Nitrate radical generation via continuous generation of dinitrogen pentoxide in a laminar flow reactor coupled to an oxidation flow reactor

Oxidation flow reactors (OFRs) are an emerging tool for studying the formation and oxidative aging of organic aerosols and other applications. The majority of OFR studies to date have involved the generation of the hydroxyl radical (OH) to mimic daytime oxidative aging processes. In contrast, the use of the nitrate radical (NO3) in modern OFRs to mimic nighttime oxidative aging processes has been limited due to the complexity of conventional techniques that are used to generate NO3. Here, we present a new method that uses a laminar flow reactor (LFR) to continuously generate dinitrogen pentoxide (N2O5) in the gas phase at room temperature from the NO2 + O3 and NO2 + NO3 reactions. The N2O5 is then injected into a dark Potential Aerosol Mass (PAM) OFR and decomposes to generate NO3; hereafter, this method is referred to as “OFR-iN2O5” (where “i” stands for “injected”). To assess the applicability of the OFR-iN2O5 method towards different chemical systems, we present experimental and model characterization of the integrated NO3 exposure, NO3 : O3, NO2 : NO3, and NO2 : O2 as a function of LFR and OFR conditions. These parameters were used to investigate the fate of representative organic peroxy radicals (RO2) and aromatic alkyl radicals generated from volatile organic compound (VOC)+NO3 reactions, and VOCs that are reactive towards both O3 and NO3. Finally, we demonstrate the OFR-iN2O5 method by generating and characterizing secondary organic aerosol from the β-pinene+NO3 reaction.

Abstract. Oxidation flow reactors (OFRs) are an emerging tool for studying the formation and oxidative aging of organic aerosols and other applications. The majority of OFR studies to date have involved the generation of the hydroxyl radical (OH) to mimic daytime oxidative aging processes. In contrast, the use of the nitrate radical (NO 3 ) in modern OFRs to mimic nighttime oxidative aging processes has been limited due to the complexity of conventional techniques that are used to generate NO 3 . Here, we present a new method that uses a laminar flow reactor (LFR) to continuously generate dinitrogen pentoxide (N 2 O 5 ) in the gas phase at room temperature from the NO 2 + O 3 and NO 2 + NO 3 reactions. The N 2 O 5 is then injected into a dark Potential Aerosol Mass (PAM) OFR and decomposes to generate NO 3 ; hereafter, this method is referred to as "OFR-iN 2 O 5 " (where "i" stands for "injected"). To assess the applicability of the OFR-iN 2 O 5 method towards different chemical systems, we present experimental and model characterization of the integrated NO 3 exposure, NO 3 : O 3 , NO 2 : NO 3 , and NO 2 : O 2 as a function of LFR and OFR conditions. These parameters were used to investigate the fate of representative organic peroxy radicals (RO 2 ) and aromatic alkyl radicals generated from volatile organic compound (VOC) + NO 3 reactions, and VOCs that are reactive towards both O 3 and NO 3 . Finally, we demonstrate the OFR-iN 2 O 5 method by generating and characterizing secondary organic aerosol from the β-pinene + NO 3 reaction.
generates oxygenated volatile organic compounds (OVOCs) and/or secondary organic aerosol (SOA), including particulate organic nitrates or nitroaromatics. The importance of these sources and processes are likely to continue to increase for the foreseeable future due to climate change (Melaas et al., 2016;Short, 2017).
Laboratory studies have attempted to elucidate the mechanisms associated with NO 3 -initiated oxidative aging processes in the gas and condensed phases and in environmental chambers and flow tubes. Traditional NO 3 generation techniques typically utilize N 2 O 5 as the radical precursor. N 2 O 5 is generated from the reaction NO + O 3 → NO 2 + O 2 , followed by the reactions NO 2 + O 3 → NO 3 + O 2 and NO 2 + NO 3 → N 2 O 5 . The synthesized N 2 O 5 is collected and stored in a cold trap under dry conditions to minimize hydrolysis of N 2 O 5 to nitric acid (HNO 3 ). This method has limitations that hinder widespread usage: specifically, long-term storage and handling of N 2 O 5 at low temperature and under dry conditions is difficult, and the continuous generation of N 2 O 5 that is required for oxidation flow reactors (OFRs) or other continuous flow chambers is challenging. Thus, field studies investigating the NO 3 -induced SOA formation potential of ambient air are extremely limited (Palm et al., 2017). Alternative NO 3 generation techniques that utilize reactions between chlorine atoms and chlorine nitrate (ClONO 2 ) or fluorine atoms and HNO 3 require cold storage of ClONO 2 and handling or generation of halogen species that are reactive towards organic compounds (Burrows et al., 1985).
To address issues associated with traditional NO 3 generation techniques, we developed and characterized a new method that is well suited to applications where a continuous source of N 2 O 5 and NO 3 is required, such as OFR studies. The method is capable of continuous N 2 O 5 generation in the gas phase at room temperature using a laminar flow reactor (LFR) that is coupled to a dark OFR. N 2 O 5 injected into the OFR decomposes to generate NO 3 and initiate oxidation of reactive VOCs. Hereafter, we refer to this method as "OFR-iN 2 O 5 " (where "i" stands for "injected"). We present experimental and model characterization of OFR-iN 2 O 5 as a function of LFR and OFR conditions, and we demonstrate the application of OFR-iN 2 O 5 to generate and characterize SOA from the β-pinene + NO 3 reaction.   (Wood et al., 2003;Boyd et al., 2015), although the LFR materials, flow rates, and reagent concentrations were different. A compressed gas cylinder containing 1.00 ± 0.02 % NO 2 in N 2 (Praxair) was used to supply NO 2 . While not used for this study, replacing NO 2 with NO to avoid NO 2 -to-HNO 3 conversion inside the gas cylinder and increasing [O 3 ] accordingly achieves similar results. O 3 was generated by passing 1750-1800 cm 3 min −1 of pure O 2 through a custom O 3 chamber housing a mercury fluorescent lamp (GPH212T5VH, Light Sources, Inc.) or 500-1800 cm 3 min −1 O 2 through a corona discharge ozone generator (Enaly 1KNT). We used 1800 cm 3 min −1 of O 2 carrier gas flow through the LFR (Re ∼ 110, i.e., laminar flow) to achieve τ LFR = 20 s for reasons that are discussed in Sect. 3.1. The NO 2 mixing ratio entering the LFR, [NO 2 ] 0, LFR , was calculated from the NO 2 mixing ratio in the compressed gas mixture and the dilution ratio of 0-50 or 0-1300 cm 3 min −1 gas flow into O 2 which was controlled using mass flow controllers. The O 3 mixing ratio entering the LFR, [O 3 ] 0, LFR , was measured using a 2B Technologies 106-MFT or a Teledyne M452 flowthrough O 3 analyzer when generated from the mercury lamp or corona discharge source, respectively. The output of the LFR was mixed with a carrier gas containing 3.8 L min −1 synthetic air and then injected into a Potential Aerosol Mass (PAM) OFR (Aerodyne Research, Inc.), which is a horizontal 13.3 L aluminum cylindrical chamber operated in continuous flow mode (Kang et al., 2007;Lambe et al., 2011Lambe et al., , 2019 with 6.5 L min −1 flow through the reactor. The mean residence time in the OFR (τ OFR ) was 120 ± 34 s (±1σ ), as obtained from measurements of 10 s pulsed inputs of NO 2 to the OFR obtained using a 2B Technologies Model 405 NO x analyzer (Fig. S1). Across all experiments, the relative humidity in the OFR (RH OFR ) was controlled in the range of 7 %-85 % at 23-25 • C by passing the carrier gas through a Nafion humidifier (Perma Pure LLC) or heated recirculating water bath (NESLAB Instruments, Inc.) prior to mixing with the LFR outflow. The O 3 mixing ratio at the exit of the OFR was measured with a 2B Technologies Model 106-M ozone analyzer.

OFR-iN 2 O 5 characterization studies
In one set of experiments, the integrated NO 3 exposure (NO 3exp ), defined here as the product of the average NO 3 concentration and τ OFR , was characterized by measuring the decay of VOC tracers reactive towards NO 3 using a Tofwerk/Aerodyne Vocus proton transfer reaction timeof-flight mass spectrometer (PTR-MS; Krechmer et al., 2018). For this purpose, the tracer decay method is advantageous to direct NO 3 measurements at the OFR inlet and/or outlet, because potential NO 3 concentration gradients inside the OFR that might otherwise bias NO 3exp are accounted for. Tracers that were liquid at room temperature were injected into the OFR through a 10.2 cm length of 0.0152 cm i.d. Teflon tubing at a liquid flow rate of about 0.94 µL h −1 using a syringe pump, prior to evaporation into a 2.4 L min −1 N 2 carrier gas. In preliminary studies, tracers such as isoprene and β-pinene were too reactive towards NO 3 to facilitate accurate characterization of NO 3exp over the majority of the OFR-iN 2 O 5 conditions that were investigated. Thus, experiments described in this paper used mixtures of tracers with bimolecular k NO 3 ranging from approximately 10 −16 to 10 −13 cm 3 molecules −1 s −1 and k O 3 < 10 −19 cm 3 molecules −1 s −1 (Table S1). Acetonitrile was used as a nonreactive tracer. In "low O 3 " experiments ([O 3 ] 0, LFR = 10 to 300 ppm) a mixture of acetonitrile, butanal, thiophene, 2, 3-dihydrobenzofuran, and naphthalene-d 8 (C 10 D 8 ), each with mixing ratios of approximately 660, 50, 56, 40, and 18 ppb, respectively, was used. For this tracer mixture, the total external NO 3 reactivity (NO 3 R ext ), which is the summed product of each tracer mixing ratio and its NO 3 rate constant, was approximately 0.07 s −1 . Naphthalene-d 8 was introduced by flowing 5 cm 3 min −1 N 2 through a Teflon tube packed with solid C 10 D 8 . In "high O 3 " experiments ([O 3 ] 0, LFR = 6100 to 7400 ppm), which generated higher NO 3exp , a mixture of acetonitrile (275 ppb), toluene (45 ppb), o-xylene (40 ppb), p-cymene (31 ppb), 1, 2, 4-trimethylbenzene (35 ppb), 1butanol (53 ppb), benzaldehyde (47 ppb), butanal (53 ppb), and thiophene (56 ppb) was used, with NO 3 R ext ≈ 0.38 s −1 .
In another set of experiments that were conducted as part of the Aerosol Chemical Monitor Calibration Center (ACMCC) particulate organonitrates (pON) experiment (Albinet et al., 2019), direct measurements of NO 3 generated via OFR-iN 2 O 5 were performed using a newly developed "incoherent broad band cavity enhanced absorption spectroscopy" (IBBCEAS) technique Fouqueau et al., 2020). The IBBCEAS instrument that was used measured absorption as a function of wavelength between λ = 640 and 680 nm, thereby allowing simultaneous measurements of NO 2 and O 3 along with NO 3 . During this experiment, pON were generated in a PAM OFR that used [O 3 ] 0, LFR = 150-160 ppm and [NO 2 ] 0, LFR : [O 3 ] 0, LFR = 0.75, 1.0, and 2.0. IBBCEAS has been used to measure trace NO 3 levels in laboratory and field studies (Venables et al., 2006;Kennedy et al., 2011) utilizing measurement principles that are described in detail by Fiedler et al. (2003) and Langridge et al. (2008). Briefly, measurements were conducted by exciting a high-finesse optical cavity formed by two high reflectivity mirrors with an incoherent broadband source centered on the λ = 662 nm absorption cross section of NO 3 (2 × 10 −17 cm 2 , Orphal et al., 2003). Photons resonate between the two mirrors, allowing an effective path length of up to 4.5 km inside the cavity. The absorption coefficient of the sample in the cavity, α(λ), was calculated using Eq. (1): where α(λ) is the absorption coefficient of the OFR sample in the instrument, I (λ) and I 0 (λ) were the measured transmitted intensities in the presence and absence of the sample, d = 61 cm was the distance between the cavity mirrors, and R(λ) was the mirror reflectivity (∼ 99.98 %). I 0 (λ) was obtained by stopping the OFR sample through the instrument and flowing nitrogen from a cylinder (Air Liquide). A period of at least 30 s was allowed between the measurement of I 0 (λ) and I (λ) to ensure the complete purge of the instrument. R(λ) was measured before each experiment using a certified calibration cylinder containing 600 ppb NO 2 in zero air (Air Liquide). Concentrations were calculated by applying a least square fit to the measured α(λ) considering the absorbing species in the sample: where NO 2 , NO 3 , and O 3 are the species absorbing in the spectral region of the instrument, α(λ) represents the respective absorption cross sections convoluted with the apparatus function (Vandaele et al., 1998;Voigt et al., 2001;Orphal et al., 2003), and p(λ) represents a cubic polynomial to correct baseline deformations due to small LED intensity variations. To avoid saturation of the IBBCEAS in these experiments, the OFR sample was diluted by a controlled dilution factor ranging from 9 to 41, and the detection response was deliberately lowered by reducing the optical path length. The sampling line and optical cavity were made of PFA. The residence time in the IBBCEAS sampling line and instrument ranged from 8.3 to 21.8 s. At these residence times, the calculated transmission efficiencies of NO 3 from the OFR to the IBBCEAS ranged from 0.3 % to 11 %, assuming a NO 3 wall loss rate constant of 0.27 s −1 (Kennedy et al., 2011). Corrections to measured NO 3 and NO 2 values accounting for N 2 O 5 thermal decomposition and sample dilution were applied to the IBBCEAS results presented in this paper.
To demonstrate the application of OFR-iN 2 O 5 to generate SOA, the chemical composition and mass concentration of β-pinene + NO 3 condensed-phase oxidation products was measured with an Aerodyne long-time-of-flight aerosol mass spectrometer (L-ToF-AMS) and/or an aerosol chemical speciation monitor (ACSM). A syringe pump was used to deliver β-pinene (10 %, v/v, in carbon tetrachloride or 50 %, v/v, in ethanol) into the carrier gas flow at liquid flow rates ranging from 0.94 to 19 µL h −1 . Results presented in this paper assume an AMS or ACSM collection efficiency of 0.5 (Middlebrook et al., 2012) and a relative ionization efficiency of particulate organics equal to 1.6 (Xu et al., 2018).

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A. T. Lambe et al.: N 2 O 5 and NO 3 generation in a coupled LFR-OFR

Photochemical model
We used the KinSim chemical kinetic solver to calculate concentrations of radical and oxidant species Jimenez, 2017, 2019). The KinSim mechanism shown in Table S2  output from the LFR scaled by a measured dilution factor of 4.4; RH and T measured in the OFR; τ OFR = 120 s, k w OFR , NO 3 , and k w OFR , N 2 O 5 ; and input VOC tracer concentrations and their k NO 3 values. Because the calculated N 2 O 5 residence time in the OFR inlet (∼ 0.04 s) was short compared with the N 2 O 5 decomposition timescale at T = 23-25 • C (∼ 20 s), potential thermal decomposition of N 2 O 5 during the dilution step was not considered in the model.

LFR and OFR k w, NO 3 and k w, N 2 O 5 values
Published k w, NO 3 values onto tubing with a 1 cm (Teflon) and a 4 cm (Pyrex) i.d. are 0.2 and 0.1 s −1 , respectively (Dubé et al., 2006;Wood et al., 2003), which bound the 2.22 cm i.d. of the LFR used in this study. Assuming k w is inversely proportional to the internal diameter of the tube, we assumed k w LFR , NO 3 = 0.15 s −1 . Extrapolating this value to the OFR (20.32 cm i.d.) yielded k w OFR , NO 3 = 0.02 s −1 . At fixed OFR-iN 2 O 5 conditions that are summarized in Table S3, varying k w LFR , NO 3 between 0 and 0.3 s −1 changed the NO 3exp achieved in the OFR by 0.3 %. Results were even less sensitive to the k w OFR , NO 3 assumed for the OFR because of its larger diameter and higher NO 3 R ext .
Published k w, N 2 O 5 values onto dry (RH ≈ 20 %) Pyrex or PFA tubing with 4 and 7 cm i.d. are 0.04 and 0.009 s −1 , respectively (Wagner et al., 2008;Gržinić et al., 2015). Extrapolating these values to the LFR used here and then averaging them together yielded k w, N 2 O 5 = 0.05 s −1 , which was applied in the LFR-KinSim model. In preliminary OFR-KinSim modeling studies, we assumed k w, N 2 O 5 = 0.014 s −1 (Palm et al., 2017). However, as will be discussed in Sect. 3.3, k w, N 2 O 5 was humidity-dependent and required modifications to match measured NO 3exp values as a function of RH OFR .

LFR design considerations
The optimal LFR residence time (τ LFR ) was identified using model simulations of the injection of 300 ppm O 3 and NO 2 into the LFR followed by dilution and injection of the LFR output into an OFR operated with τ OFR = 120 s. Fig-ure S2 plots the NO 3exp achieved in the OFR as a function of τ LFR ranging from 1 to 60 s. Potential entry length effects that may have influenced results obtained below τ LFR ≈ 4-5 s were not considered in the model. Figure S2 shows that the maximum NO 3exp in the OFR was obtained at τ LFR = 20 s at room temperature (unheated case); other NO 3exp values were normalized to this condition. Below τ LFR = 20 s, NO 3exp was suppressed due to higher NO 2 levels entering the OFR. Above τ LFR = 20 s, NO 3exp was suppressed due to lower N 2 O 5 levels entering the OFR because of more extensive LFR wall loss.
In traditional studies of NO 3 oxidative aging processes that are conducted at low pressure and short residence time (τ ∼ 1 s), N 2 O 5 is heated to generate a burst of NO 3 prior to injection into the system (Knopf et al., 2011). While not experimentally considered in this work, we modeled the NO 3exp achieved assuming complete thermal dissociation of N 2 O 5 between the LFR and OFR -for example, by heating to 120 • C for 300 ms (Wood et al., 2003). Figure S2 suggests that the effect of heating N 2 O 5 on NO 3exp was most significant at short τ LFR , where [N 2 O 5 ] at the exit of the LFR was higher due to less wall loss and room-temperature decomposition. For example, at τ LFR = 8 s, the modeled NO 3exp was 2.8 times higher in the complete-dissociation case than in the unheated case, whereas NO 3exp increased by factors of 2.3 and 1.5 at τ LFR = 20 and 60 s. Thus, a combination of reducing τ LFR and heating N 2 O 5 at the exit of the LFR increases NO 3exp and should be explored for future advanced implementations of OFR-iN 2 O 5 .  Figure 2b shows time series of acetonitrile (C 2 H 3 N), butanal (C 4 H 8 O), thiophene (C 4 H 4 S), 2, 3dihydrobenzofuran (C 8 H 8 O), and naphthalene-d 8 (C 10 D 8 ) signals measured during the same period. Following NO 3 generation, the fractional decay of C 2 H 3 N, C 4 H 8 O, C 4 H 4 S, and C 8 H 8 O increased with increasing tracer k NO 3 , as expected. C 8 H 8 O was too reactive to measure any significant changes in its decay as a function of OFR-iN 2 O 5 conditions, as shown in Fig. 2 To confirm that the VOC degradation shown in Fig. 2b was due to reaction with NO 3 , Fig. 3   wavelength-dependent absorption cross section of NO 3 obtained by Orphal et al. (2003) and plotted in Fig. 3b. Additionally, Fig. S3 shows the relative rate coefficient obtained from the decay of C 4 H 8 O and C 4 H 4 S measured with PTR-MS. We measured a relative rate coefficient of 2.83, which is in agreement with a relative rate coefficient value of 3.22 ± 0.95 calculated from C 4 H 8 O + NO 3 and C 4 H 4 S+NO 3 rate coefficients (Atkinson, 1991;D'Anna et al., 2001). Ions corresponding to peroxy butyl nitrate, nitrothiophene, and nitronaphthalene-d 7 , which are known NO 3 oxidation products of C 4 H 8 O, C 4 H 4 S, and C 10 D 8 , respectively (Atkinson et al., 1990;Jenkin et al., 2003;Saunders et al., 2003;Cabañas et al., 2005), were also detected with PTR-MS. Tracer decay experiments similar to the measurements shown in Fig. 2 were repeated over [O 3 ] 0, LFR ranging from 10 to 7400 ppm, [NO 2 ] 0, LFR ranging from 0 to 7200 ppm, and RH OFR ranging from 7 % to 85 %. For experiments where [O 3 ] 0, LFR > 6000 ppm, NO 3exp was calculated from the decay of o-xylene because (1) p-cymene has a large ionized fragment at C 7 H + 9 (thus interfering with detection of toluene), (2) NO 3 oxidation products were generated that interfered with detection of oxygenated tracers (butanol, benzaldehyde, and butanal), and (3) the remaining tracers that were used were too reactive towards NO 3 to accurately constrain NO 3exp .  (Vandaele et al., 1998;Orphal et al., 2003).   Figure 4 suggests that humidity-dependent k w, N 2 O 5 values ranging from 0.01 to 0.08 s −1 were required to cover the range of measured NO 3exp . These values agreed within a factor of 2 or better with humidity-dependent k w, N 2 O 5 values ranging from 0.014 to 0.040 s −1 measured by Palm et al. (2017) in a similar OFR and were applied in subsequent model calculations. Figure 5 shows NO 3exp as a function of [O 3 ] 0, LFR for measurements with [NO 2 ] 0, LFR : [O 3 ] 0, LFR = 0.5 ± 0.1 and RH OFR = 11 ± 2 %. The equivalent ambient photochemical age shown on the right y axis was calculated assuming a 14 h average nighttime NO 3 mixing ratio of 30 ppt and a 10 h daytime NO 3 mixing ratio of 0 ppt (Asaf et al., 2010). NO 3exp increased with increasing [O 3 ] 0, LFR due to increased NO 3 production from higher [N 2 O 5 ]. Over the range of measured conditions, increasing [O 3 ] 0, LFR from 33 to 7092 ppm increased NO 3exp from 6.4 × 10 12 to 4.0 × 10 15 molecules cm −3 s −1 . The black line in Fig. 5 represents NO 3exp modeled using the mechanism shown in Table S2 In a related set of experiments, IBBCEAS measurements of the NO 2 : NO 3 ratio at the exit of the OFR (obtained from Fig. 3a spectra) Fig. 7d. The measured NO 2 : NO 3 values are comparable to, or lower than, the modeled NO 2 : NO 3 values obtained under similar conditions and, therefore, broadly support using model results to further investigate the fate of (1) RO 2 formed from NO 3 oxidation of VOCs, (2) alkyl radicals that are reactive towards NO 2 and O 2 , and (3) VOCs that are reactive towards O 3 and NO 3 in the following sections.

Fate of organic peroxy radicals (RO 2 ) formed from NO 3 + VOC reactions
Organic peroxy radicals (RO 2 ) react with NO, NO 2 , NO 3 , HO 2 , or other RO 2 to generate alkoxy (RO) radicals, peroxynitrates (RO 2 NO 2 ), hydroperoxides or organic peroxides, and may additionally undergo autooxidation via sequential isomerization and O 2 addition. To investigate the fate of RO 2 as a function of OFR-iN 2 O 5 conditions, we applied the methodology of  by calculating the fractional oxidative loss of a generic alkyl or acyl RO 2 to each of these species over the range of conditions shown in Fig. 7. Kinetic data from Orlando and Tyndall (2012) that were used in these calculations are summarized in Table S4. Under almost all OFR-iN 2 O 5 conditions shown in Fig. 7, RO 2 reactions with NO, HO 2 , and RO 2 were minor (< 1 %) loss pathways compared with reaction with NO 2 and NO 3 . We conducted a model sensitivity analysis in which the RO 2 + RO 2 reaction rate was enhanced by increasing NO 3 R ext from 0.07 to 0.7 s −1 and increasing the RO 2 + RO 2 rate constant from 1 × 10 −11 to 1 × 10 −10 cm 3 molecule −1 s −1 (Berndt et al., 2018a, b). Despite these perturbations, the relative contribution of RO 2 +RO 2 reactions to total RO 2 loss remained < 1 % across this range of OFR-iN 2 O 5 conditions. To investigate the relative importance of competing RO 2 + NO 2 and RO 2 + NO 3 pathways, we defined the fractional reactive loss of RO 2 due to NO 3 , F RO 2 +NO 3 : (3) Figure 8a and b show F RO 2 +NO 3 calculated for alkyl and acyl RO 2 , respectively. To simplify the analysis, we assumed that the thermal decomposition of RO 2 NO 2 species formed from RO 2 + NO 2 reactions was slow compared with τ OFR . This assumption generates a lower limit F RO 2 +NO 3 value for the alkyl RO 2 case, where RO 2 NO 2 decomposition occurs on timescales of seconds or less (Orlando and Tyndall, 2012) but has minimal influence on the acyl-RO 2 case due to higher thermal stability of peroxyl acyl nitrates. For alkyl RO 2 , Fig. 8a shows that F RO 2 +NO 3 = 0.5 was achieved between [NO 2 , O 3 ] 0, LFR = (125 ppm, 250 ppm) and (3240 ppm, 1800 ppm). For acyl RO 2 , due to faster reaction with NO 2 , Fig. 8b shows that F RO 2 +NO 3 = 0.5 was achieved using [NO 2 , O 3 ] 0, LFR = (350 ppm, 700 ppm) to (1.1 %, 0.6 %).
To investigate the feasibility of generating OFR-iN 2 O 5 conditions where RO 2 loss is dominated by autooxidation, we calculated the lifetime of alkyl and acyl RO 2 (τ RO 2 ) over the range of OFR-iN 2 O 5 conditions shown in Fig. 7 and Fig. 8a and b. As shown in Fig. 8d   timescales range from 0.005 to 200 s depending on the specific RO 2 composition (Crounse et al., 2013), OFR-iN 2 O 5 may achieve autooxidation-dominant conditions for some RO 2 but not for others.

Fate of aromatic alkyl radicals (R) formed from NO 3 + VOC reactions
The majority of aromatic alkyl radicals (R) that are generated from NO 3 oxidation of VOCs quickly react with O 2 to generate RO 2 . However, NO 3 oxidation of a subset of aromatic VOCs generates R that react more slowly with O 2 , thereby enabling competing reactions with NO 2 . For example, the phenoxy radical (C 6 H 5 O) generated from NO 3 oxidation of phenol (C 6 H 5 OH) has k O 2 : k NO 2 < 2.4 × 10 −9 (Platz et al., 1998), and the C 10 H 7 NO 3 radical that is generated from NO 3 oxidation of naphthalene (C 10 H 8 ) has k O 2 : k NO 2 < 4 × 10 −7 (Atkinson et al., 1994). Alkyl radicals generated from NO 3 oxidation of other PAHs may behave similarly to C 10 H 7 NO 3 , but kinetic data are unavailable in the literature. To investigate the relative importance of competing R + NO 2 and R + O 2 reactions in these systems, we defined the fractional reactive loss of R with respect to O 2 , F R+O 2 : (4) Figure 8c shows F R+O 2 over the same OFR-iN 2 O 5 operating conditions used to generate Fig. 7 and Fig. 8a

Fate of VOCs reactive towards O 3 and NO 3
We defined the fractional reactive loss of a VOC with respect to NO 3 , F VOC+NO 3 : and we established F VOC+NO 3 = 0.9 as the criterion for NO 3 -dominated oxidative loss. Figure 9 plots NO 3 : O 3 at which F VOC+NO 3 = 0.9 for several classes of organic compounds with published k NO 3 and k O 3 values greater than 10 −16 and 10 −19 cm −3 molecules −1 s −1 , respectively. Therefore, this figure excludes compounds such as alkanes and monocyclic aromatics that react slowly with NO 3 and are essentially unreactive towards O 3 (F NO 3 ≈ 1).  Figures 7 and 9 as well as kinetic data from the literature suggest that the injection of 2 ppm NO 2 and 200 ppm O 3 into the LFR was sufficient to achieve F VOC+NO 3 ≥ 0.9 for phenols, PAHs with no double bonds, and mono-and sesquiterpenes with one double bond at low RH OFR . Increasing [NO 2 ] 0, LFR to 150 ppm and [O 3 ] 0, LFR to 300 ppm additionally achieved F VOC+NO 3 ≥ 0.9 for acenaphthylene, isoprene, and mono-and sesquiterpenes with one double bond at elevated RH OFR . Further increasing [NO 2 ] 0, LFR to 5400 ppm and [O 3 ] 0, LFR to 3000 ppm achieved F VOC+NO 3 ≥ 0.9 for ≥ C3 linear alkenes, unsaturated aldehydes, and monoand sesquiterpenes with two double bonds at low RH OFR . While [NO 2 , O 3 ] = [20 %, 10 %] (not shown) achieved F VOC+NO 3 ≥ 0.9 for (E)-3-penten-2-one and ethene, the corresponding NO 3exp ≈ 10 14 molecules cm −3 s achieved at this condition ( Fig. 7a) was insufficient to oxidize more than 1 %-2 % of the initial ethene concentration due to its slow NO 3 rate constant (Atkinson, 1991).

NO 3 estimation equation for OFR-iN 2 O 5
Previous studies reported empirical OH exposure algebraic estimation equations for use with OFRs Peng et al., 2015Peng et al., , 2018Lambe et al., 2019). These equations parameterize OH exp as a function of readily measured experimental parameters, thereby providing a simpler alternative to detailed photochemical models for experimental planning Figure 9. NO 3 : O 3 at which F VOC+NO 3 = 0.9 for representative VOCs with k NO 3 > 10 −16 and k O 3 > 10 −19 cm 3 molecules −1 s −1 (Manion et al., 2015). Horizontal bands represent upper and lower limit values calculated assuming k w, N 2 O 5 = 0.01 and 0.08 s −1 . and analysis. Here, we expand on those studies by deriving an NO 3exp estimation equation for OFR-iN 2 O 5 . Model results obtained from the base case of the model -a VOC reacting with NO 3 at 2.5 × 10 −12 cm 3 molecule −1 s −1 as a surrogate for NO 3 R ext -were used to derive the following equation that allows for the estimation of NO 3exp for OFR-iN 2 O 5 : The phase space of OFR-iN 2 O 5 parameters for fitting Eq. (6) to the NO 3exp model results was defined as follows: [O 3 ] 0, LFR = 10-1000 ppm, [NO 2 ] 0, LFR = 10-1000 ppm, [NO 2 ] 0, LFR : [O 3 ] 0, LFR ≤ 2, NO 3 R ext = 1-200 s −1 , k w OFR , N 2 O 5 = 0.01-0.08 s −1 , T OFR = 0-40 • C, and τ OFR = 60-300 s. The cases where [O 3 ] 0, LFR > 1000 ppm and/or [NO 2 ] 0, LFR : [O 3 ] 0, LFR > 2 were not considered due to less practical interest. We explored 11, 11, 7, 4, and 5 logarithmically evenly distributed values in the ranges of [O 3 ] 0, LFR , [NO 2 ] 0, LFR (11 values over 10-1000 ppm), NO 3 R ext , k w, N 2 O 5 , and τ OFR , respectively. Due to significantly different chemical regimes in different parts of the phase space, fit coefficients that are reported in Table 1 were obtained by fitting the same functional form  Fig. 5. Logarithms of first-and secondorder terms were successively added until no further fit quality improvement was achieved. Figure 10 compares NO 3exp estimated from Eq. (6) and calculated from the model described in Sect. 2.2. The mean absolute value of the relative deviation was 49 % which is comparable to results obtained for previous estimation equations with significant NO y chemistry (Peng et al., 2018). NO 3 R ext of a system will change over the course of multiple generations of NO 3 oxidation due to changes in kinetic rate coefficients between different species and NO 3 (k NO 3 ). The sensitivity of Eq. (6) to changes in NO 3 R ext depends in part on the relative magnitudes of NO 3 R ext and the internal NO 3 reactivity, NO 3 R int , which is approximately equal to k NO 2 +NO 3 [NO 2 ]. If NO 3 R int NO 3 R ext , changes in NO 3 R ext would have minimal influence on Eq. (6). In one case study, we examined changes in NO 3 R ext following conversion of biogenic VOCs (BVOCs) to gas-phase carbonyl oxidation products with known k NO 3 values. Table S5 compares k NO 3 of isoprene to methyl vinyl ketone and methacrolein, α-pinene to pinonaldehyde, sabinene to sabinaketone, and 3-carene to caronaldehyde. At the limit where 100 % of each BVOC is converted to its carbonyl oxidation product, NO 3 R ext decreases by a factor of 200 or greater. Unsaturated organic nitrates that are generated from BVOC + NO 3 may also be reactive towards NO 3 , but k NO 3 for these species are not available. In another case study, we examined changes in NO 3 R ext following conversion of 2406 A. T. Lambe et al.: N 2 O 5 and NO 3 generation in a coupled LFR-OFR BVOCs to SOA. An effective k NO 3 for SOA was calculated using the following equation adapted from Lambe et al. (2009): where F diff is a correction factor accounting for diffusion limitations to the particle surface in the transition regime (Fuchs and Sutugin, 1970), γ is the fraction of collisions between NO 3 and SOA resulting in reaction; D p is the surface area-weighted mean particle diameter; ρ p is the particle density; N A is Avogadro's number; c is the mean molecular speed of NO 3 (3.2×10 4 cm s −1 at T = 298 K); M SOA is the mean molecular weight of the SOA; and D NO 3 = 0.08 cm 2 s −1 is the NO 3 diffusion coefficient in air (Rudich et al., 1996). Figure S4 shows k SOA+NO 3 as a function of D p ranging from 1 to 1000 nm, assuming ρ p = 1.4 g cm −3 , M SOA = 250 g mol −1 (Nah et al., 2016), and an upper limit γ = 0.1 for BVOC-derived SOA (Ng et al., 2017). For reference, the range of slowest (isoprene) and fastest (humulene) known k BVOC+NO 3 are indicated by the vertical blue line on the y axis. At the limit where 100 % of a BVOC is converted to SOA, NO 3 R ext decreases by a factor of 10 or greater depending on k BVOC+NO 3 and D p . Taken together, these results suggest that NO 3 R ext decreases following NO 3 oxidation of BVOCs to carbonyl oxidation products and/or SOA. In this case, inputting NO 3 R ext of the BVOC precursor to Eq. (6) generates a lower limit to NO 3exp over multiple generations of NO 3 oxidation. Results for other systems will depend on the k NO 3 values of associated gasand condensed-phase precursors and their oxidation products.
3.6 SOA generation from β-pinene + NO 3 To apply the OFR-iN 2 O 5 technique to SOA formation studies, we generated SOA from β-pinene + NO 3 in the absence of seed particles using [O 3 ] 0, LFR = 300 ppm, [NO 2 ] 0, LFR = 150 ppm, and RH OFR ≈ 1 %. PTR-MS measurements confirmed the complete consumption of β-pinene, and numerous product ions were detected. The largest ions detected were (H + )C 9 H 14 O and (H + )C 10 H 14 which may correspond to nopinone (C 9 H 14 O) and fragmentation or decomposition products of C 10 H 17 NO 4 , respectively (Hallquist et al., 1999;Claflin and Ziemann, 2018). The mass yield of SOA ranged from 0.03 to 0.39 over β-pinene mixing ratios ranging from 20 to 400 ppbv that were injected into the OFR. These yield values are broadly consistent with previous environmental chamber studies (Ng et al., 2017) but are lower than chamber SOA yields obtained at the same β-pinene mixing ratio, Figure 10. NO 3exp calculated from the estimation equation (Eq. 6 and Table 1) as a function of NO 3exp calculated from the full OFR-iN 2 O 5 KinSim mechanism (Table S2). Solid and dashed lines correspond to the 1 : 1 and the 1 : 3, and 3 : 1 lines, respectively.
presumably due to the absence of seed particles in the OFR (Lambe et al., 2015). To compare the results obtained using OFR-iN 2 O 5 with a conventional environmental chamber method, Fig. 11a and b show HR-ToF-AMS spectra of SOA generated from NO 3 oxidation of β-pinene in the Georgia Tech chamber (Boyd et al., 2015) and in the OFR, along with a scatter plot of relative ion abundances present in the two spectra (Fig. 11c). The same spectra are presented on a logarithmic scale in Fig. S5. As is evident, β-pinene + NO 3 SOA generated in the chamber and OFR exhibit a high degree of similarity (linear regression slope = 0.98 and r 2 = 0.99). The largest ion signal was observed at NO + , which, along with the signal at NO + 2 and NO + : NO + 2 = 6.7, is consistent with the formation of particulate organic nitrates (Farmer et al., 2010). Signals observed at CHO + , C 2 H 3 O + , and other C x H y O + >1 ions suggest the presence of other multifunctional oxidation products.

Conclusions
OFR-iN 2 O 5 complements recently developed methods that enable NO x -dependent photooxidation studies in OFRs such as OFR-iN 2 O and OFR-iC 3 H 7 ONO (Lambe et al., 2017;Peng et al., 2018;Lambe et al., 2019) Figure 11. AMS spectra of SOA generated from NO 3 oxidation of β-pinene in (a) the Georgia Tech environmental chamber (Boyd et al., 2015) and (b) OFR-iN 2 O 5 . The scatter plot in (c) shows spectra generated in the OFR and in the chamber plotted against each other. towards NO 3 than OH; (2) NO 3exp is higher than OH exp ; and (3) (NO 3 R) int of OFR-iN 2 O 5 , which is dominated by the NO 3 + NO 2 reaction, is larger and easier to manipulate than the internal OH reactivity of OFR-iN 2 O and OFR-iC 3 H 7 ONO, which is dominated by OH + HO 2 and OH + NO 2 reactions. To identify optimal OFR-iN 2 O 5 conditions for different applications, we characterized NO 3exp , τ RO 2 , F RO 2 +NO 3 , F R+O 2 , and F VOC+NO 3 at [O 3 ] 0, LFR = 10 ppm to 10 %, [NO 2 ] 0, LFR : [O 3 ] 0, LFR = 0.01 to 2.0, and RH OFR = 7 % to 85 %. Optimal NO 3exp was achieved by minimizing [H 2 O] in the OFR and associated humidity-dependent N 2 O 5 wall losses. This is contrary to most OFR techniques that are used to generate OH radicals, where optimal OH exp is achieved by maximizing [H 2 O] and the associated OH production from the O( 1 D) + H 2 O reaction and/or H 2 O photolysis at λ = 185 nm. Figure 12 presents image plots that represent OFR-iN 2 O 5 conditions suitable for generating optimal NO 3exp , NO 3 : O 3 , NO 2 : NO 3 , and τ RO 2 values at the lower and upper limit k w, N 2 O 5 values that were measured. Most OFR-iN 2 O 5 conditions using [O 3 ] 0, LFR > 200 ppm generated NO 3exp > 1.5 × 10 12 molecules cm −3 s (Fig. 12a, b), which is sufficient to oxidize isoprene and compounds with similar k NO 3 ; for reference, NO 3exp > 1.6 × 10 11 molecules cm −3 s is required to oxidize α-pinene. At [O 3 ] 0, LFR > 200 ppm and [NO 2 ] 0, LFR : [O 3 ] 0, LFR > 0.5, OFR-iN 2 O 5 generated NO 3 : O 3 > 10 −3 at k w, N 2 O 5 = 0.01 s −1 (Fig. 12c), which achieved F VOC+NO 3 > 0.9 for mono-and sesquiterpenes with one double bond, most PAHs, and phenol/methoxyphenol species. Achieving NO 3 : O 3 > 10 −3 at k w, N 2 O 5 = 0.08 s −1 was more challenging (Fig. 12d). Increasing [O 3 ] 0, LFR decreased [NO 2 ] : [NO 3 ] and, therefore, increased F RO 2 +NO 3 (Fig. 12e, f). In contrast, decreasing [O 3 ] 0, LFR or increasing k w, N 2 O 5 , and, consequently, NO 3exp , increased τ RO 2 (Fig. 12g, h), potentially allowing more time for the autooxidation processes to occur. The best overlap between OFR-iN 2 O 5 conditions that achieved F RO 2 +NO 3 > 0.9 and τ RO 2 > 1 s was obtained with [NO 2 ] 0, LFR ≈ 2-3 ppm and [O 3 ] 0, LFR ≈ 200-300 ppm. Because atmospheric NO 2 : NO 3 is highly variable and often much larger than NO 2 : NO 3 achieved using OFR-iN 2 O 5 (Brown et al., 2003;Stutz et al., 2004), simply attempting to maximize F RO 2 +NO 3 may not always be necessary and has trade-offs such as decreasing NO 3 : O 3 and F VOC+NO 3 . OFR-iN 2 O 5 was more difficult to apply to species such as unsaturated carbonyls and mono-and sesquiterpenes with multiple double bonds that react more efficiently with O 3 than other VOCs; here, alternative NO 3 generation techniques that do not introduce O 3 to the OFR warrant consideration, even though they are more difficult to implement (Palm et al., 2017).
Because OFR-iN 2 O 5 can continuously generate N 2 O 5 and NO 3 at room temperature, it is significantly easier to apply in continuous flow reactor studies than related techniques. However, in addition to the aforementioned considerations, high N 2 O 5 and HNO 3 concentrations that are generated using OFR-iN 2 O 5 complicate the application of techniques such as iodide-adduct chemical ionization mass spectrometry due to efficient reactions between the iodide reagent ion and N 2 O 5 or HNO 3 (Lee et al., 2014). Additionally, the humidity-dependent N 2 O 5 wall loss rate must be accurately characterized to model the performance of a specific OFR-iN 2 O 5 configuration. Future applications of OFR-iN 2 O 5 will investigate the NO 3 -initiated OVOC and SOA formation potential of simple and complex precursors in laboratory and field studies.
Code and data availability. Data and KinSim mechanisms presented in this paper are available upon request. The KinSim kinetic solver is freely available at http://tinyurl.com/kinsim-release (Peng and Jimenez, 2020).
Author contributions. ATL, ECW, and AA conceived and planned the experiments. ATL, JEK, FM, LRW, PLC, AA, and JEP carried out the experiments. MC and AF performed the IBBCEAS measurements and data analysis. AL, JLJ, and ZP conceived and planned the model simulations, and ATL and ZP carried out the model simulations. ATL, ECW, ZP, and JLJ contributed to the interpretation of the results. AL took the lead in writing the paper. All authors provided feedback on the paper.
Competing interests. The authors declare no competing interests.
Acknowledgements. Andrew T. Lambe thanks Christopher Boyd and Sally Ng (Georgia Tech) for sharing AMS data obtained in their environmental chamber, and the following colleagues for helpful discussions: Megan Claflin, Manjula Canagaratna, John Jayne, and Douglas Worsnop from ARI; William Brune from Pennsylvania State University; Manfred Winnewisser from Ohio State University; Karl Christe from the University of Southern California; and Robert Woodward-Massey, Youfeng Wang, and Chunxiang Ye from Peking University. The authors thank the ACMCC and participants of the ACMCC pON experiment in December 2018.
Financial support. The ACMCC pON experiment was supported by the French Ministry of Environment and part of the COST Action CA16109 COLOSSAL and the Aerosol, Clouds, and Trace gases Research InfraStructure (ACTRIS). Zhe Peng and Jose L. Jimenez were supported by the US NSF (grant no. AGS-1822664) and EPA STAR (grant no. 83587701-0). This paper has not been reviewed by the EPA and no endorsement should be inferred.
Review statement. This paper was edited by Keding Lu and reviewed by three anonymous referees.