red) dashed line, reaction with NO 3 contributes > 20 % to the fate of phenol (isoprene). Figure 8. Secondary organic aerosol (SOA) potential (estimated from the total hydrocarbon measurement) in the OFR of Karjalainen et al. (2016) formed during periods of time in the OFR corresponding to good/risky/bad high-/low-NO conditions as a function of dilution factor. Vertical lines denoting dilution factors of 1, 12 (as actually used in that study), and 100 are also shown. and even a nearly total inhibition of OFR chemistry due to complete titration of O 3 by NO in the case of OFR254. We take the study of Karjalainen et al. (2016), who used an OFR to oxidize diluted car exhaust in real time, as a case study to investigate the extent to which these issues may affect typical combustion source studies and to explore approaches to mitigate the problems. During the first 200 s of their experiment (defined as the "cold start" period when the catalyst is cold and emissions are high), NO and total hydrocarbon in the emissions of the test vehicle reached ∼ 400 and ∼ 600 ppm, respectively. We first simulate the oxidation of those emissions without any dilution (even though × 12 dilution was used in their experiments) to explore the most extreme conditions. Our model simulation indicates that such an extremely concentrated source would generally lead to bad high-or low-NO conditions (depending on NO concentration) in their OFR (Fig. 7), even though it was run at relatively high H 2 O and UV. OH suppression can be as high as 3 orders of magnitude, VOC fates by non-tropospheric photolysis and reactions of alkenes and phenols with NO 3 can be nearly 100 %, Figure 9. Location of individual 1 s data points vs. OFR185-iNO reaction conditions. Data points are shown from the test vehicle of Karjalainen et al. (2016) and average exhaust from gasoline vehicle on-road emissions measured by Bishop and Stedman (2013). Onroad emissions are classified by vehicle year and the distribution of each category is shown as a cross representing 1 SD (standard deviation; with lognormal distribution assumed). The x and y axes are NO and external OH reactivity (excluding N-containing species) due to vehicle emissions in an OFR in the cases of (a) no dilution and (b, c) dilution by a factor of 100. The Karjalainen et al. (2016) points are classified as cold start (during the first 200 s) and hot stabilized (during 200-1000 s). In addition, the same image plots as the panels of cases HH (high H 2 O and high UV; see Table 2 for the case label code) and HL in Fig. 4 (OFR185-iNO) are shown as background for comparison. and up to ∼ 1/3 of OH-toluene adduct may be recombined with NO 2 instead of forming an adduct with O 2 . After the test vehicle entered the "hot stabilized" stage (200-1000 s), its VOC emissions (on the order of ppm) were still too high for an undiluted OFR to yield a good condition (Fig. S9). OH suppression can still reach 2 orders of magnitude, nontropospheric photolysis and sometimes reactions with NO 3 can still dominate over reactions with OH in VOC fates, and reactions of OH-toluene adduct with NO 2 can still be substantial at some small NO emission spikes. Moreover, although NO emissions were roughly at ppm level even during the hot stabilized period, the NO effective lifetime may be very short during that period, leading to low-NO conditions in their OFR.
As suggested in Peng et al. (2016) for a low-NO OFR, the dilution of sources can also mitigate strong deviations in OFR-iNO chemistry vs. atmospherically relevant conditions. A dilution by a factor of 12, as actually used by Karjalainen et al. (2016), appears to be sufficient to bring most of the hot stabilized period under good conditions (Fig. S9). However, most VOC, or in other words most SOA formation potential, was emitted during the cold start period when risky and bad conditions still prevailed (Figs. 7 and 8). Even if the emissions are diluted by x100, the cold-start emission peak (Fig. 7) is still under risky conditions. Although bad conditions are eliminated and a good condition is present most of time, this emission peak under risky conditions may contribute > 50 % to total SOA formation potential (Fig. 8). For SOA formed under good condition to be dominant, a dilution factor of > 400 would be needed. Note that a strong dilution lowers aerosol mass loading in vehicle emissions. As a result, the condensation of gases onto particles is slower than in raw exhausts. However, condensational sinks after dilution may still be significantly higher than typical ambient values (Matti Maricq, 2007;Donahue et al., 2016).
Note that the emissions of the test vehicle of Karjalainen et al. (2016) are rather clean compared to the typical 2013 US on-road fleet (i.e., all at the hot stabilized stage) measured by Bishop and Stedman (2013;Figs. 9 and S10). For the emissions of an average on-road fleet, a dilution by a factor of 100 or larger would be necessary to ensure that most emissions are processed in OFR185 under good conditions at the highest H 2 O and UV in this study (Figs. 9b and S10b,e,h). In the case of lower H 2 O and/or UV, an even larger dilution factor would be required.
Conducting OFR185-iNO experiments at high UV lowers the dilution factor needed for good conditions. However, it also renders good high-NO conditions impossible (see Sect. 3.2 and Fig. S4). If one wants to oxidize vehicle exhausts in a high-NO environment in an OFR, as in an urban atmosphere, OFR185 at low UV is necessary. Consequently, a much stronger dilution is in turn necessary to keep the operation conditions good. Nevertheless, not all vehicle emissions can be moved into the good high-NO region through a simple dilution (Figs. 9c and S10c, f, i). Further-more, a low UV would seriously limit the highest OH exp that OFRs can achieve (∼ 3 × 10 11 molecules cm −3 s for modeled good high-NO conditions in this study), while a much higher OH exp would be desirable to fully convert SOA formation potential into measurable SOA mass. If both good high-NO conditions and high OH exp are required, new techniques (e.g., injection of N 2 O at the percent level as proposed by  may be necessary.

Conclusions
In this study, OFR chemistry involving NO y species was systematically investigated over a wide range of conditions. NO initially injected into the OFR was found to be rapidly oxidized under most conditions. In particular, due to high O 3 concentrations, the NO lifetime in OFR254-iNO was too short to result in significant RO 2 consumption by NO compared to that by HO 2 under all conditions with active chemistry. Nevertheless, it is not completely impossible for OFR185-iNO to have a significant RO 2 fate by NO and minor non-tropospheric photolysis at the same time (good high-NO conditions). According to our simulations, these conditions are most likely present at high H 2 O, low UV, low OHR ext , and NO in of tens to hundreds of ppb.
However, many past OFR studies with high NO injection were conducted under conditions remarkably different from the abovementioned very narrow range. NO in and/or OHR ext in those studies were often much higher than good high-NO conditions require (particularly, > 3 orders of magnitude in some OFR studies using combustion emissions as input). In addition to non-tropospheric organic photolysis, OFR oxidation of highly concentrated sources can cause multiple large deviations from tropospheric OH oxidation, i.e., RO 2 suppression by high NO 2 , substantial nitroaromatic formation from the recombination of NO 2 and OH-aromatic adducts, and fast reactions of VOCs with NO 3 compared to those with OH.
Working at lower NO x (sub ppm level) and VOC concentrations or dilution can mitigate these experimental problems. In general, a strong dilution (by a factor of > 100) is needed for an OFR that processes typical on-road vehicle emissions. Humidification can also make good conditions more likely. By using these measures, good conditions can be guaranteed as long as NO and/or precursor concentrations are sufficiently low, while high-NO conditions cannot be ensured. To aid the design and interpretation of OFR experiments with high NO injection, we provide our detailed modeling results in a visualized form (Fig. S3). For OFR users in need of both high OH exp and high NO, simple NO injection is not a good option. New techniques (e.g., the injection of N 2 O as proposed by  or other innovations) may be necessary to meet this need.
Data availability. The model outputs in this study are available from the authors upon request (jose.jimenez@colorado.edu). All data shown in the figures in this paper (including the Supplement) can be downloaded from http://cires1.colorado.edu/jimenez/group_ pubs.html.