Impact of temperature-dependent non-PAN peroxynitrate formation, RO₂NO₂, on nighttime atmospheric chemistry

Abstract

The formation of peroxynitrates (RO₂NO₂) from the reaction of peroxy radicals (RO₂) and nitrogen dioxide (NO₂) and their subsequent redissociation are typically not included in chemical mechanisms. This is often done to save computational time as the assumption is that the equilibrium is strongly towards the RO₂ + NO₂ reaction for most conditions. Exceptions are the reactions of the methyl peroxy radical due to its abundance in the atmosphere and of acyl-RO₂ radicals due to the long lifetime of peroxyacyl nitrates RO₂NO₂ (PANs). In this study, the nighttime oxidation of cis-2-butene and trans-2-hexene in the presence of NO₂ is investigated in the atmospheric simulation chamber SAPHIR, Forschungszentrum Jülich, Germany, at atmospherically-relevant conditions at different temperatures (≈276 K, ≈293 K, ≈305 K). Measured concentrations of peroxy and hydroperoxy radicals as well as other trace gases (ozone, NO₂, volatile organic compounds) are compared to state-of-the-art zero-dimensional box model calculations. Good model-measurement agreement can only be achieved when reversible RO₂ + NO₂ reactions are included for all RO₂ species using literature values available from the latest SAR by [Jenkin et al., Atmos. Chem. Phys., 2019, 19, 7691]. The good agreement observed gives confidence that the SAR, derived originally for aliphatic RO₂, can be applied to a large range of substituted RO₂ radicals, simplifying generalised implementation in chemical models. RO₂NO₂ concentrations from non-acyl RO₂ radicals of up to 2 × 10 cm⁻³ are predicted at 276 K, impacting effectively the kinetics of RO₂ radicals. Under these conditions, peroxy radicals are slowly regenerated downwind of the pollution source and may be lost in the atmosphere through deposition of RO₂NO₂. Based on this study, 60% of RO₂ radicals would be stored as RO₂NO₂ at a temperature of 10 °C and in the presence of a few ppbv of NO₂. The fraction increases further at colder temperatures and/or higher NO₂ mixing ratios. This does not only affect the expected concentrations of RO₂ radicals but, as the peroxynitrates can react with OH radicals or photolyse, they could comprise a net sink for RO₂ radicals as well as increase the production of NO_x (= NO + NO₂) in different locations depending on their lifetime. Omitting this chemistry from the kinetic model can lead to misinterpreted product formation and may prevent reconciling observations and model predictions.

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1 Introduction

In the atmosphere, volatile organic compounds (VOCs) and volatile inorganic compounds are removed via oxidation which drives their chemical degradation. In the lower troposphere, the daytime oxidation processes are driven by ozone (O₃), and the hydroxyl radical (OH), which is often found to be the predominant oxidant. Another tropospheric oxidant is the nitrate radical (NO₃) which plays a major role during the night.¹ NO₃ is formed by the reaction of nitrogen dioxide (NO₂) with O₃:

NO₂ + O₃ → NO₃+ O₂, (1)

and is typically in a rapid thermal equilibrium with dinitrogen pentoxide (N₂O₅). The fast photolysis of NO₃ back to NO₂ and O₃ and its loss reaction with nitric oxide (NO) lead to an atmospheric lifetime of a few seconds,² preventing substantial daytime concentrations. Still, in forests below the canopy (high VOC concentrations, low NO concentrations (<0.3 ppbv), among other favourable conditions), the reaction of NO₃ with VOCs might compete with other loss reactions of NO₃ (photolysis, reaction with NO) and contributes to the tropospheric oxidation during the day.^2–4 At night, when there is no OH production from photolytic processes, the oxidation of VOCs is driven by O₃ and NO₃.

In recent field studies utilising the laser-induced-fluorescence (LIF) technique for radical measurements, discrepancies between measured and modelled RO₂ radical concentrations were found at night at moderate O₃ (∼(1–70) ppbv), NO₂ (∼(3–50) ppbv), and low NO (∼(0–0.3) ppbv) mixing ratios in the vicinity of Beijing,^5,6 China, Wangdu,⁷ China, and London,⁸ UK. Just recently, two studies focussing on investigating the oxidation of isoprene⁹ and anthropogenic alkenes¹⁰ by NO₃ resulted in new detailed chemical mechanisms for these compounds as intricate as their oxidation by OH. These studies highlighted the inability of detecting a large fraction of NO₃ -containing isoprene-RO₂⁹ as well as NO₃–RO₂ from short-chain alkenes.¹⁰ Both the isomerisation (isoprene)⁹ and the decomposition (short-chain alkenes)¹⁰ of the NO₃ -alkoxy radical do not lead to the formation of HO₂ or OH, which is required for the RO₂ measurement by the LIF technique:

However, for long-chain alkenes such as for example trans-2-hexene, all RO₂ are detectable.¹⁰ The discrepancies found at nighttime in the field^5–8 may be partly explainable by the missing detection of the LIF instrument of single short-chain alkenes, contained in the measured air mixture. Still large discrepancies remain between measured and modelled RO₂ radicals for high NO (up to ∼100 ppbv) and NO₂ (up to ∼70 ppbv).^5–8,11

Despite improvements in the agreement between measured and modelled RO₂ radicals observed in the experiments in the SAPHIR chamber,¹⁰ discrepancies are still observed in particular right after the injection of the VOC when the RO₂ radical production is the highest, as well as in the time dependence of the RO₂ radical concentrations. The conditions in the chamber were chosen to facilitate the formation of NO₃ radicals, and were characterised by zero NO and medium NO₂ (17–40 ppbv) and ozone (7–30 ppbv). For these conditions, RO₂ radicals formed in the oxidation by either O₃ or NO₃ are assumed to be mainly lost by their reaction with HO₂ or RO₂. NO₂ will be the dominant reaction partner for these RO₂ radicals, producing a short-lived peroxynitrate (RO₂NO₂) which is in a very fast equilibrium (τ_RO2NO2 ≈ 0.2 s at 298 K) with its decomposition in the lower troposphere:

The impact of eqn (3) on the RO₂ radical and the formed RO₂NO₂ is thought to be negligible due to the instability of RO₂NO₂ in lower tropospheric oxidation processes, therefore, the reaction of RO₂ and NO₂ forming RO₂NO₂ is omitted in most atmospheric models for non-acyl RO₂ radicals except for CH₃O₂.¹² For the latter, the formation of alkyl peroxynitrates has been thought to be mostly relevant at cold temperatures in polar regions,^13,14 in the upper troposphere, where Browne et al.¹⁴ found that including the methyl peroxynitrate (CH₃O₂NO₂) chemistry is relevant at temperatures below 240 K, or in biomass burning plumes that are lofted to high altitudes.¹⁴ In contrast, the reactions of acyl-RO₂ radicals with NO₂ are typically implemented in all chemical models due to the long lifetime (∼40–45 min at 298 K) of the corresponding peroxyacyl nitrate RO₂NO₂ (PANs) and, consequently, their relevance on regional and even global scales.¹³

A recent study by Khan et al.¹⁵ investigated the global effect of the reversible formation of RO₂NO₂ on NO_x, i.e. NO + NO₂, OH, and O₃, using the generic rate coefficients from Jenkin et al.¹² for more than 40 non-acyl RO₂ radicals. Loss rates for the formed RO₂NO₂ species via reaction of OH and photolysis were also included. In their study, it was shown that even on the ground, up to 25% more NO_x would be expected at the equator as photolysis and reaction with OH accelerate the consumption of RO₂NO₂. This indicates that their role and importance might need to be reevaluated.

A measure for the ratio of RO₂ and RO₂NO₂ concentrations at equilibrium is given by the equilibrium constant K, the ratio of the forward and backward reaction rate constants k_RO2+NO2 and k_RO2NO2, respectively:

K = k_RO2+NO2/k_RO2NO2. (4)

For the alkyl peroxynitrates CH₃O₂NO₂ and ethyl peroxynitrate (C₂H₅O₂NO₂), the equilibrium constant is 7 × 10⁻¹¹ cm³ at 276 K, respectively (Table 1). In contrast, peroxyacetyl nitrate (CH₃C(O)O₂) has an equilibrium constant of 1 × 10⁻⁸ cm³ due to its longer lifetime. While at high temperatures formation of alkyl peroxynitrates is not important, the equilibrium shifts more towards the RO₂NO₂ products at lower temperatures, making it worthwhile to evaluate the impact of RO₂NO₂ formation during winter conditions.

Table 1 Temperature-dependent rate coefficients for the formation and decomposition of different alkyl peroxynitrates, adopted from Jenkin et al.¹² Rate coefficients are given for ambient pressure (1013 hPa) and T = 276 K, 292 K, and 305 K

RO2 or RO2NO2	k 0	k ∞	F c	k 276 K	k 292 K,1 atm	k 305 K,1 atm
a Recommended by IUPAC.^16 b Determined from isomeric mixtures formed from the reaction of chlorine with butane^17,18 and recommended by Jenkin et al.^12 c Determined from isomeric mixtures formed from the reaction of chlorine with hexane^18 and recommended by Jenkin et al.^12 d Pressure-independent generic rate coefficient recommended by Jenkin et al.^12
Forward reaction, kRO2+NO2 [cm^3 s^−1]
CH3O2^a	1.2 × 10^−30 (T/300)^−6.9[M]	1.8 × 10^−11	0.36	7.1 × 10^−12	6.2 × 10^−12	5.5 × 10^−12
C2H5O2^a	1.3 × 10^−29 (T/300)^−6.2 [M]	8.8 × 10^−12	0.31	5.6 × 10^−12	5.3 × 10^−12	5.0 × 10^−12
n- and sec- C4H9O2^b		9.6 × 10^−12		9.6 × 10^−12	9.6 × 10^−12	9.6 × 10^−12
RO2^d		9.0 × 10^−12 (=kfPN)		9.0 × 10^−12	9.0 × 10^−12	9.0 × 10^−12
Reverse reaction, kRO2NO2 [s^−1]
CH3O2NO2^a	9.0 × 10^−5exp (−9690/T)[M]	1.1 × 10^16 exp (−10 560/T)	0.36	0.1	0.7	3.2
C2H5O2NO2^a	4.8 × 10^−4exp (−9285/T)[M]	8.8 × 10^15 exp (−10 440/T)	0.31	0.2	1.7	7.5
n- and sec- C4H9O2NO2b		8.3 × 10^15 exp (−10 368/T)		0.4	3.2	14.3
C 6H13O2NO2 isomers^c		7.5 × 10^15 exp (−10 368/T)		0.4	2.8	12.9
RO2NO2^d		7.6 × 10^15 exp (−10 400/T)(=kbPN)		0.3	2.6	11.8

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In this work, the impact of the RO₂ + NO₂ reaction on modelled RO₂ radical concentrations is studied for RO₂ radicals from the oxidation of cis-2-butene and trans-2-hexene by O₃ and NO₃ at different temperatures (≈276 K, ≈293 K, ≈305 K). Experiments were performed in the atmospheric simulation chamber SAPHIR at Forschungszentrum Jülich, Germany. Nighttime conditions with high NO₂ (>20 ppbv) and moderate O₃ (∼10 ppbv) mixing ratios were tested which facilitate the formation of NO₃ and mimic conditions often found at night. Concentrations of HO₂ and RO₂ radicals, as well as of O₃, NO₂, and VOCs were measured and are compared to zero-dimensional box model calculations, incorporating state-of-the-art oxidation schemes. The reaction of non-acyl RO₂ radicals with NO₂ forming RO₂NO₂ and its backward reaction are implemented in the chemical mechanisms of cis-2-butene and trans-2-hexene by using literature values,^12,16–18 and the implications of the findings on the nighttime atmospheric RO₂ chemistry are discussed. The newly introduced ozonolysis scheme and RO₂ isomerisation reactions, suggested by Novelli et al.¹⁰ for cis-2-butene and trans-2-hexene, as well as their temperature dependence are tested and model-measurement comparisons are used to improve the chemical mechanisms for these species.

2 Methodology

2.1 Experiments in the atmospheric simulation chamber SAPHIR

The experiments were conducted in the outdoor atmospheric simulation chamber SAPHIR at Forschungszentrum Jülich, Germany. The 270 m³ chamber (5 m diameter, 18 m length) allows to study atmospheric processes in a well-characterised system and is confined by an inert double-wall Teflon (FEP) film, enabling high transmittance of impinging solar radiation. A shutter system allows the shielding of the chamber from solar radiation to also mimic nighttime conditions. The temperature inside the chamber is not controlled and thus dependent on ambient conditions. The chamber utilises ultra-pure synthetic air, mixed from ultra-pure nitrogen and oxygen (79.1% N₂, 20.9% O₂, Linde, purity > 99.9999%). Contaminations are prevented from entering the chamber by an over-pressure of ≈33 Pa above ambient pressure. A replenishment flow is applied to account for small leakages and the air sampled by the instruments, causing a dilution for all trace gases with an average first order loss rate of 9.7 × 10⁻⁶ s⁻¹ in the experiments in this study. Two fans are installed to mix the air in the chamber, so that all instruments sample the same air. A detailed description of SAPHIR can be found in previous works.^19–22

Nighttime experiments for cis-2-butene and trans-2-hexene were performed at different temperatures. The nighttime oxidation of cis-2-butene was studied at two different temperatures (T ≈ 276 K (cold), 295 K (medium)). The nighttime chemistry of trans-2-hexene was investigated at three temperatures (T ≈ 276 K (cold), 292 K (medium), 305 K (hot)). At low temperatures (T ≈ 280 K), a pure ozonolysis experiment in the absence of NO₂ was also performed for trans-2-hexene.

The experimental procedure of the experiments is shown in Fig. 1–3. Before each experiment, the chamber was flushed to remove trace gases from the previous experiment. No detectable OH reactivity, equivalent to the inverse lifetime of OH, was observed in the dark, clean, and dry chamber. Cis-2-Butene (Air Liquide, 1% in N₂, purity 99.4%) or trans-2-hexene (Sigma Aldrich, purity 97%) were first injected in the clean, dry, and dark chamber, reaching mixing ratios close to atmospheric conditions (<6 ppbv). Afterwards, 170–210 ppmv of carbon monoxide (CO, Air Liquide, purity 99.997%) was added to the chamber acting as OH scavenger by converting OH into HO₂ to avoid its reaction with cis-2-butene or trans-2-hexene. In one oxidation experiment of trans-2-hexene, 142 ppmv of methane (CH₄, Air Liquide, purity 99.5%) were injected instead to aim for lower HO₂ radical concentrations. Since more reactions are involved to form HO₂, a slower production of HO₂ can be achieved, and higher RO₂ radical concentrations are expected due to the formation of CH₃O₂. Nitrogen dioxide (Linde, 500 ppmv in N₂, purity 99.991%) of up to 35 ppbv was then injected in all experiments with the exception of the ozonolysis study. Afterwards, ozone generated by a silent discharge ozoniser (O3onia) was injected to reach mixing ratios between 12 ppbv and 33 ppbv (96 ppbv in the ozonolysis experiment), initiating the production of NO₃ in the reaction with NO₂ (eqn (1)). Due to the fast reaction of cis-2-butene and trans-2-hexene with O₃ and NO₃, they are consumed on a timescale of ∼2–5 hours, and the alkene was injected a second time and third time (experiments with cis-2-butene at 295 K and trans-2-hexene at 305 K). To boost the oxidation by NO₃, NO₂ was injected a second time as well. In all experiments, no NO was present in the chamber and OH radical concentrations were below the detection limit, leading to a negligible contribution of OH chemistry. All experiments were conducted in dry conditions (H₂O < 0.07 ppmv) and in complete darkness.

Fig. 1 Comparison of modelled and measured (5 minutes average) trace gases and HO₂ and RO₂ radicals in the experiment with cis-2-butene for cold (276 K) and medium (295 K) temperatures. Model results displayed as FZJ (blue) and FZJ + RO₂NO₂ (brown) models refer to the FZJ mechanism without and with including additional formation of non-acyl RO₂NO₂, respectively. Dashed lines indicate the total RO₂ radical concentration predicted by the model, while solid lines are the RO₂ radical concentration predicted to be detectable by the RO_x LIF system, as discussed in Section 2.2. Injections of chemical species into the chamber are marked by vertical lines.

Fig. 2 Comparison between modelled and measured (5 minutes average) trace gases and HO₂ and RO₂ radical concentrations in the trans-2-hexene experiment performed at ≈276 K with CO as OH scavenger. Model results displayed as FZJ (blue) and FZJ + RO₂NO₂ (brown) models refer to the FZJ mechanism with and without including additional formation of non-acyl RO₂NO₂, respectively. In addition, FZJ + RO₂NO₂ disc.-corr. (red) denotes the model run considering the overestimation of ozonolysis-generated RO₂ radical concentrations by a factor of 1.7, observed in the ozonolysis of trans-2-hexene (see text). Injections of chemical species into the chamber are marked by vertical lines.

Fig. 3 Comparison between modelled and measured (5 minutes average) trace gases and HO₂ and RO₂ radical concentrations in the nighttime oxidation experiment of trans-2-hexene in presence of CH₄. Model results displayed as FZJ (blue) and FZJ + RO₂NO₂ (brown) models refer to the FZJ mechanism with and without including additional formation of non-acyl RO₂NO₂, respectively. Solid lines indicate the total RO₂ radical concentration predicted by the model without the RO₂NO₂ interference, while dashed lines are the RO₂ radical concentration predicted by the model considering a 2% interference by RO₂NO₂. Injections of chemical species into the chamber are marked by vertical lines.

2.2 Instrumentation

Measurements of the radicals OH, HO₂, and RO₂ were conducted with a laser-induced fluorescence (LIF) instrument (RO_x LIF).^23,24 Chamber air is sucked into a low-pressure detection cell (≈ 4 hPa) where OH radicals are excited by a laser pulse (repetition frequency = 8.5 kHz) at a wavelength of 308 nm. The subsequently emitted fluorescence light, which is directly proportional to the sampled OH radical concentration, is detected by gated photon counting.^25–27 By adding NO in a second detection cell, a fraction of HO₂ radicals is chemically converted to OH and, thus, HO_x (= OH + f HO₂, f < 1) can be detected.^24–26,28 Possible interferences in the HO_x measurement may appear in the presence of specific RO₂ radicals, when HO₂ is rapidly produced by the RO₂ + NO reaction.²⁸ By working at lower NO concentrations, RO₂ interferences are minimised and do not play a role in the presented experiments. RO₂ radicals are indirectly measured after they are converted into HO₂ or OH in a converter (≈25 hPa) by adding NO. OH, formed from the reaction of HO₂ with NO, is converted back to HO₂ in the converter by addition of excess CO. The HO₂ radicals are then sampled by a detection cell and converted to OH by a continuous addition of pure NO, which enables a high conversion efficiency of HO₂,²³ so that the sum of OH, HO₂, and RO₂ (=RO_x) is measured, from which [RO₂] can be derived. An interference signal in the presence of NO₃ that is equivalent to a RO₂ radical concentration of 3.6 × 10⁶ cm⁻³ per pptv of NO₃ was observed in the RO_x system. A previous study²⁹ also reported a NO₃ interference signal equivalent to HO₂ and RO₂ radical concentrations of 1.0 × 10⁶ cm⁻³ and 1.7 × 10⁶ cm⁻³ per pptv of NO₃, respectively. More details can be found in the ESI‡ Section B. Modelled RO₂ radical concentrations were corrected for this interference which only impacted the experiment at highest temperature when very high concentrations of NO₃ were reached. Modelled HO₂ radical concentrations were corrected using the parametrisation determined by Fuchs et al.²⁹ Recently, it was found that -nitrate-alkoxy radicals decompose in the converter of the RO₂ detection system forming NO₂ and therefore these radicals are not detectable with the LIF technique that requires the formation of either OH or HO₂ in the detection system.^9,10 Examples include alkoxy radicals (RO) produced in the oxidation of anthropogenic alkenes by NO₃ such as CH₃ CH(NO₃)CH(CH₃)O (MCM notation: C₄₂NO₃₃O) formed in the oxidation of cis-2-butene by NO₃. The rate coefficient of the decomposition of CH₃ CH(NO₃)CH(CH₃)O (MCM notation: C₄₂NO₃₃O), forming NO₂, was optimised based on the observed RO₂ in the experiments of the nighttime oxidation of cis-2-butene, resulting in a decomposition rate of 3.0 × 10³ s⁻¹ (this work) compared to 9.5 × 10³ s⁻¹ predicted theoretically¹⁰ at 276 K. Further details can be found in the ESI‡ Section C.

The OH reactivity (k_OH) was measured by a pump-and-probe technique utilising LIF to detect the amount of OH reacting with the sampled air in a flow tube.^30,31 Time series of cis-2-butene and trans-2-hexene and calibrated time series of acetaldehyde were measured by proton-transfer-reaction time-of-flight mass spectrometry (PTR-ToF-MS, Ionicon).^32,33 Normalised counts of cis-2-butene and trans-2-hexene are converted to parts per billion (ppb) by using the observed OH reactivity at the point in time of the VOC injection. Ozone was detected by UV absorption (Ansyco), and CO, CH₄, formaldehyde, and water vapour were monitored utilising cavity ring-down spectroscopy (CRDS, Picarro). Furthermore, NO and NO₂ were measured by a chemilumiscence instrument (EcoPhysics). More detailed information about the performance of the instruments can be found in the ESI‡ Section D. NO₃ and N₂O₅ measurements were not available for any experiment, therefore corresponding wall loss rates were introduced and adjusted to match the observed VOC decay.

2.3 Model calculations

To compare measurements with model results, a zero-dimensional box model is used, starting from the chemical mechanistic information in the FZJ mechanisms for cis-2-butene and trans-2-hexene published by Novelli et al.¹⁰; these are themselves built upon the Master Chemical Mechanism (MCM v3.3.1, http://mcm.leeds.ac.uk).^34,35 Dilution is taken into account by considering a first-order loss for all implemented species as described in Section 2.1. Temperature and pressure are constrained to measured data. The injection of O₃, NO₂, cis-2-butene, trans-2-hexene, CO, and CH₄ into the chamber is reproduced by an active source during the injection period, with a source strength that is matched to the measured increase of the observables. The temperature-dependent reaction rate of trans-2-hexene with O₃ is taken from Atkinson and Arey.¹ At medium and high temperatures, the reaction rate of trans-2-hexene and NO₃ is taken to be twice as large as the temperature-independent reaction rate used in the MCM; the latter is estimated from the SAR in Jenkin et al.³⁴ The increased rate is consistent with the study by Novelli et al.¹⁰ The FZJ mechanisms for cis-2-butene and trans-2-hexene used here as the base kinetic models differ from the MCM by the following points:

• Ozonolysis scheme for cis-2-butene and trans-2-hexene including the formation of O=CHCH₂OO˙ (ethanal-2-peroxy, MCM notation: HCOCH₂O₂) and O=CHCHO(OO˙)CH₂CH₃ (butanal-2-peroxy, MCM notation: BUTALAO2). The subsequent bimolecular chemistry for these radicals follows the MCM.

• Isomerisation reactions for ethanal-2-peroxy and butanal-2-peroxy based on quantum chemical calculations, leading to the formation of O=C(OOH)CH₂OO˙ (ethyl-1-peracid-2-peroxy) and O=C(OOH)CH(OO˙)C₂H₅ (butyl-1-peracid-2-peroxy), respectively (Fig. S1, ESI‡).

• Updated alkoxy decomposition rates for RO radicals formed in the oxidation of cis-2-butene and trans-2-hexene by NO₃ based on quantum chemical calculations.

• Optimised yield of the RO and OH radical from the reaction of RO₂ with HO₂ for the first generation NO₃–RO₂ (MCM notation: C₆₂NO₃₃O₂, C₆₃NO₃₂O₂) formed in the oxidation of trans-2-hexene by NO₃.

The follow-up chemistry for additionally included RO₂ and RO radicals was implemented following the SARs in Jenkin et al.,¹² Vereecken et al.,^10,36–38 and Novelli et al.¹⁰ For the model-measurement comparison when NO₃ chemistry is contributing, the fraction of RO₂ which is not measurable by the radical instrument¹⁰ (Section 2.2) must be taken into account, i.e. distinguishing between “total RO₂” and “detectable RO₂”.

The effect of the isomerisation reactions of the RO₂ radicals from the ozonolysis reaction, ethanal-2-peroxy and butanal-2-peroxy, on the predicted RO₂ speciation is investigated by comparing model runs using the FZJ mechanisms with and without including RO₂ isomerisation reactions. In another sensitivity model run, not only reactions of methyl peroxy (CH₃O₂) and PAN-like RO₂ (RC(=O)OO˙) with NO₂ are included, as implemented in the FZJ mechanism, but also the reaction of NO₂ with all formed non-acyl RO₂ species. In this sensitivity run, RO₂ + NO₂ reactions forming RO₂NO₂ as well as the corresponding backward reactions (eqn (3)) are introduced for all formed RO₂ species. Rate constants for the forward and backward reactions for CH₃O₂, ethyl peroxy (C₂H₅O₂), and acetonyl peroxy (CH₃ C(=O)CH₂O₂) are taken from recommendations by IUPAC.¹⁶ Recommendations in Jenkin et al.,¹² partially based on Zabel et al.,¹⁸ are used for the forward and backward reaction rate constants for C₄ peroxy radicals, and for the backward reaction rate constant for C₆–RO₂NO₂ in this work. For all RO₂ for which rate constants cannot be taken from literature, such as for n-C₃H₇O₂, a pressure-independent generic forward reaction rate constant, k_fPN, and a rounded average of reported backward reaction rate constants for C₂ to C₈ alkyl RO₂, k_bPN, recommended by Jenkin et al.,¹² are used. However, the contribution of n-C₃H₇O₂ to the total RO₂ amounts to 2% and is thus negligible. It is important to mention that all the rate coefficients used from literature and SAR are for non-NO₃ substituted RO₂ radicals but are used here due to the lack of specific values for nitrate RO₂ radicals. An overview of temperature-dependent rate coefficients for the formation and decomposition of non-acyl RO₂NO₂ is shown in Table 1, together with the corresponding rate coefficients at T = 276 K, 292 K, and 305 K. We also determined the k_bPN and k_fPN values by a fitting procedure against the experimental data, retrieving values that are within 30% of the literature data above. This supports applying literature data for alkyl-RO₂ to our NO₃-RO₂ radicals, but the fitted values carry a large uncertainty and are not used in the results and discussion below

3 Results

3.1 Nighttime chemistry of cis-2-butene

Measured and modelled time series of HO₂ and RO₂ radical concentrations in the two nighttime experiments investigating the oxidation of cis-2-butene are shown in Fig. 1. For the two experiments in this work, injected O₃, NO₂, and cis-2-butene concentrations are below 15 ppbv, 30 ppbv and 15 ppbv, respectively, and expected NO₃ concentrations do not exceed 8 pptv. For these conditions, on average, NO₃ contributed about 40% at 276 K and 50% at 295 K to the oxidation of cis-2-butene (Table S2, ESI‡). As described in Section 2.2, only 16% and 5% of the most dominant RO₂ that is formed, CH₃ CH(OO˙)CH(ONO₂)CH₃ (MCM notation: C₄₂NO₃₃O₂), are detected by the instrument at cold (T ≈ 276 K) and medium (T ≈ 295 K) temperatures, respectively. The higher the temperature becomes, the faster the decomposition of the alkoxy radical is. Therefore, the modelled total RO₂ and the modelled detectable RO₂ are discussed separately in the following.

For cold conditions, there is a large difference in the total modelled RO₂ between the FZJ mechanisms with and without including the additional formation of RO₂NO₂, with the latter predicting a much lower concentration (by a factor of 7 on average) in the first two hours of oxidation and a much slower increase. When the detectable modelled RO₂ are compared to the measured RO₂ radical concentrations at low temperatures, the mechanism including non-acyl RO₂NO₂ formation (FZJ + RO₂NO₂ model) reproduces the data very well with a model-to-measurement ratio of 0.84, and excellent reproduction of the time dependence. The mechanism without including RO₂ + NO₂ reactions (FZJ model) can reasonably reproduce the detectable RO₂ after one hour after the cis-2-butene injections (average model-to-measurement ratio = 0.8). However, their concentration is largely overestimated by up to a factor of 4.5 right after the injection, with a distinctly earlier concentration peak. The smaller difference between the two model results observed for the second injection of cis-2-butene is due to a larger contribution of CH₃O₂ (from close to 0% after the first cis-2-butene injection to ∼ 20% after the second). As the reaction of CH₃O₂ with NO₂ is included in both the FZJ and MCM mechanisms, the effect of the correction is smaller.

Differences of total RO₂ radical concentrations between the two FZJ mechanisms are also observed in the experiment at medium temperatures. However, the difference is much less pronounced and the average ratio of concentrations obtained between the two FZJ mechanisms is 1.1. A small underestimation of the measured RO₂ (by a factor of 1.2) by both mechanisms can be observed by comparing it to the detectable RO₂. The FZJ mechanism without alkyl-RO₂ + NO₂ reactions would predict a small peak of the detectable RO₂, while concentrations are better described if these reactions are considered (Fig. 1). From the second injection on, RO₂ radical concentrations predicted by both mechanisms converge to the same value.

The measured HO₂ radical concentrations are well described by both FZJ mechanisms and agree within 36% (FZJ model) and 21% (FZJ + RO₂NO₂ model) after the first VOC injection and within 5% (both FZJ models) after the second VOC injection in the experiment at cold conditions and within 7% (both FZJ mechanisms) in the experiment at medium temperatures. A comparison of the concentration of acetaldehyde, a major product of the ozonolysis of cis-2-butene, obtained by the different models is shown in Fig. S11 (ESI‡) for the experiment at cold conditions. The different mechanisms predict similar product concentrations with a model-to-measurement ratio of 0.7.

3.2 Nighttime chemistry of trans-2-hexene

Fig. 2 shows measured HO₂ and RO₂ radical concentrations for the experiment with trans-2-hexene performed at ≈276 K. In contrast to cis-2-butene, the amount of RO₂ that cannot be detected is negligible,¹⁰ so that the total RO₂ can be directly compared to the measurements.

The addition of RO₂ + NO₂ reactions leads to a less steep increase of the RO₂ radical concentrations which is in much better agreement with the measurements after the first injection of trans-2-hexene (within 2% compared to 20% for the FZJ model). Similar to cis-2-butene, at 276 K the FZJ mechanism expects a fast increase of RO₂ radicals, which is not observed in the measurements.

As ozone contributes up to 40% to the oxidation of trans-2-hexene, and discrepancies were observed earlier when ozone dominated the oxidation at 292 K in the study by Novelli et al.,¹⁰ an ozonolysis experiment was performed for trans-2-hexene. Fig. S2 (ESI‡) shows the comparison between measured and modelled HO₂ and RO₂ radicals for the MCM and the FZJ mechanisms. An agreement within 20% and 30% between measured and modelled HO₂ is found for the MCM and the FZJ mechanism, respectively. Although the FZJ mechanism improves the agreement between measured and modelled RO₂ radicals, still a ratio of modelled to measured of 1.7 remains at the point of injection of trans-2-hexene. The impact of this discrepancy, in the presence of NO₂, was estimated by assuming an overall overestimation of a factor of 1.7 for RO₂ formed from ozonolysis and correcting their concentrations modelled by the FZJ mechanism including RO₂NO₂ formation by this factor. As a consequence, the total modelled RO₂ radical concentrations would be 25% lower (cold temperatures) at the peak RO₂ after the first injection (Fig. 2) with an average ratio of modelled to measured RO₂ of ≈0.7. Although the agreement between measured and modelled RO₂ is decreased when an overestimation of RO₂ of 1.7 is assumed (from 12% to 37% for the first 2.5 hours of oxidation), the modelled RO₂ shows the same behaviour in reaching the peak RO₂ radical concentrations and a worse agreement is found for the mechanism without additional NO₂ reactions (model-to-measurement ratio of 1.9 for the first 2.5 hours of oxidation). More details about the interpretation of the ozonolysis experiment can be found in the ESI‡ Section A.

As compared to cis-2-butene (Fig. 1) and to the ozonolysis experiment (Fig. S2, ESI‡), the HO₂ radicals are largely underestimated by both models. HO₂ radicals are mainly formed from the reaction of CO with OH (≈61% of the total production rate) which is formed directly from the ozonolysis of trans-2-hexene, among other production pathways such as isomerisation reactions of second-generation RO₂ (30% of the total production rate). A similar discrepancy between measured and modelled HO₂ radicals was observed when performing the same experiment but using CH₄ instead of CO as an OH scavenger (Fig. 3).

The observed model-measurement discrepancy could be due to an artefact in the LIF instrument detecting HO₂, if there was a mechanism artificially producing HO₂ in the HO_x detection cell. An instrumental interference by NO₂ and peroxynitric acid (HNO₄, formed in the reaction of HO₂ with NO₂) can be excluded because this would also impact the HO₂ radical concentration measured in the experiment with cis-2-butene, for which no model-measurement discrepancy for HO₂ was observed (Fig. 1). Furthermore, an interference from the contemporary decomposition of RO₂ radicals is minimised by running the HO_x detection cell at reduced NO (Section 2.2) and no indication of an interference was observed when changing the NO concentrations in the HO_x cell. A clear correlation of the model-measurement difference in HO₂ radical concentrations is only found with the modelled non-acyl RO₂NO₂ concentrations (Fig. 4), indicating that the model-measurement discrepancy of HO₂ is likely due to an instrumental interference in the HO₂ measurements from RO₂NO₂. This would be consistent with the good agreement observed for the ozonolysis experiment (Fig. S2, ESI‡). An interference of ≈2% of the non-acyl RO₂NO₂ in the HO_x cell would be enough to explain the measured HO₂ radical concentration (Fig. 2 and 3).

Fig. 4 Correlation between observed model-measurement deviations of HO₂ with modelled non-acyl RO₂NO₂ concentrations. Displayed are NO₃ oxidation experiments of trans-2-hexene.

It is currently not clear how the non-acyl RO₂NO₂ would be detected as HO₂ in the HO_x cell of the LIF instrument, especially as no discrepancy was observed for cis-2-butene. RO₂ radicals are obtained by subtracting the measured HO₂ and OH radicals from the sum of all three radical species (OH + HO₂ + RO₂), as detected in the RO_x LIF system. Therefore, an interference in the HO_x measurement would result in a lower measured RO₂ radical concentration as compared to the “real” value. Using the modelled HO₂ radical instead of the measured value would increase the RO₂ radical concentrations by 20% and 30% in the experiments at low temperatures with CO (Fig. S15, ESI‡) and CH₄ (Fig. 3) as OH scavenger, respectively. As the HO₂ radical concentrations for the conditions of the experiments in this study are low, their impact is limited and no change in the time profile of the RO₂ radical is observed. More details can be found in Section G of the ESI.‡

Two more experiments at 292 K and 305 K were performed with trans-2-hexene (Fig. S12, ESI‡). Although a worse agreement between measured and modelled RO₂ was observed (average model-measurement ratio of 1.5 and 1.2 for 292 K and 305 K, respectively) as compared with the experiment at 276 K, a shift in the peak for measured RO₂ radical concentration could be observed which does not show any “delay” as found in the experiment at cold temperatures (Fig. 2). This is consistent with the faster decomposition rate of the formed RO₂NO₂ at those temperatures and is also reproduced by both models where negligible differences are seen already maximum 30 minutes after the VOC injection.

As compared to the experiment at 276 K (cold), a better agreement between modelled and measured HO₂ radical is obtained. Model calculations tend to overestimate the HO₂ radicals at 276 K. Just recently, a study by McKee et al.³⁹ showed that at high temperatures production of nitryl hydride (HNO₂) from the reaction of HO₂ and NO₂ can be expected. By including this reaction in the model calculations of the experiment at hot conditions (T = 305 K), the comparison of the model with the measurement improves leading to a model-to-measurement ratio of 1.3 on average (compared to 1.6 if the HNO₂ formation is not considered, Fig. S12, ESI‡). More discussion about possible reasons for the observed discrepancies found at 292 K and 305 K for trans-2-hexene can be found in the ESI‡ Section G.

The comparison of acetaldehyde concentrations predicted by the mechanisms is shown in Fig. S14 (ESI‡), showing similar concentrations for the different temperatures. The mechanisms overall underestimate the measured acetaldehyde concentrations by a factor of 1.7 and 3 in the experiments at medium and hot temperatures, respectively, but in the experiment at cold conditions a good agreement is achieved (within 15%). The reason for this temperature-dependent discrepancy cannot be easily explained and needs further investigations.

4 Discussion

An overview of the concentrations of non-acyl peroxynitrates, formed in the nighttime oxidation, is shown in Fig. 5 for cis-2-butene and in Fig. S13 (ESI‡) for trans-2-hexene. Acyl peroxynitrates are excluded here because their formation is implemented identically in both mechanisms, and in the following, RO₂ and RO₂NO₂ refer only to non-acyl peroxy radicals and their respective peroxynitrates, unless noted otherwise.

Fig. 5 Formed non-acyl RO₂NO₂ concentrations and the fraction of non-acyl RO₂ stored as RO₂NO₂ (RO₂NO₂/(RO₂ +RO₂NO₂)) for the two cis-2-butene oxidation experiments in the presence of NO₂ applying the FZJ mechanism either without (FZJ model, blue) or with (FZJ + RO₂NO₂ model, brown) the additional formation of alkyl-RO₂NO₂. Model results of the RO₂NO₂ concentrations, based on the FZJ mechanism without including additional formation of RO₂NO₂ (FZJ model), refer to CH₃O₂NO₂ concentrations. Vertical lines refer to the injection of chemical species.

The RO₂NO₂ concentrations expected from the FZJ mechanism are systematically lower than the RO₂NO₂ concentrations expected from the FZJ + RO₂NO₂ mechanism, including non-acyl RO₂NO₂ formation, as only the formation of CH₃O₂NO₂ is implemented (Section 2.3). A strong increase of peak RO₂NO₂ concentrations from 140 pptv to up to 480 pptv is observed over the temperature range of 295–276 K. While the main loss path for RO₂ radicals in the FZJ model is the loss in the reaction with HO₂ (k∼ (2 − 10) × 10⁻³ s⁻¹), the reaction with NO₂ (k∼ (5 − 9) s⁻¹, Table 1) is the predominant, temporary loss of RO₂ in the FZJ + RO₂NO₂ mechanism, including formation of non-acyl RO₂NO₂, due to the large NO₂ mixing ratios (up to 40 ppbv).

The fraction of RO₂ stored in the reservoir RO₂NO₂ species can be derived from the ratio of corresponding concentrations: RO₂NO₂/(RO₂ + RO₂NO₂) (Table 2, Fig. 5 and Fig. S13, ESI‡). In the experiment at cold conditions, the conversion of RO₂via reaction with NO₂ leads to more than 90% of non-acyl RO₂ that is present in form of the reservoir species RO₂NO₂ throughout the experiment. In comparison, 80% to 40% of the non-acyl RO₂ are stored as RO₂NO₂ throughout the experiment at medium temperatures (Fig. 5), in which the temperature increased from 290 K to 300 K, leading to a shift of equilibrium towards RO₂. When one of the VOCs is injected a large fraction of the RO₂ radicals formed is converted into the reservoir species RO₂NO₂, leading to the slower increase of the free, measurable RO₂ radical concentrations in the FZJ + RO₂NO₂ mechanism, including additional RO₂NO₂ formation, compared to the FZJ mechanism (Fig. 1 and 2). This emphasises the importance of including the formation of peroxynitrates in chemical mechanisms, especially at lower temperatures where the RO₂NO₂/RO₂ ratio can reach a factor of 20.

Table 2 Equilibrium constants of the formation and decomposition of non-acyl RO₂NO₂ (eqn (4)) formed in the oxidation of trans-2-hexene by NO₃, derived from the pressure-independent generic forward reaction rate, k_fPN, and the backward reaction rate for C₆H₁₃O₂ isomers (Table 1), recommended by Jenkin et al.¹²

Temperature [K]	K|eqn (3) [cm^3]
305	7.0 × 10^−13
292	3.2 × 10^−12
276	2.5 × 10^−11

---

At temperatures typically reached in mid latitudes, RO₂NO₂ concentrations are expected to be on the order of 1 × 10¹⁰ cm⁻³ at the conditions tested in this work and can therefore impact the fate of RO_x species. In cities as Beijing,⁵ China, temperatures around 255 K can be reached in winter, leading to a significant fraction of non-acyl RO₂ stored as reservoir RO₂NO₂ species, and thus to different RO₂ radical concentrations. Low temperatures are also present at high altitudes, where biomass burning plumes can introduce polluted conditions, allowing alkyl-RO₂NO₂ other than CH₃O₂NO₂ to be formed and impacting the effective RO₂ radical concentration.

One important finding of this study is that the rate coefficients used for forward and backward reactions (Table 1 and 2) do an excellent job in bringing measurements and model results in agreement despite not being derived for the NO₃-substituted RO₂ radicals as investigated here. This indicates that the substituent on the RO₂ radical does not seem to have an impact on the reaction rate. This allows to generalise the finding beyond the molecules and conditions explored in the SAPHIR chamber.

Fig. 6 shows the fraction of RO₂NO₂/(RO₂ +RO₂NO₂) for different temperatures and NO₂ mixing ratios. Conditions observed in different cities^5,6,8,40 are highlighted and are found to favour the formation of non-acyl RO₂NO₂. Especially at wintertime in Beijing, a significant amount of RO₂ is expected to be stored as RO₂NO₂. In contrast, NO₂ and temperature observed in September in a boreal forest² do not facilitate the production of RO₂NO₂. Though, for relatively low values of NO₂ of ∼1 ppbv and ∼10 °C (280 K) that can also be found in forested environments, more than 20% of RO₂ radical is stored as RO₂NO₂. For a mixing ratio of NO₂ up to 10 ppbv, the fraction can increase up to 80%. Although a large part of the RO₂NO₂ will decompose back to RO₂ and NO₂, depending on temperature and lifetime, RO₂NO₂ can be transported and contribute to the NO_x levels further away from their emission sources. In addition, nothing is known about the additional loss rate of RO₂NO₂ by reaction with OH and photolysis. Khan et al.¹⁵ introduced these loss reactions based on similarity with other molecules and show they could have an impact in particular at the equator.

Fig. 6 Fraction of peroxy radicals stored as RO₂NO₂ as a function of temperature and NO₂ mixing ratios. Contour lines mark certain RO₂NO₂/(RO₂ + RO₂NO₂) ratios. Values were determined from a steady-state calculation, assuming the generic forward and backward reaction rate coefficients k_fPN and k_bPN (Table 1) for reaction (3), respectively. White stars mark regimes that were observed in a boreal forest,² in London,⁸ Pasadena,⁴⁰ and Beijing at cold⁵ and medium temperatures.⁶

5 Summary & conclusions

In this study, the nighttime chemistry of cis-2-butene and trans-2-hexene was investigated under nighttime conditions. Experiments were performed in an outdoor simulation chamber under controlled conditions. The measurements show a clear dependence of the RO₂ radical concentration time profiles on temperature, with the lowest temperatures having a significantly delayed RO₂ peak concentration compared to what would be expected for direct formation of short-lived RO₂ radicals. Measured trace gases and radicals were compared with different chemical mechanisms, implemented in zero-dimensional box model calculations based on the FZJ mechanism.¹⁰ This model improves upon the Master Chemical Mechanism by including a state-of-the-art ozonolysis scheme for cis-2-butene and trans-2-hexene, updated chemistry for nitrate peroxy radicals (NO₃–RO₂) from NO₃ radical chemistry as well as for oxygenated peroxy radicals from ozonolysis. An extended model, FZJ + RO₂NO₂, additionally includes the reversible reactions of all non-acyl RO₂ radicals with NO₂ forming RO₂NO₂. In addition, the decomposition rate of –NO₃–RO radicals, first introduced by a study by Novelli et al.,¹⁰ is adjusted to best match observed radical concentrations.

The measured time profiles of the RO₂ radical concentrations are reproduced best when accounting for the reaction of RO₂ with NO₂ for all RO₂, not solely those for CH₃O₂ and acyl-RO₂ radicals as typically included in atmospheric models. Especially for cold conditions, including the formation of reservoir RO₂NO₂ species significantly improves the modelled RO₂ and an average agreement with the measured RO₂ within 16% is achieved for cis-2-butene. This reaction allows reversible formation of alkyl peroxynitrate reservoir species, leading to a reduction of the effective concentration of free RO₂ radicals that is especially pronounced at lower temperatures. In addition, the RO₂ radical concentrations observed are equally (within 20% on average) described by both FZJ mechanisms (FZJ model with and without including additional RO₂NO₂ formation) above 290 K. With decreasing temperatures, including the formation and subsequent decomposition of RO₂NO₂ in the model reduces the predicted total free RO₂ radical concentration and delays peak RO₂ radical concentrations as observed in the experiments, thereby significantly improving the shape of modelled RO₂ time profiles.

A discrepancy between modelled and measured HO₂ radical concentration, which for the low-temperature conditions reached a factor of 3 on average, was observed for trans-2-hexene. Sensitivity analyses indicate that this discrepancy correlates best with a measurement interference by non-acyl RO₂NO₂, where an interference of ≈2% would be sufficient to reproduce the measured HO₂. However, as this discrepancy does not influence the time-dependence of the RO₂ radical concentration profiles in the chamber experiments, it has no impact on the conclusions.

Under the conditions of the experiments in this work, up to 2 × 10 cm⁻³ of non-acyl RO₂NO₂ are expected at 276 K, comprising about 95% of RO₂. Under winter conditions in polluted cities such as Beijing, China, where temperatures of 255 K are reached,⁵ even higher fractions of the RO₂ present as RO₂NO₂ reservoir species are expected. This will have consequences for radical chemistry, the spatial distribution of RO₂ and NO₂, and the loss of radicals through deposition of RO₂NO₂.¹³

The general forward and backward reaction rates from SAR¹² which refer to non-substituted RO₂ radicals do an excellent job in bringing measured and modelled RO₂ radicals in agreement for the conditions of this study (NO₃–RO₂). This suggests that substituents on the RO₂ radical have a small effect on the reaction rates making the implementation in global models easier. Although the largest impact of these reactions can be expected for cold temperatures (higher altitudes), already for NO₂ mixing ratios as low as few ppbv and a temperature of 280 K, a fraction of RO₂NO₂/(RO₂ + RO₂NO₂) of 20% can be expected (Fig. 6). Given the large uncertainties of the follow-up chemistry of RO₂NO₂, it is not easy to assess, a priori, their effect in different environments and more studies are needed to shed light on their chemistry. Generally, the impact of the formation of RO₂NO₂ manifests likely as a time delay in the response of the chemical mixture to changes in VOC emission and oxidation, NO_x levels, temperature, and other environmental factors.

Discrepancies remain between modelled and measured RO₂ radicals in the ozonolysis experiment of trans-2-hexene and for NO₂ + O₃ experiments of trans-2-hexene at higher temperatures (292 K and 305 K). Uncertainties in the ozonolysis may be related to the chemistry of peracid-substituted RO₂ radicals formed in RO₂H-migration reactions. Insufficient data are available to resolve this issue at this time, but it is shown that the discrepancy is too small to significantly affect the O₃ + NO₃ nighttime experiments in this work.

Data availability

Data from the experiments in the SAPHIR chamber used in this work are available on the EUROCHAMP data home page (https://data.eurochamp.org/). Experiments with cis-2-butene performed at T ≈ 276 K and T ≈ 295 K are available at https://doi.org/10.25326/MBQ2-QY95⁴¹ and https://doi.org/10.25326/6BV7-MR14,⁴² respectively. Experimental data from the nighttime oxidation experiments of trans-2-hexene in the presence of NO₂ and CO conducted at T ≈ 276 K, T ≈ 292 K, and T ≈ 305 K are accessible at https://doi.org/10.25326/DV74-3P36,⁴³ https://doi.org/10.25326/E63B-9J58,⁴⁴ and https://doi.org/10.25326/5CDB-Q698,⁴⁵ respectively. Data from the nighttime experiment of trans-2-hexene in the presence of NO₂ and CH₄ as well as from the ozonolysis experiment of trans-2-hexene are available at https://doi.org/10.25326/DSQH-4 × 71⁴⁶ and https://doi.org/10.25326/89B1-GR69,⁴⁷ respectively.

Conflicts of interest

The authors declare that they have no conflict of interest.

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Footnotes

† The data of the experiments in the SAPHIR chamber used in this work are available on the EUROCHAMP data home page (https://data.eurochamp.org/). More information can be found in the Data availability statement.

‡ Electronic supplementary information (ESI) available: The supplement related to this article is available online, and contains detailed information about the ozonolysis experiment of trans-2-hexene, the NO₃ interference of the radical instrument, the modified alkoxy decomposition rate used for cis-2-butene-RO, instrumentation details, contributions of NO₃ and O₃ to the VOC oxidation, the time series of measured acetaldehyde concentrations, and the discussion of the nighttime oxidation of trans-2-hexene at medium and hot temperatures. See DOI: https://doi.org/10.1039/d3cp04163h

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