Highly oxygenated organic molecule (HOM) formation in the isoprene oxidation by NO₃ radical

Highly oxygenated organic molecules (HOM) are found to play an important role in the formation and growth of secondary organic aerosol (SOA). SOA is an important type of aerosol with significant impact on air quality and climate. Compared with the oxidation of volatile organic compounds by ozone (O₃) and hydroxyl radical (OH), HOM formation in the oxidation by nitrate radical (NO₃), an important oxidant at nighttime and dawn, has received less attention. In this study, HOM formation in the reaction of isoprene with NO₃ was investigated in the SAPHIR chamber (Simulation of Atmospheric PHotochemistry In a large Reaction chamber). A large number of HOM, including monomers (C₅), dimers (C₁₀), and trimers (C₁₅), both closed-shell compounds and open-shell peroxy radicals (RO₂), were identified and were classified into various series according to their formula. Their formation pathways were proposed based on the peroxy radicals observed and known mechanisms in the literature, which were further constrained by the time profiles of HOM after sequential isoprene addition to differentiate first- and second-generation products. HOM monomers containing one to three N atoms (1–3N-monomers) were formed, starting with NO₃ addition to carbon double bond, forming peroxy radicals, followed by autoxidation. 1N-monomers were formed by both the direct reaction of NO₃ with isoprene and of NO₃ with first-generation products. 2N-monomers (e.g., C₅H₈N₂O_n(n=7–13), C₅H₁₀N₂O_n(n=8–14)) were likely the termination products of C₅H₉N₂O_n•, which was formed by the addition of NO₃ to C5-hydroxynitrate (C₅H₉NO₄), a first-generation product containing one carbon double bond. 2N-monomers, which were second-generation products, dominated in monomers and accounted for ∼34 % of all HOM, indicating the important role of second-generation oxidation in HOM formation in the isoprene + NO₃ reaction under our experimental conditions. H shift of alkoxy radicals to form peroxy radicals and subsequent autoxidation (“alkoxy–peroxy” pathway) was found to be an important pathway of HOM formation. HOM dimers were mostly formed by the accretion reaction of various HOM monomer RO₂ and via the termination reactions of dimer RO₂ formed by further reaction of closed-shell dimers with NO₃ and possibly by the reaction of C5–RO₂ with isoprene. HOM trimers were likely formed by the accretion reaction of dimer RO₂ with monomer RO₂. The concentrations of different HOM showed distinct time profiles during the reaction, which was linked to their formation pathway. HOM concentrations either showed a typical time profile of first-generation products, second-generation products, or a combination of both, indicating multiple formation pathways and/or multiple isomers. Total HOM molar yield was estimated to be 1.2 %${}_{-\mathrm{0.7}\mathit{\%}}^{+\mathrm{1.3}\mathit{\%}}$, which corresponded to a SOA yield of ∼3.6 % assuming the molecular weight of C₅H₉NO₆ as the lower limit. This yield suggests that HOM may contribute a significant fraction to SOA yield in the reaction of isoprene with NO₃.

1 Introduction

Highly oxygenated organic molecules (HOM) are an important class of compound formed in the oxidation of volatile organic compounds (VOC), including biogenic VOC (BVOC) and anthropogenic VOC (Crounse et al., 2013; Ehn et al., 2014; Jokinen et al., 2014; Rissanen et al., 2014; Jokinen et al., 2015; Krechmer et al., 2015; Mentel et al., 2015; Rissanen et al., 2015; Kenseth et al., 2018; Molteni et al., 2018; Garmash et al., 2020; McFiggans et al., 2019; Molteni et al., 2019; Quéléver et al., 2019). A number of recent studies have demonstrated that HOM play a pivotal role in both nucleation and also particle growth of pre-existing particles, thus contributing to secondary organic aerosol (SOA) (Ehn et al., 2014; Kirkby et al., 2016; Tröstl et al., 2016). Particularly, in the early stage of aerosol growth, HOM may contribute a significant fraction of SOA mass (Tröstl et al., 2016).

HOM are formed by the autoxidation of peroxy radicals (RO₂), which means they undergo intramolecular H shift forming alkyl radicals, followed by O₂ addition leading to formation of new RO₂ as shown below (Vereecken et al., 2007; Crounse et al., 2013; Ehn et al., 2017; Bianchi et al., 2019; Møller et al., 2019; Nozière and Vereecken, 2019; Vereecken and Nozière, 2020).

Besides autoxidation, the RO₂ can also react with HO₂, RO₂, and NO₃, either forming a series of termination products (Reactions R1–3), including organic hydroxyperoxide, alcohol, and carbonyl, or forming alkoxy radicals (RO, Reactions R4–5) via the following reactions.

$$\begin{array}{}\text{(R1)}& {\displaystyle }{\mathrm{RO}}_{\mathrm{2}}+{\mathrm{R}}^{\prime }{\mathrm{O}}_{\mathrm{2}}\to \mathrm{ROH}+\mathrm{R}=\mathrm{O}\text{(R2)}& {\displaystyle }{\mathrm{RO}}_{\mathrm{2}}+{\mathrm{R}}^{\prime }{\mathrm{O}}_{\mathrm{2}}\to \mathrm{R}=\mathrm{O}+{\mathrm{R}}^{\prime }\mathrm{OH}\text{(R3)}& {\displaystyle }{\mathrm{RO}}_{\mathrm{2}}+{\mathrm{HO}}_{\mathrm{2}}\to \mathrm{ROOH}\text{(R4)}& {\displaystyle }{\mathrm{RO}}_{\mathrm{2}}+{\mathrm{R}}^{\prime }{\mathrm{O}}_{\mathrm{2}}\to \mathrm{RO}+{\mathrm{R}}^{\prime }\mathrm{O}+{\mathrm{O}}_{\mathrm{2}}\text{(R5)}& {\displaystyle }{\mathrm{RO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{3}}\to \mathrm{RO}+{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}\text{(R6)}& {\displaystyle }{\mathrm{RO}}_{\mathrm{2}}+{\mathrm{R}}^{\prime }{\mathrm{O}}_{\mathrm{2}}\to {\mathrm{ROOR}}^{\prime }+{\mathrm{O}}_{\mathrm{2}}\end{array}$$

The termination products are detected in the mass spectra at masses M+1, M−15, and M−17, respectively, with M being the molecular mass of the parent RO₂ (Ehn et al., 2014; Mentel et al., 2015). In case RO₂ is an acyl peroxy radical, percarboxylic acids and carboxylic acids are formed instead of hydroperoxides and alcohols in Reactions (R3) and (R1), respectively (Atkinson et al., 2006; Mentel et al., 2015). RO₂ can also form HOM dimers by the accretion reaction of two RO₂: Reaction (R6) (Berndt et al., 2018a, b; Valiev et al., 2019). Additionally, HOM can be formed via H shift in RO followed by O₂ addition (referred to as the “alkoxy-proxy” pathway) (Finlayson-Pitts and Pitts, 2000; Vereecken and Peeters, 2010; Vereecken and Francisco, 2012; Mentel et al., 2015). These pathways are summarized in a recent comprehensive review (Bianchi et al., 2019), which also further clarifies HOM definition.

Currently, most laboratory studies of HOM formation focus on the VOC oxidation by OH and O₃ (Crounse et al., 2013; Ehn et al., 2014; Jokinen et al., 2014; Rissanen et al., 2014; Jokinen et al., 2015; Krechmer et al., 2015; Mentel et al., 2015; Rissanen et al., 2015; Kirkby et al., 2016; Tröstl et al., 2016; Kenseth et al., 2018; Molteni et al., 2018; Garmash et al., 2020; McFiggans et al., 2019; Molteni et al., 2019; Quéléver et al., 2019; Wang et al., 2020; Yan et al., 2020). HOM formation in the oxidation of VOC with NO₃ has received much less attention. NO₃ is another important oxidant of VOC mainly operating during nighttime. Particularly, NO₃ has high reactivity with unsaturated BVOC such as monoterpene and isoprene. It is often the dominant oxidant of these compounds at night, especially in regions where biogenic and anthropogenic emissions mix (Geyer et al., 2001; Brown et al., 2009, 2011). The reaction products contribute to SOA formation (Xu et al., 2015; Lee et al., 2016). Also, the organic nitrates produced in these reactions play an important role in nitrogen chemistry by altering NO_x concentration, which further influences photochemical recycling and ozone formation on the next day. Among these reaction products, HOM can also be formed (Xu et al., 2015; Lee et al., 2016; Yan et al., 2016). Despite the potential importance, studies of HOM formation in the oxidation of BVOC by NO₃ are still limited compared with the HOM formation via oxidation by O₃ and OH. Although a number of laboratory studies have investigated the reaction of NO₃ with BVOC (Ng et al., 2008; Fry et al., 2009; Rollins et al., 2009; Fry et al., 2011; Kwan et al., 2012; Fry et al., 2014; Boyd et al., 2015; Schwantes et al., 2015; Nah et al., 2016; Boyd et al., 2017; Claflin and Ziemann, 2018; Faxon et al., 2018; Draper et al., 2019; Takeuchi and Ng, 2019; Novelli et al., 2021; Vereecken et al., 2021), these studies mostly focus on either SOA yield and composition or on the gas-phase chemistry mechanism mainly for “traditional” oxidation products that stem from a few oxidation steps.

Importantly, HOM formation in the reaction of NO₃ with isoprene, the most abundant BVOC accounting for more than half of the global BVOC emissions, has not been explicitly addressed yet, to the best of our knowledge. Although isoprene from plants is mainly emitted under light conditions, i.e., in the daytime, isoprene can remain high after sunset in significant concentrations (Starn et al., 1998; Stroud et al., 2002; Brown et al., 2009) because of the reduced consumption by OH and is found to decay rapidly. A substantial fraction of isoprene can then be oxidized by NO₃ (Brown et al., 2009). Regarding the budget of NO₃, the reaction of isoprene with NO₃ can contribute a significant or even dominant fraction of NO₃ loss at night in regions where VOC is dominated by isoprene such as the northeastern US (Brown et al., 2009). Under some circumstances, the reaction of isoprene with NO₃ can contribute a significant fraction during the afternoon and afterwards (Ayres et al., 2015; Hamilton et al., 2021). The reaction of isoprene with NO₃ is the subject of a number of studies (Ng et al., 2008; Perring et al., 2009; Rollins et al., 2009; Kwan et al., 2012; Schwantes et al., 2015; Vereecken et al., 2021). These studies focus on the oxidation mechanism and “traditional” oxidation products, as well as SOA yields. The initial step is the NO₃ addition to one of the C = C double bounds, preferentially to the carbon C1 (Schwantes et al., 2015), followed by O₂ addition forming a nitrooxyalkyl peroxy radical (RO₂). This RO₂ can undergo the reactions described above, forming a series of products such as C5-nitrooxyhydroperoxide, C5-nitrooxycarbonyl, and C5-hydroxynitrate (Ng et al., 2008; Kwan et al., 2012) as well as methyl vinyl ketone (MVK), potentially methacrolein (MACR), formaldehyde, OH radical, and NO₂ as minor products (Schwantes et al., 2015). A high nitrate yield (57 %–95 %) was found (Perring et al., 2009; Rollins et al., 2009; Kwan et al., 2012; Schwantes et al., 2015). Products in the particle phase such as C₁₀ dimers were also detected (Ng et al., 2008; Kwan et al., 2012; Schwantes et al., 2015). The SOA yield varies from 2 % to 23.8 % depending on the organic aerosol concentration (Ng et al., 2008; Rollins et al., 2009). These studies have provided valuable insights into oxidation mechanism, particle yield, and composition. However, because HOM formation was not the focus of these studies, only a limited number of products, mainly moderately oxygenated ones (oxygen number ≤2 in addition to NO₃ functional groups), were detected in the gas phase. The detailed mechanism of HOM formation and their yields in the reaction of BVOC+NO₃ are still unclear.

In this study, we investigated the HOM formation in the oxidation of isoprene by NO₃. We report the identification of HOM, including HOM monomers, dimers, and trimers. According to the reaction products and the literature, we discuss the formation mechanism of these HOM. The formation mechanism of various HOM is further constrained with time series of HOM upon repeated isoprene additions. We also provide an estimate of HOM yield in the isoprene + NO₃ reaction and assess their roles in SOA formation.

2 Experimental

2.1 Chamber setup and experiments

Experiments investigating the reaction of isoprene with NO₃ were conducted in the SAPHIR chamber (Simulation of Atmospheric PHotochemistry In a large Reaction chamber) at the Forschungszentrum Jülich, Germany. The details of the chamber have been described before (Rohrer et al., 2005; Zhao et al., 2015a, b, 2018). Briefly, SAPHIR is a Teflon chamber with a volume of 270 m³. It can utilize natural sunlight for illumination and is equipped with a louvre system to switch between light and dark conditions. In this study, the experiments were conducted in the dark with the louvres closed.

Temperature and relative humidity were continuously measured. Gas- and particle-phase species were characterized using a comprehensive set of instruments with the details described before (Zhao et al., 2015b). VOC were characterized using a Proton Transfer Reaction Time-of-Flight Mass Spectrometer (PTR-ToF-MS, Ionicon Analytik, Austria). NO_x and O₃ concentrations were measured using a chemiluminescence NO_x analyzer (ECO PHYSICS TR480) and a UV photometer O₃ analyzer (ANSYCO, model O341M), respectively. OH, HO₂, and RO₂ concentrations were measured using a laser-induced fluorescence system (LIF) (Fuchs et al., 2012). NO₃ and N₂O₅ were detected by a custom-built instrument based on cavity ring-down spectroscopy. The design of the instrument is similar to that described by Wagner et al. (2011). NO₃ was directly detected in one cavity by its absorption at 662 nm and the sum of NO₃ and N₂O₅ in a second, heated cavity, which had a heated inlet to thermally decompose N₂O₅ to NO₃. The sampling flow rate was 3 to 4 L/min. The detection by cavity ring-down spectroscopy was achieved by a diode laser that was periodically switched on and off with a repetition rate of 200 Hz. Ring-down events were observed by a digital oscilloscope PC card during the time when the laser was switched off and were averaged over 1 s. The zero-decay time that is needed to calculate the concentration of NO₃ was measured every 20 s by chemically removing NO₃ in the reaction with excess nitric oxide (NO) in the inlet system. The accuracy of measurements was limited by the uncertainty in the correction for inlet losses of NO₃ and N₂O₅. In the case of N₂O₅ a transmission of (85 ± 10) % was achieved and, in the case of NO₃, (50 ± 30) %.

Before an experiment, the chamber was flushed with high-purity synthetic air (purity >99.9999 % O₂ and N₂). Experiments were conducted under dry conditions (RH < 2  %), and temperature was at 302 ± 3 K. NO₂ and O₃ were added to the chamber first to form N₂O₅ and NO₃, reaching concentrations of ∼60 ppb for NO₂ and ∼100 ppb for O₃. After around half an hour, isoprene was sequentially added into the chamber for three times at intervals of ∼1 h. Around 40 min after the third isoprene injection, NO₂ was added to compensate for the loss of NO₃ and N₂O₅. Afterwards, three isoprene additions were repeated in the same way as before. O₃ was added before the fifth and sixth isoprene additions to compensate for its loss by reaction. The schematic for the experimental procedure is shown in Fig. S1. Experiments were designed such that the chemical system was dominated by the reaction of isoprene with NO₃ and the reaction of isoprene with O₃ did not play a major role (<3 % of the isoprene consumption). Figure S2 shows the relative contributions of the reaction of O₃ and NO₃ with isoprene to the total chemical loss of isoprene using the NO₃ and O₃ concentrations measured. The reaction with NO₃ accounted for >95 % of the isoprene consumption for the whole experiment periods. The contribution of the reaction of isoprene with a trace amount of OH, mainly produced in the reaction of isoprene + O₃ via Criegee intermediates (Nguyen et al., 2016), is negligible as the OH yield is less than one (Malkin et al., 2010), and thus its contribution is less than that of isoprene + O₃. This is consistent with the contribution determined using measured OH concentration, despite some uncertainty in measured OH concentration due to the interference from NO₃. In these experiments, RO₂ fate is estimated to be dominated by its reaction with NO₃ according to the measured NO₃, RO₂, and HO₂ concentrations and their rate constants for the reactions with RO₂ (MCM v3.2; Jenkin et al., 1997, 2003; Saunders et al., 2003; Jenkin et al., 2015, via the website: http://mcm.york.ac.uk/, last access: 28 June 2021) despite uncertainties in the measured RO₂ and HO₂ concentration due to interference from NO₃. As a large portion of RO₂ is not measured by LIF (Vereecken et al., 2021) and thus RO₂ is underestimated, we expected the reaction of RO₂+RO₂ to also be important. Overall, we estimate that the RO₂ fate is dominated by the reaction RO₂+NO₃ with a significant contribution of RO₂+RO₂.

2.2 Characterization of HOM

In this study we refer to a similar definition for HOM by Bianchi et al. (2019); i.e., HOM typically contain six or more oxygen atoms formed via autoxidation and related chemistry of peroxy radicals. HOM were detected using a Chemical Ionization time-of-flight Mass Spectrometer (Aerodyne Research Inc., USA) with nitrate as the reagent ion (CIMS) (Eisele and Tanner, 1993; Jokinen et al., 2012). ¹⁵N nitric acid was used to produce ¹⁵NO${}_{\mathrm{3}}^{-}$ in order to distinguish the NO₃ group into target molecules formed in the reaction from the reagent ion. The details of the instrument are described in our previous publications (Ehn et al., 2014; Mentel et al., 2015; Pullinen et al., 2020). The CIMS has a mass resolution of ∼4000 (m/dm). Examples of peak fitting are shown in Fig. S3. HOM concentrations were estimated using the calibration coefficient of H₂SO₄ as described by Pullinen et al. (2020) because the charge efficiency of HOM and H₂SO₄ can be assumed to be equal and close to the collision limit (Ehn et al., 2014; Pullinen et al., 2020). The details of the calibration with H₂SO₄ are provided in Supplement Sect. S1. Since HOM contain more than six oxygen atoms and their clusters with nitrate ions are quite stable (Ehn et al., 2014), the charge efficiency of HOM is thus assumed to be equal to that of H₂SO₄, which is close to the collision limit (Viggiano et al., 1997). If HOM do not charge with nitrate ions at their collision limit or the clusters formed break during the short residence time in the charger, its concentration would be underestimated as pointed out by Ehn et al. (2014). Thus, our assumption provides a lower limit of the HOM concentration. The HOM yield was derived using the concentration of the HOM produced, divided by the concentration of isoprene that was consumed by NO₃. The uncertainty of HOM yield was estimated to −55 %/+103 %. The loss of HOM to the chamber was corrected using a wall loss rate of 6 × 10⁻⁴ s⁻¹ as quantified previously (Zhao et al., 2018). HOM concentrations were also corrected for dilution due to the replenishment flow needed to maintain a constant overpressure of the chamber (loss rate ∼1 × 10⁻⁶ s⁻¹) (Zhao et al., 2015b). The influence of wall loss correction and dilution correction on HOM yield was ∼12 % and <1 %, respectively. Although the wall loss rate of vapors in this study might not be exactly the same as in our previous photooxidation experiments (Zhao et al., 2018), HOM yield is not sensitive to the vapor wall loss rate. An increase in wall loss rate by 100 % or a decrease by 50 % only changes the HOM yield by 11 % and −6 %, respectively.

3 Results and discussion

3.1 Overview of HOM

The mass spectra of HOM in the gas phase formed in the oxidation of isoprene by NO₃ are shown in Fig. 1. A large number of HOM were detected. Almost all peaks are assigned HOM containing nitrogen atoms, with possibly few exceptions such as C₅H₁₀O₈ and C₅H₈O₁₁ with very minor peaks (≲1 % of the maximum peak). The reaction products can be roughly divided into three classes: monomers (C5, ∼200–400 Th), dimers (C10, ∼400–600 Th), and trimers (C15, ≳600 Th), according to their mass-to-charge ratio ($m/z$). The detailed peak assignment of monomers, dimers, and trimers is discussed in the following sections.

Figure 1 Mass spectrum of the HOM formed in the oxidation of isoprene by NO₃. HOM are detected as clusters with the reagent ion ¹⁵NO${}_{\mathrm{3}}^{-}$, which is not shown in the molecular formula in the figure for simplicity. Panels (a) and (b) show the average spectrum during the first isoprene addition period (P1) and for the whole period of six isoprene additions (P1–6), respectively. The insets show the contributions of different classes of HOM. 1–3N-monomer refers to the monomers containing one to three nitrogen atoms in the molecular formula.

3.2 HOM monomers and their formation

3.2.1 Overview of HOM monomers

HOM monomers showed a roughly repeating pattern in the mass spectrum at every 16 Th (corresponding to the mass of oxygen) (Fig. 1a). Here a number of series of HOM monomers with continuously increasing oxygenation were found, such as C₅H₉NO_n, C₅H₇NO_n, C₅H₈N₂O_n, and C₅H₁₀N₂O_n (Tables 1 and S1–2 and Fig. 2). These monomers included both stable closed-shell molecules and open-shell radicals, such as C₅H₈NO_n• and C₅H₉N₂O_n•. The open-shell molecules were likely RO₂ radicals because of their much longer lifetime and hence higher concentrations compared with alkoxy radicals (RO) and alkyl radicals (R). Since the observed stable products were mostly termination products of RO₂ reactions, we describe the stable products in a RO₂-oriented approach. It is worth noting that some of the termination products may contain multiple isomers formed from different pathways.

Figure 2 Kendrick mass defect plot for O of HOM monomers. The $m/z$ in the molecular formula includes the reagent ion ¹⁵NO${}_{\mathrm{3}}^{-}$, which is not shown for simplicity. The size (area) of circles is set to be proportional to the average peak intensity of each molecular formula during the first isoprene addition period (P1). The species at $m/z$ 351 and 353 (labeled in grey) are the adducts of C₅H₈N₂O₈ and C₅H₁₀N₂O₈ with H[15N]₂O${}_{\mathrm{6}}^{-}$, respectively. The blue dashed lines with arrows indicate the termination products hydroperoxide (M+H), alcohol ($M-\mathrm{O}+\mathrm{H}$), and ketone ($M-\mathrm{O}-\mathrm{H}$), with M the molecular formula of a HOM RO₂.

Table 1 HOM monomers formed in the oxidation of isoprene by NO₃.

^a RO₂ denotes peroxy radical, and ROOH, ROH, R=O, and RO₂NO₂ denote the termination products containing hydroperoxy, hydroxyl, carbonyl group, and peroxynitrate, respectively. ^b Peak assignment of compounds with $n=\mathrm{13},\mathrm{14}$ may be subject to uncertainties.

HOM monomers were classified into 1N-, 2N-, and 3N-monomers according to the number of nitrogen atoms that they contain. HOM without nitrogen atoms were barely observed except for very minor peaks (≲1 % of the maximum peak) possibly assigned to C₅H₁₀O₈ and C₅H₈O₁₁. The contribution of 2N-monomers such as C₅H₁₀N₂O_n and C₅H₈N₂O_n was higher than that of the 1N-HOM monomers, and that of 3N-monomers was the lowest (Fig. 1, inset). The most abundant monomers were C₅H₁₀N₂O₈, C₅H₁₀N₂O₉, and C₅H₈N₂O₈. The termination products of C₅H₉NO₈, C₅H₉NO₉, and C₅H₇NO₈ also showed relatively high abundance. These limited numbers of compounds dominated the HOM monomers. Since 2N-monomers were second-generation products as discussed below, the higher-abundance 2N-monomers indicate that the second-generation HOM play an important role in the reaction of NO₃ with isoprene in the reaction conditions of our study, as also seen by Wu et al. (2020). This is more evident for the mass spectrum averaged over six isoprene addition periods (Fig. 1b), where the abundances of C₅H₁₀N₂O_n and C₅H₈N₂O_n were more dominant. This observation is in contrast with the finding for the reaction of O₃ with BVOC, which contains only one double bond such as α-pinene (Ehn et al., 2014), where HOM are mainly first-generation products formed via autoxidation. The higher abundance of HOM 2N-monomers than 1N-monomers is likely because HOM production rate via the autoxidation of 1N-monomer RO₂ following the reaction of isoprene with NO₃ may be slower than that of the reaction of 1N-monomers (including both HOM and non-HOM monomers) with NO₃. We would like to note that some less oxygenated 1N-monomers such as C₅H₉NO${}_{\mathrm{4}/\mathrm{5}}$ and C₅H₇NO₄ may have high abundance but are not detected by NO${}_{\mathrm{3}}^{-}$-CIMS and are not HOM and thus not included in HOM 1N-monomers.

3.2.2 1N-monomers

In our experiments we observed a C₅H₈NO_n• (n=7–12) series (series M1) as well as its corresponding termination products C₅H₇NO_n−1, C₅H₉NO_n−1, and C₅H₉NO_n via the reactions with RO₂ and HO₂, which contain carbonyl, hydroxyl, and hydroperoxy group, respectively. Overall, the peak intensities of C₅H₉NO_n and C₅H₇NO_n series first increased and then decreased as oxygen number increased (Fig. 2), with the peak intensity of C₅H₉NO₈ and C₅H₇NO₈ being the highest within their respective series when averaged over the whole experiment period.

C₅H₈NO_n• with odd numbers of oxygen atoms (n=7, 9, 11, series M1a) were possibly formed by the attack of NO₃ to one double bond, preferentially to C1 according to previous studies (Skov et al., 1992; Berndt and Böge, 1997; Schwantes et al., 2015) and followed by autoxidation (Scheme 1a). We would like to note that NO${}_{\mathrm{3}}^{-}$-CIMS only observed HOM with oxygen numbers ≥6 in this study due to its selectivity of detection. C₅H₈NO_n• with even numbers of oxygen atoms (n=8, 10, series M1b in Table 1) were possibly formed after H shift of an alkoxy radical formed in Reactions (R4) or (R5) and subsequent O₂ addition (“alkoxy–peroxy” channel) (Scheme 1b), where the alkoxy radicals can be formed from both the RO₂+NO₃ and RO₂+RO₂ reactions. The hydroxy RO₂ formed can undergo further autoxidation, adding two oxygen atoms after each H shift. We would like to note that the scheme and other schemes in this study only show example isomers and pathways to form these molecules. It is likely that many of the reactions occurring are not the dominant channels as otherwise there would be much higher HOM yield as discussed below.

Scheme 1 The example pathways to form HOM RO₂ C₅H₈NO_n• (n=7, 9, 11) series (a) and C₅H₈NO_n• (n=8, 10) series (b) in the reaction of isoprene with NO₃. The detected products are in bold.

Some HOM monomers may contain multiple isomers and be formed via different pathways. For example, C₅H₉NO_n can contain alcohols derived from RO₂ C₅H₈NO_n+1•, hydroperoxides derived from RO₂ C₅H₈NO_n•, or the ketones from RO₂C₅H₁₀NO_n+1•. Some RO₂ C₅H₈NO_n• may be formed via the reaction of first-generation products with NO₃ in addition to direct reaction of isoprene with NO₃. For example, C₅H₈NO₇• can be formed by the reaction of NO₃ with C₅H₈O₂, which is a first-generation product observed previously in the reaction of isoprene with NO₃ or OH (Scheme S1b) (Kwan et al., 2012). Moreover, RO₂ C₅H₈NO_n• can be formed from C5-carbonylnitrate, a first-generation product, with OH (Scheme S1a). Trace amount of OH can be produced in the reaction of isoprene with NO₃ (Kwan et al., 2012; Wennberg et al., 2018). OH can also be formed via Criegee intermediates formed in the isoprene + O₃ reaction (Nguyen et al., 2016), but this OH source was likely minor because the contribution of the isoprene + O₃ reaction to total isoprene loss was negligible (<5 %, Fig. S2). In addition, C₅H₈NO₈• may also be formed by the reaction of NO₃ with C₅H₈O₃, which is a first-generation product observed in the reaction of isoprene with OH (Kwan et al., 2012). The C₅H₈NO_n• formed via direct reaction of isoprene with NO₃ is a first-generation RO₂, while that formed via other indirect pathways is a second-generation RO₂. The time profiles of the isomers from these two pathways, however, are expected to be different, as will be discussed below.

Time series of HOM can shed light on their formation mechanisms. It is expected that first-generation products will increase quickly with isoprene addition and reach a maximum earlier in the presence of wall loss of organic vapor, while second-generation products will reach a maximum in the later stage or increase continuously if the production rate is higher than the loss rate. As a reference to analyze the time profiles of HOM, the time profiles of isoprene, NO₃, and N₂O₅ are also shown (Fig. S4). After isoprene was added in each period, NO₃ and N₂O₅ dropped dramatically and then gradually increased. We found that termination products within the same M1 series showed different time profiles. For example, in C₅H₉NO_n series, C₅H₉NO₈ clearly increased instantaneously with isoprene addition and decreased quickly afterwards (Fig. 3a), indicating that it was a first-generation product, which was expected according to mechanism Scheme 1. C₅H₉NO₆ and C₅H₉NO₁₀ had a general increasing trend with time. While C₅H₉NO₆ increased continuously with time, C₅H₉NO₁₀ reached maximum intensity in the late phase of each isoprene addition period and then decreased naturally or after isoprene addition. The faster loss of C₅H₉NO₁₀ than C₅H₉NO₆ may result from the faster wall loss due to its lower volatility. C₅H₉NO₇ and C₅H₉NO₉ showed a mixing time profile with features of the former two kinds of time profiles, increasing almost instantaneously with isoprene additions, especially in the first two periods, while increasing continuously or decreasing first with isoprene additions and then increasing later in each period. This kind of time series indicates that there were significant contributions from both first- and second-generation products.

Figure 3 Time series of peak intensity of several HOM monomers of C₅H₉NO_n series (a) and of C₅H₁₀N₂O_n series (b). They are likely the termination products of RO₂ C₅H₈NO_n• and C₅H₉N₂O_n•, respectively. The dashed lines indicate the time of isoprene additions. The long-dashed arrow indicates the time of NO₂ addition. The dash-dotted arrows indicate the time of O₃ additions.

The second-generation products may be different isomers formed in pathways other than shown in Scheme 1. Second-generation C₅H₉NO₆ can be formed via C₅H₈NO₇•, which can also be formed by the reaction of NO₃ and O₂ with C₅H₈O₂ as mentioned above (Scheme S2b) or by the reaction of OH with C₅H₇NO₄ (Scheme S2a). The time profiles of C₅H₈NO₇• did show more contribution of second-generation processes because C₅H₈NO₇• continuously increased with time in general. If the pathways via the reaction of NO₃ and O₂ with C₅H₈O₂ and the reaction of OH with C₅H₇NO₄ contribute most to C₅H₉NO₆, C₅H₉NO₆ would show mostly a time profile of second-generation products. Similarly, second-generation C₅H₉NO₇ can be formed via C₅H₈NO₇• or C₅H₈NO₈•. The time series of C₅H₈NO₈• did show the contribution of both the first- and second-generation processes, which generally increased with time while also responding to isoprene addition (Fig. S5). Similarly to C₅H₉NO₆, the second-generation pathways for C₅H₉NO₇, C₅H₉NO₉, and C₅H₉NO₁₀ are shown in Schemes S1, S3, and S4. For the RO₂ in C₅H₈NO_n• series other than C₅H₈NO${}_{\mathrm{7}/\mathrm{8}}\mathrm{•}$, the peak of C₅H₈NO_n• overlaps with C₅H₁₀N₂O_n in the mass spectra, which is a much larger peak and thus cannot be differentiated from C₅H₁₀N₂O_n. Therefore, it is not possible to obtain reliable separate time profiles in order to differentiate their major sources. It is worth noting that nitrate CIMS may not be able to detect all isomers of C₅H₉NO₆ due to the sensitivity limitation. Therefore, we cannot exclude the possibility that the absence of some first-generation isomers of C₅H₉NO₆ was due to the low sensitivity of these isomers.

Among the termination products of the 1N-monomer RO₂, carbonyl and hydroxyl/hydroperoxide species had comparable abundance in general (Table S1), suggesting that disproportionation reactions between RO₂ and RO₂ forming hydroxy and carbonyl species (R1–2) were likely an important RO₂ termination pathway. However, dependence of the exact ratio of carbonyl species to hydroxyl/hydroperoxide species on the number of oxygen atoms did not show a clear trend (Table S1), suggesting that the reactions of HOM RO₂ depended on their specific structure. There was no clear difference in the abundance between the termination products from C₅H₈NO_n• with odd and even numbers of oxygen atoms in general, although the most abundant termination product of C₅H₈NO_n•, i.e., C₅H₇NO₈, was likely formed from C₅H₈NO₉• in series M1a. This fact indicates that both the peroxy pathway and alkoxy–peroxy pathway were important for the HOM formation in the isoprene + NO₃ reaction under our conditions, in agreement with the significant formation of alkoxy radicals from the reaction of RO₂ with NO₃ and RO₂.

In addition to the termination products of RO₂ M1, minor peaks of the RO₂ series C₅H₁₀NO_n• (n=8–9) (M4, Table 1) and their corresponding termination products including hydroperoxide, alcohol, and carbonyl species were detected (Table S3). C₅H₁₀NO_n were likely formed by sequential addition of NO₃ and OH to two double bonds of isoprene (Scheme S5). OH can react quickly with isoprene or with the first-generation products of the reaction of isoprene with NO₃, thus forming C₅H₁₀NO_n•. In addition, a few very minor but noticeable peaks of C₅H₉O_n• and their corresponding termination products C₅H₁₀O_n and C₅H₈O_n were also observed. These HOM may be formed by the reactions of isoprene with trace amounts of OH and with O₃, although their contributions to reacted isoprene were negligible. These HOM were also observed in the reaction of isoprene with O₃ with and without OH scavengers (Jokinen et al., 2015).

Among 1N-monomer HOM, C₅H₉NO₇ has been observed in the particle phase using ESI-TOFMS by Ng et al. (2008), while others have not been observed in previous laboratory studies of the reaction of isoprene with NO₃, to our knowledge. A number of C₅ organic nitrates have been observed in field studies. For example, C₅H_7–11NO_6–8 and C₅H_7–11NO_4–9 have been observed in the gas phase (Massoli et al., 2018) and the particle phase (Lee et al., 2016; Chen et al., 2020), respectively, in a rural area of the southeastern US, where isoprene is abundant. Xu et al. (2021) observed a number of C₅ 1N-HOM such as C₅H${}_{\mathrm{7},\mathrm{9},\mathrm{11}}$NO_6,7 in the polluted megacities of Nanjing and Shanghai of eastern China during summer. While many of these HOM have daytime sources and are attributed to photooxidation in the presence of NO_x, nighttime oxidation with NO₃ also contributed to their formation (Lee et al., 2016; Chen et al., 2020; Xu et al., 2021). C₅H_7–11NO_4–9 were also observed in chamber experiments of the reaction of isoprene with OH in the presence of NO_x (Lee et al., 2016). C₅H_xNO_4–9 and C₅H_xNO_4–10 have also been observed in the gas phase and particle phase, respectively, in a monoterpene-dominating rural area in southwestern Germany (Huang et al., 2019).

3.2.3 2N-mononmers

The 2N-monomer RO₂ series C₅H₉N₂O_n• (n=8–14) were observed, as well as its likely termination products, C₅H₈N₂O_n and C₅H₁₀N₂O_n, which contain a carbonyl and hydroxyl or hydroperoxide functional group, respectively. The RO₂ series C₅H₉N₂O_n• with an odd number of oxygen atoms (n=9, 11) (M2a in Table 1) were likely formed from the first-generation product C₅H₉NO₄ (C5-hydroxynitrate) by adding NO₃ to the remaining double bond, forming C₅H₉N₂O₉•, followed by autoxidation (Scheme 2a). This RO₂ series can also be formed by the addition of NO₃ to the double bond of first-generation products (e.g., C₅H₉NO₅, C5-nitrooxyhydroperoxide) and a subsequent alkoxy–peroxy step (Scheme 2b). C₅H₉N₂O_n• with an even number of oxygen atoms (n=8, 10, 12) (M2b in Table 1) can be formed by the addition of NO₃ to the double bond of C₅H₉NO₅ followed by autoxidation (Scheme 3a) or of C₅H₉NO₄ followed by an alkoxy–peroxy step (Scheme 3b). The formation pathways of C₅H₉N₂O${}_{\mathrm{13}/\mathrm{14}}\mathrm{•}$ and C₅H₉N₂O₈• cannot be well explained, as they contain too many or too few oxygen atoms to be formed via the pathways in Scheme 2 or 3. In Schemes 2 and 3, we show the reactions starting from 1-NO₃-isoprene-4-OO as an example. In the Supplement, we have also shown the pathways starting from 1-NO₃-isoprene-2-OO peroxy radicals, which is indicated in a recent study by Vereecken et al. (2021) to be the dominant RO₂ in the reaction of isoprene with NO₃.

Scheme 2 The example pathways to form C₅H₉N₂O_n (n=9, 11) HOM RO₂ series by RO₂ channel (a) and alkoxy–peroxy channel. The detected products are in bold.

Scheme 3 The example pathways to form C₅H₉N₂O_n (n=10, 12) HOM RO₂ series by RO₂ channel (a) and alkoxy–peroxy channel (b). The detected products are in bold.

Formation through either Scheme 2 or 3 means that C₅H₈N₂O_n and C₅H₁₀N₂O_n were second-generation products. The time series of C₅H₁₀N₂O_n species clearly indicates that they were indeed second-generation products. C₅H₁₀N₂O_n species generally did not increase immediately with isoprene addition (Fig. 3b) but increased gradually with time and reached its maximum in the later stage of each period before decreasing with time (in periods 1 and 6) or decreasing after the next isoprene addition (periods 2–5). This time profile can be explained by the time series of the precursor of C₅H₁₀N₂O_n, C₅H₉N₂O_n• (RO₂) (Fig. S6). The changing rate (production rate minus destruction rate) of C₅H₁₀N₂O_n concentration was dictated by the concentration of C₅H₉N₂O_n• and the wall loss rate. During periods 2 to 5, C₅H₉N₂O_n• gradually increased but decreased sharply after the isoprene additions, resulting from chemical reactions of C₅H₉N₂O_n• and additionally from wall loss. When the rate of change of the C₅H₁₀N₂O_n concentration was positive, the concentration of C₅H₁₀N₂O_n increased with time. After isoprene additions, the rate of change of the C₅H₁₀N₂O_n concentration decreased dramatically to even negative, leading to decreasing concentrations. Similarly to C₅H₁₀N₂O_n, the C₅H₈N₂O_n series did not respond immediately to isoprene additions (Fig. S7), which is expected for second-generation products according to the mechanism discussed above (Schemes 2–3). Particularly, the continuing increase in C₅H₈N₂O_n even after isoprene was completely depleted (at ∼ 21:40, Fig. S7) clearly indicates that these compounds were second-generation products, although in the end they decreased due to wall loss.

According to the finding by Ng et al. (2008), C5-hydroxynitrate decays much more quickly than C5-nitrooxyhydroperoxides. Additionally, C5-hydroxynitrate concentration is expected to be higher than that of nitrooxyhydroperoxides because RO₂+RO₂ forming alcohol is likely more important than RO₂+HO₂ forming hydroperoxide in this study. Therefore, it is likely that C₅H₉N₂O_n• M2a series were mainly formed from C₅H₉NO₄ instead of C₅H₉NO₅, while C₅H₉N₂O_n• M2b were formed from C₅H₉NO₄ followed by an alkoxy–peroxy step. That is, Schemes 2a and 3b appear more likely.

Similarly to C₅H₈NO_n•, the intensity of carbonyl species from C₅H₉N₂O_n• was also comparable with that of hydroxyl/hydroperoxide species, suggesting that RO₂+RO₂ reaction forming ketone and alcohol was likely an important pathway of HOM formation in the isoprene + NO₃ reaction. In general, the intensities of the termination products from C₅H₉N₂O_n• with both even and odd oxygen numbers were comparable. This again suggests that both peroxy and alkoxy–peroxy pathways were important for HOM formation in the isoprene + NO₃ reaction. The intensity of C₅H₈N₂O_n first increased and then decreased with oxygen number, while C₅H₁₀N₂O_n decreased with oxygen number, with C₅H₁₀N₂O₈ and C₅H₈N₂O₈ being the most abundant within their respective series.

Some 2N-monomers have been detected in previous studies of the reaction of isoprene with NO₃. C₅H₁₀N₂O₈ was detected in the particle phase by Ng et al. (2008), and C₅H₈N₂O₇ was detected in the gas phase by Kwan et al. (2012). C₅H₉N₂O₉• has been proposed to be formed via the pathway as in Scheme 2a (Ng et al., 2008), and it was directly detected in our study. C₅H₈N₂O₇ species has been proposed as a dinitrooxy epoxide formed by the oxidation of nitrooxyhydroperoxide (Kwan et al., 2012) instead of being a dinitrooxy ketone proposed in our study, a termination product of C₅H₉N₂O₈•. Admittedly, C₅H₈N₂O₇ may contain both isomers. In addition, Ng et al. (2008) detected C₅H₈N₂O₆ in the gas phase, which was not detected in this study, likely due to the selectivity of NO${}_{\mathrm{3}}^{-}$-CIMS. 2N-monomers have also been observed in previous field studies. For example, Massoli et al. (2018) observed C₅H₁₀N₂O_8–10 in rural Alabama, US, during the SOAS campaign. Xu et al. (2021) observed C₅H_8,10N₂O₈ and C₅H₁₀N₂O₈ in the polluted megacities of Nanjing and Shanghai during summer.

One could suppose that C₅H₇N₂O_n• should also be formed since C5-nitrooxycarbonyl (C₅H₇NO₄) also contains one double bond that can be attacked by NO₃ in a second oxidation step. However, concentrations of C₅H₇N₂O_n were too low to assign molecular formulas with confidence except for C₅H₇N₂O₉•, clearly showing that C₅H₇N₂O_n• was not important. This fact is consistent with the finding by Ng et al. (2008) that C5-nitrooxycarbonyls react slowly with NO₃. Additionally, the peroxy radical formed in the reaction of C5-nitrooxycarbonyls with NO₃ likely leads to more fragmentation in H shift as found in the OH oxidation of methacrolein (Crounse et al., 2012), which may also contribute to the low abundance of C₅H₇N₂O_n. The presence of HOM containing two N atoms is in line with the finding by Faxon et al. (2018), who detected products containing two N atoms in the reaction of NO₃ with limonene, which also contain two carbon double bonds. It is anticipated that for VOC with more than one double bond, NO₃ can add to all the double bonds as for isoprene and limonene.

3.2.4 3N-monomers

HOM containing three nitrogen atoms, C₅H₉N₃O_n (n=9–16), were observed. These compounds were possibly peroxynitrates formed by the reaction of RO₂ (C₅H₉N₂O_n•) with NO₂. The time series of C₅H₉N₃O_n was examined to check whether they match such a mechanism. If C₅H₉N₃O_n were formed by the reaction of C₅H₉N₂O_n−2• with NO₂, the concentration would be a function of the concentrations of C₅H₉N₂O_n−2• and NO₂ as follows:

$$\begin{array}{rl}{\displaystyle \frac{\mathrm{d}\left[{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{9}}{\mathrm{N}}_{\mathrm{3}}{\mathrm{O}}_n\right]}{\mathrm{d}t}}& =k\left[{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{9}}{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{n-\mathit{2}}\mathrm{•}\right]\left[{\mathrm{NO}}_{\mathrm{2}}\right]\\ & -k_{\mathrm{wall}}\left[{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{9}}{\mathrm{N}}_{\mathrm{3}}{\mathrm{O}}_n\right],\end{array}$$

where [C₅H₉N₃O_n], [C₅H₉N₂O_n−2•], and [NO₂] are the concentrations of these species, k is the rate constant, and k_wall is the wall loss rate. Because the products of C₅H₉N₂O_n−2• and NO₂ were at their maximum at the end of each period and decreased rapidly after isoprene addition (Fig. S8), the concentration should have its maximum increasing rate at the end of each isoprene addition period. However, we found that only C₅H₉N₃O${}_{\mathrm{12},\mathrm{15},\mathrm{16}}$ showed such a time profile (Fig. S9), while C₅H₉N₃O${}_{\mathrm{9},\mathrm{10},\mathrm{11},\mathrm{13},\mathrm{14}}$ generally increased with time, different from what one would expect based on the proposed pathway. Therefore, it is likely that C₅H₉N₃O${}_{\mathrm{12},\mathrm{15},\mathrm{16}}$ were mainly formed via the reaction of C₅H₉N₂O_n• with NO₂, whereas C₅H₉N₃O${}_{\mathrm{9},\mathrm{10},\mathrm{11},\mathrm{13},\mathrm{14}}$ were not. Moreover, C₅H₉N₃O₉ cannot be explained by the reaction C₅H₉N₂O_n• (n≥9) with NO₂ or NO₃, because these reactions would add at least one more oxygen atom. One possible pathway to form C₅H₉N₃O₉ was the direct addition of N₂O₅ to the carbon double bond of C5-hydroxynitrate, forming a nitronitrate. Such a mechanism was proposed previously in the heterogeneous reaction of N₂O₅ with 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) because -NO₂ and -NO₃ groups were detected (Lai and Finlayson-Pitts, 1991). This pathway generally matched the time series of C₅H₉N₃O${}_{\mathrm{9},\mathrm{10},\mathrm{11},\mathrm{13},\mathrm{14}}$ typical of second-generation products since C5-hydroxynitrate was a first-generation product. It is possible that the main pathway of C₅H₉N₃O${}_{\mathrm{9},\mathrm{10},\mathrm{11},\mathrm{13},\mathrm{14}}$ was the reaction of C₅H₉NO${}_{\mathrm{4},\mathrm{5},\mathrm{6}}$ with N₂O₅, although the reaction of N₂O₅ with C=C double bonds in common alkenes and unsaturated alcohols is believed to be unimportant (Japar and Niki, 1975; Pfrang et al., 2006).

3N-monomer, C₅H₉N₃O₁₀, has been observed in the particles formed in the isoprene + NO₃ reaction by Ng et al. (2008). Here a complete series of C₅H₉N₃O_n was observed. C₅H₉N₃O₁₀ was previously proposed to be formed by another pathway, i.e., the reaction of RO₂ (C₅H₉N₂O₉•) and NO₃ (Ng et al., 2008). We further examined the possibility of such a pathway in our study. Similarly to NO₂, if C₅H₉N₃O_n were formed by the reaction of C₅H₉N₂O_n−2• with NO₃, the concentration would have its maximum increasing rate at the end of each isoprene addition period. Among C₅H₉N₂O_n•, the precursors of C₅H₉N₃O_n, C₅H₉N₂O${}_{\mathrm{9},\mathrm{10},\mathrm{13},\mathrm{14}}\mathrm{•}$ showed a maximum increasing rate and a subsequent decrease after isoprene addition. The difference in oxygen number between C₅H₉N₃O${}_{\mathrm{12},\mathrm{15},\mathrm{16}}$, the termination products, and C₅H₉N₂O${}_{\mathrm{9},\mathrm{10},\mathrm{13},\mathrm{14}}\mathrm{•}$, the corresponding RO₂ with the consistent time profile, is mostly two. Since the reaction of C₅H₉N₂O_n with NO₂ and NO₃ results in increased oxygen numbers by two and by one, respectively, we infer that it is more likely that C₅H₉N₃O${}_{\mathrm{12},\mathrm{15},\mathrm{16}}$ were formed by the reaction of C₅H₉N₂O${}_{\mathrm{10},\mathrm{13},\mathrm{14}}\mathrm{•}$ with NO₂ rather than NO₃, and thus they were likely peroxynitrates rather than nitrates formed by the reaction of RO₂ with NO₃. Since alkyl peroxynitrates decompose rapidly (Finlayson-Pitts and Pitts, 2000; Ziemann and Atkinson, 2012), it is possible that these compounds contained peroxyacylnitrates.

Little attention has been paid to the RO₂+NO₂ pathway in nighttime chemistry of isoprene in the literature (Wennberg et al., 2018), which is likely due to the instability of the products. According to this pathway, C₅H₈N₂O_n, which was proposed as a ketone formed via C₅H₉N₂O₉• in the M2 series (Table 1) as discussed above, can also comprise peroxynitrate formed by the reaction of C₅H₈NO_n• (M1a RO₂) with NO₂. 3N dimers such as C₅H₉N₃O₁₀ have been observed in a recent field study in polluted cities in eastern China (Xu et al., 2021).

3.3 HOM dimers and their formation

A number of HOM dimer series were observed, including C₁₀H₁₆N₂O_n (n=10–17), C₁₀H₁₇N₃O_n (n=11–19), and C₁₀H₁₈N₄O_n (n=15–18), C₁₀H₁₈N₂O_n (n=10–16), C₁₀H₁₅N₃O_n (n=13–17), and C₁₀H₁₉N₃O_n (n=14–15) series (Tables 2, S3). C₁₀H₁₆N₂O_n series (dimer 1, Table 2) was likely formed by the accretion reaction of two monomer RO₂ of M1a/b (Reaction R7).

$$\begin{array}{}\text{(R7)}& {{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{8}}\mathrm{NO}}_{n\mathrm{1}}\mathrm{•}+{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{8}}{\mathrm{NO}}_{n\mathit{2}}\mathrm{•}\to {{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{16}}{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_{n\mathrm{1}+n\mathrm{2}-\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}\end{array}$$

Similarly, C₁₀H₁₈N₄O_n series (dimer 2, Table 2) were likely formed by the accretion reaction of two monomer RO₂ of M2 (Reaction R8). As n1 and n2 are ≥9, the number of oxygen in C₁₀H₁₈N₄O_n is expected to be ≥16. This is consistent with our observation that only C₁₀H₁₈N₄O_n with n≥16 had significant concentrations.

$$\begin{array}{}\text{(R8)}& {{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{9}}{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_{n\mathrm{1}}\mathrm{•}+{{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{9}}{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_{n\mathrm{2}}\mathrm{•}\to {{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{18}}{\mathrm{N}}_{\mathrm{4}}\mathrm{O}}_{n\mathrm{1}+n\mathrm{2}-\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}\end{array}$$

Table 2 HOM dimers and trimers formed in the oxidation of isoprene by NO₃.

^a ROOR denotes organic peroxide. ^b The numbering refers to Table 1.

C₁₀H₁₇N₃O_n series (dimer 3, Table 2) were likely formed by the cross-accretion reaction of one M1 RO₂ and one M2 RO₂ (Reaction R9). Since n1 is ≥5 and n2 is ≥9, the number of oxygen atoms in C₁₀H₁₇N₃O_n is expected to be ≥12, which is also roughly consistent with our observation that only C₁₀H₁₇N₃O_n with n≥11 were detected.

$$\begin{array}{}\text{(R9)}& {{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{8}}\mathrm{NO}}_{n\mathrm{1}}\mathrm{•}+{{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{9}}{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_{n\mathrm{2}}\mathrm{•}\to {{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{17}}{\mathrm{N}}_{\mathrm{3}}\mathrm{O}}_{n\mathrm{1}+n\mathrm{2}-\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}\end{array}$$

Similarly, C₁₀H₁₈N₂O_n(n=10–16) and C₁₀H₁₅N₃O_n(n=13–17) series (dimer 4, dimer 5, Table 2) were likely formed from the accretion reaction between one M1 RO₂ and one M4 RO₂ and between one M1 RO₂ and one M3 RO₂ (C₅H₇N₂O₉•). Other dimer series than dimers 1–5 were also present. However, they had quite low intensity (Fig. 4), which was consistent with the low abundance of their parent monomer RO₂. They can be formed from various accretion reactions of monomer RO₂. For example, C₁₀H₁₉N₃O_n can be formed by the accretion reaction of C₅H₉N₂O_n• and C₅H₁₀NO_n• (Table 2).

Figure 4 Kendrick mass defect plot for O of HOM dimers formed in the isoprene + NO₃ reaction. The size (area) of circles is set to be proportional to the average peak intensity of each molecular formula during the first isoprene addition period (P1). The molecular formula includes the reagent ion ¹⁵NO${}_{\mathrm{3}}^{-}$, which is not shown for simplicity. The species labeled in grey (C₁₀H₁₇N₃O_12–14 H[15N]₂O${}_{\mathrm{6}}^{-}$) are the adducts of C₁₀H₁₇N₃O_12–14 with H[15N]₂O${}_{\mathrm{6}}^{-}$.

Similarly to monomers, a few species dominated in the HOM dimer spectrum. The dominant dimer series were C₁₀H₁₇N₃O_x and C₁₀H₁₆N₂O_x series, with C₁₀H₁₇N₃O_12–14 and C₁₀H₁₆N₂O_12–14 showing the highest intensity among each series (Fig. 4). In addition, the O $/$ C ratio or oxidation state of HOM dimers was generally lower than that of monomers (Figs. 2, 4), which resulted from the loss of two oxygen atoms in the accretion reaction of two monomer RO₂.

According to the mechanism above (Reactions R7–R9), we attempt to explain the relative intensities of the dimers using the signal intensities of monomer RO₂. Assuming that the rate constant for each of the HOM-RO₂ + HOM-RO₂ reactions forming dimers is the same considering that all HOM-RO₂ are highly oxygenated with a number of functional groups, it is expected that the dimer formed by the recombination between the most abundant RO₂ has the highest intensity. The most abundant monomers RO₂ were C₅H₉N₂O₉• and C₅H₉N₂O₁₀•, and thus the most abundant dimers are expected to be C₁₀H₁₆N₄O₁₆, C₁₀H₁₆N₄O₁₇, and C₁₀H₁₆N₄O₁₈. This expected result is in contrast with our observation showing that the most abundant dimers were C₁₀H₁₇N₃O_12–14 and C₁₀H₁₆N₂O_12–14 (Fig. 4). The discrepancy is possibly attributed to the presence of less oxygenated RO₂ (with O ≤ 5) that have a low detection sensitivity in the NO₃-CIMS (Riva et al., 2019) due to their lower oxygenation compared with other HOM RO₂ shown above. These RO₂ may react with C₅H₉N₂O₉• and C₅H₉N₂O₁₀•. For example, C₅H₈NO₅• (RO₂) is proposed as an important first-generation RO₂ in the oxidation of isoprene by NO₃ (Ng et al., 2008; Rollins et al., 2009; Kwan et al., 2012; Schwantes et al., 2015). Although C₅H₈NO₅• showed a very low signal in our mass spectra, it was likely to have high abundance since it was the first RO₂ formed in the reaction of isoprene with NO₃. Indeed, we found that the termination products of C₅H₈NO₅• such as C₅H₉NO₅, C₅H₇NO₄, and C₅H₉NO₄ had high abundance in another study, indicating the high abundance of C₅H₈NO₅•. The accretion reaction of C₅H₈NO₅• with C₅H₉N₂O_9–10• and C₅H₈NO_9–10• can explain the high abundance of C₁₀H₁₇N₃O_12–14 and C₁₀H₁₆N₂O_12–14 among all dimers.

Provided that C₅H₈NO₅• is abundant, we still cannot explain the relative intensities of C₁₀H₁₇N₃O₁₂, C₁₀H₁₇N₃O₁₃, and C₁₀H₁₇N₃O₁₄ that were all formed by the accretion reaction with C₅H₈NO₅•. C₁₀H₁₇N₃O₁₂ should have the highest intensity among C₁₀H₁₇N₃O_12–14 as its precursor RO₂, C₅H₉N₂O₉•, is the most abundant. This suggests that accretion reactions other than those of C₅H₈NO₅• with C₅H₉N₂O_9–10• also contributed to C₁₀H₁₇N₃O_12–14. Admittedly, the assumption of different RO₂ having similar rate constants in accretion reactions may not be valid. For example, self-reaction of tertiary RO₂ is slower than secondary and primary RO₂ (Jenkin et al., 1998; Finlayson-Pitts and Pitts, 2000). Different rate constants may also lead to the observation that the most abundant dimers could not be explained by the most abundant RO₂.

The time profiles of C₁₀H₁₆N₂O_n indicate contributions of both the first- and second-generation products. The dominance of the first- or second-generation products depended on the specific compounds. Most C₁₀H₁₆N₂O_n compounds increased instantaneously after isoprene additions, indicating significant contributions of first-generation products. Since the formation of C₁₀H₁₆N₂O_n likely involved C₅H₈NO₅• as discussed above, the instantaneous increase may result from the increase in C₅H₈NO₅• as well as other first-generation RO₂. After the initial increase, C₁₀H₁₆N₂O_10–12 then decayed with time (Fig. 5), while C₁₀H₁₆N₂O_13–15 increased again in the later phase of a period and when NO₂ and O₃ were added. The second increase indicated that C₁₀H₁₆N₂O_13–15 may contain more than one isomer, which had different production pathways. As discussed above, C₅H₈NO_n• can be either a first-generation RO₂ formed directly via the reaction of isoprene with NO₃ and autoxidation or a second-generation RO₂, e.g., formed via the reaction of C₅H₈O₂ with NO₃. Therefore, the second increase in C₁₀H₁₆N₂O_13–15 may result from the reaction of two first-generation RO₂ and of two second-generation RO₂ or between one first-generation and one second-generation RO₂. The increase in C₁₀H₁₆N₂O_14–15 after isoprene addition was not large, indicating the larger contributions from second-generation products compared with other C₁₀H₁₆N₂O_n. Overall, as the number of oxygen increased, the contribution of second-generation products to C₁₀H₁₆N₂O_n increased.

Figure 5 Time series of peak intensity of several HOM dimers of C₁₀H₁₆N₂O_n series. The dashed lines indicate the time of isoprene additions. The long-dashed arrow indicates the time of NO₂ addition. The dash-dotted arrows indicate the time of O₃ additions. The horizontal arrows indicate y-axis scales for different markers.

In contrast to C₁₀H₁₆N₂O_n series, C₁₀H₁₈N₄O_n increased gradually after each isoprene addition and then decreased afterward (Fig. 6), either naturally or after isoprene additions, which is typical for second-generation products. Since C₁₀H₁₈N₄O_n was likely formed by the accretion reaction of C₅H₉N₂O_n• (RO₂), the time profile of C₁₀H₁₈N₄O_n was as expected since C₅H₉N₂O_n• was formed via the reaction of NO₃ with first-generation products C₅H₉NO_n. The C₁₀H₁₈N₄O_n concentration depended on the product of the concentrations of two C₅H₉N₂O_n•. Taking C₁₀H₁₈N₄O₁₆ as an example, its concentration can be expressed as follows:

$$\begin{array}{rl}{\displaystyle \frac{\mathrm{d}\left[{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{18}}{\mathrm{N}}_{\mathrm{4}}{\mathrm{O}}_{\mathrm{16}}\right]}{\mathrm{d}t}}& =k\left[{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{9}}{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{9}}\right]\left[{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{9}}{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{9}}\right]\\ & -k_{\mathrm{wl}}\left[{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{18}}{\mathrm{N}}_{\mathrm{4}}{\mathrm{O}}_{\mathrm{16}}\right].\end{array}$$

When the concentration of C₅H₉N₂O₉• increased, the changing rate of C₁₀H₁₈N₄O₁₆ was positive and increased, and thus the concentration of C₁₀H₁₈N₄O₁₆ increased. When the concentration C₅H₉N₂O₉• decreased sharply after isoprene additions, the changing rate of C₁₀H₁₈N₄O₁₆ decreased and even became negative values, and thus the concentration of C₁₀H₁₈N₄O₁₆ decreased after isoprene addition.

Figure 6 Time series of peak intensity of several HOM dimers of C₁₀H₁₈N₄O_n series. The dashed lines indicate the time of isoprene additions. The long-dashed arrow indicates the time of NO₂ addition. The dash-dotted arrows indicate the time of O₃ additions. The horizontal arrows indicate y-axis scales for different markers.

Similarly to the C₁₀H₁₆N₂O_n series, while C₁₀H₁₇N₃O_n first increased instantaneously with isoprene addition, it increased again during the later stage of each period (Fig. S10), showing a mixed behavior of the first-generation products and second-generation products. The time series of C₁₀H₁₇N₃O_n was as expected in general because C₁₀H₁₇N₃O_n was likely formed via the accretion reaction of C₅H₈NO_n• (M1 RO₂) and C₅H₉N₂O_n• (M2 RO₂), which were first- or second-generation, and second-generation RO₂, respectively.

Some dimers that cannot be explained by accretion reactions, such as C₁₀H₁₆N₃O_n(n=12–15)•, C₁₀H₁₇N₂O_n(n=11–12)•, C₁₀H₁₆NO_n(n=10–14)•, C₁₀H₁₅NO_n(n=9–12), and C₁₀H₁₇NO_n(n=9–15), were also observed. These dimers had low abundance. We note that due to their low signals in the mass spectra, their assignment and thus range of n may be subject to uncertainties. Since C₁₀H₁₆NO_n(n=10–16)•, C₁₀H₁₆N₃O_n(n=12–15)•, and C₁₀H₁₇N₂O_n• contain unpaired electrons, they cannot be formed via the direct accretion reaction of two RO₂. Instead, C₁₀H₁₆N₃O_n(n=12–15)• (dimer R1) and C₁₀H₁₇N₂O_n• (dimer R2) were likely RO₂ formed by the reaction of HOM dimers containing a double bond (dimer 1) with NO₃ and with OH, respectively, followed by the reaction with O₂.

$$\begin{array}{}\text{(R10)}& {\displaystyle }{{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{16}}{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_n+{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}}\to {{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{16}}{\mathrm{N}}_{\mathrm{3}}\mathrm{O}}_n\mathrm{•}\text{(R11)}& {\displaystyle }{{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{16}}{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_n+\mathrm{OH}+{\mathrm{O}}_{\mathrm{2}}\to {{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{17}}{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}_n\mathrm{•}\end{array}$$

The corresponding termination products of C₁₀H₁₆N₃O_n• RO₂ series such as C₁₀H₁₅N₃O_n (ketone) and C₁₀H₁₇N₃O_n (hydroperoxide/alcohol) were also observed, although these compounds can also be formed via reactions between two RO₂ radicals (Reaction R9 and Table 1). Among the termination products, C₁₀H₁₅N₃O_n had low intensity. Reaction (R13) and the termination reaction of C₁₀H₁₇N₂O_n• with HO₂ provided an additional pathway to C₁₀H₁₇N₃O_n besides the Reaction (R9) pathway discussed above. Similarly, other dimers may also be formed by the termination reactions of dimer RO₂ with RO₂ or HO₂. For example, C₁₀H₁₈N₄O_n can be formed via termination reaction of C₁₀H₁₇N₄O_n• with another RO₂ wherein C₁₀H₁₇N₄O_n• can be formed as follows.

$$\begin{array}{}\text{(R12)}& {{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{17}}{\mathrm{N}}_{\mathrm{3}}\mathrm{O}}_n+{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}}\to {{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{17}}{\mathrm{N}}_{\mathrm{4}}\mathrm{O}}_n\mathrm{•}\end{array}$$

C₁₀H₁₆NO_n(n=10–14)• could be explained by the reaction of monomer RO₂ with isoprene.

$$\begin{array}{}\text{(R13)}& {{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{8}}\mathrm{NO}}_n\mathrm{•}+{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{8}}+{\mathrm{O}}_{\mathrm{2}}\to {{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{16}}\mathrm{NO}}_n\mathrm{•}\end{array}$$

Only C₁₀H₁₆NO_n• with n≥10 were detected, while according to the mechanism of self-reaction between C₅H₈NO_n•, the n range of C₁₀H₁₆NO_n• is expected to be 7–14. The absence of C₁₀H₁₆NO_n(n<10)• is likely attributed to their low abundance, which might result from low precursor concentrations, low reaction rates with isoprene, and/or faster reactive losses with other radicals. Such a reaction of RO₂ with isoprene has been proposed by Ng et al. (2008) and Kwan et al. (2012). The corresponding termination products of C₁₀H₁₆NO_n• are C₁₀H₁₅NO_n (ketone) and C₁₀H₁₇NO_n species (hydroperoxide/alcohol). C₁₀H₁₇NO_n species showed a time profile of typical first-generation products (Fig. S11), i.e., increasing immediately with isoprene addition and then decaying with time. This behavior further supports the possibility of Reaction (R13). Yet the reaction rate of alkene with RO₂ is likely low due to the high activation energy (Stark, 1997, 2000). It is worth noting that to our knowledge no experimental kinetic data on the addition of RO₂ to alkenes in the gas phase in atmospheric relevant conditions are available, though fast, low-barrier ring closure reactions in unsaturated RO₂ radicals have been reported (Vereecken and Peeters, 2004, 2012; Kaminski et al., 2017; Richters et al., 2017; Chen et al., 2021). We would like to note that there is unlikely interference to C₁₀-HOM from monoterpenes, which has been reported previously (Bernhammer et al., 2018), as the concentration of monoterpenes in the chamber during this study was below the limit of detection, which was ∼50 ppt (3σ).

Some of the dimers discussed above have been observed in previous laboratory studies. Ng et al. (2008) found C₁₀H₁₆N₂O₈ and C₁₀H₁₆N₂O₉ in the gas phase and C₁₀H₁₇N₃O₁₂, C₁₀H₁₇N₃O₁₃, C₁₀H₁₈N₄O₁₆, and C₁₀H₁₇N₅O₁₈ in the particle phase. C₁₀H₁₆N₂O₈ and C₁₀H₁₆N₂O₉ were also observed in our study, but their intensity in the MS was too low to assign molecular formulas with high confidence. The low intensity may be due to the low sensitivity of C₁₀H₁₆N₂O_8,9 in NO${}_{\mathrm{3}}^{-}$-CIMS. According to modeling results of the products formed in cyclohexene ozonolysis by Hyttinen et al. (2015), at least two hydrogen bond donor functional groups are needed for a compound to be detected in a nitrate CIMS. As C₁₀H₁₆N₂O₈ and C₁₀H₁₆N₂O₉ have no and only one H-bond donor function groups, respectively, they are expected to have low sensitivity in NO${}_{\mathrm{3}}^{-}$-CIMS. Moreover, the low intensity can be partly attributed to the much lower isoprene concentrations used in this study compared to previous studies, leading to the low concentration of C₁₀H₁₆N₂O₈ and C₁₀H₁₆N₂O₉ (Ng et al., 2008). C₁₀H₁₇N₃O₁₂, C₁₀H₁₇N₃O₁₃, C₁₀H₁₈N₄O₁₆, and C₁₀H₁₇N₅O₁₈ were all observed in the gas phase in this study, wherein the concentration of C₁₀H₁₇N₅O₁₈ was very low. The formation pathways of C₁₀H₁₇N₃O₁₂, C₁₀H₁₇N₃O₁₃, and C₁₀H₁₈N₄O₁₆ (Reaction R8) were generally similar to those proposed by Ng et al. (2008), except that the products from H shift of RO₂ were involved in the formation of C₁₀H₁₇N₃O₁₃. Among the two pathways of C₁₀H₁₈N₄O₁₆ formation (Reaction R8 and via Reaction R12), our results indicate that Reaction (R8) was the main pathway, based on the low concentrations of C₁₀H₁₇N₄O${}_{\mathrm{16}/\mathrm{17}}\mathrm{•}$ and other termination products of them, C₁₀H₁₆N₄O${}_{\mathrm{15}/\mathrm{16}}$. That the time profile of C₁₀H₁₈N₄O₁₆ was consistent with what is expected from Reaction (R8) as discussed above offers additional evidence for that conclusion.

Few field studies have reported HOM dimers formed via the reaction of NO₃ with isoprene. This might be because NO₃ + isoprene-HOM dimers can have the identical molecular formula to the HOM monomers from monoterpene oxidation. Possible contribution of dimer formation in the isoprene oxidation to C6–10 HOM in the particle phase observed at a rural site, Yorkville, US, is reported by Chen et al. (2020), although these HOM are thought to be more likely from monoterpene oxidation.

3.4 HOM trimers and their formation

A series of HOM trimers were observed, such as C₁₅H₂₄N₄O_n(n=17–22), C₁₅H₂₅N₅O_n(n=20–22), C₁₅H₂₅N₃O_n(n=13–20), C₁₅H₂₆N₄O_n(n=17–21), and C₁₅H₂₄N₂O_n(n=12–16). Among the trimers, C₁₅H₂₄N₄O_n was the most abundant series (Fig. S12). The C₁₅H₂₄N₄O_n series can be explained by the accretion reaction of one monomer HOM RO₂ and one dimer HOM RO₂.

$$\begin{array}{}\text{(R14)}& \begin{array}{rl}& {{\mathrm{C}}_{\mathrm{10}}{\mathrm{H}}_{\mathrm{16}}{\mathrm{N}}_{\mathrm{3}}\mathrm{O}}_{n\mathrm{1}}\mathrm{•}+{{\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{8}}\mathrm{NO}}_{n\mathrm{2}}\mathrm{•}\\ & \to {{\mathrm{C}}_{\mathrm{15}}{\mathrm{H}}_{\mathrm{24}}{\mathrm{N}}_{\mathrm{4}}\mathrm{O}}_{n\mathrm{1}+n\mathrm{2}-\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}\end{array}\end{array}$$

The formation pathways of dimer RO₂ C₁₀H₁₆N₃O_n (n=12–15) and C₁₀H₁₇N₂O_n are shown above (Reactions R10 and R11).

The other trimers were likely formed via similar pathways (Table 2 and Supplement Sect. S2). Since NO${}_{\mathrm{3}}^{-}$-CIMS cannot provide the structural information of these HOM trimers, we cannot elucidate the major pathways. However, in all these pathways, dimer-RO₂ is necessary to form a trimer, and most of the dimer-RO₂ formation pathways require at least one double bond in the dimer molecule except for the reaction of RO₂ with isoprene. Since one double bond has already reacted in the monomer-RO₂ formation, we anticipate that in the reaction with NO₃ it will be more favorable for precursors (VOC) containing more than one double bond to form trimer molecules than precursors containing only one double bond, as it is easier to generate new RO₂ radicals from these dimers by attack on the remaining double bond(s).

The time profile of C₁₅H₂₄N₄O_n showed the mixed behavior of first- and second-generation products (Fig. S13), consistent with the mechanism discussed above since C₅H₈NO_n• and C₁₀H₁₆N₃O_n• were of first- or second-generation and second-generation, respectively. The contributions of the second-generation products became larger as the number of oxygen atoms increased. In contrast, C₁₅H₂₅N₃O_n showed instantaneous increase with isoprene addition (Fig. S14), which was typical for time profiles of first-generation products. Both proposed formation pathways of C₁₅H₂₅N₃O_n (Reactions RS6 and RS7) contained a second-generation RO₂, which was not in line with the time profile observed. The observation cannot be well explained unless we assume molecular adducts of a dimer with one monomer. It is also possible that some C₁₀H₁₇N₂O_n• were formed very, very quickly or that there were other formation pathways of C₁₅H₂₅N₃O_n not accounted for here.

We are not aware of field studies reporting NO₃ + isoprene-HOM trimers, which is likely for the same reason for dimers discussed above. It is challenging to distinguish HOM trimers formed in the reaction NO₃ with isoprene from the dimers formed by cross-reaction of the RO₂ from monoterpene oxidation (C10-RO₂) with that from isoprene oxidation (C5-RO₂), as their molecular formulas can be identical.

3.5 Contributions of monomers, dimers, and trimers to HOM

The concentration (represented by peak intensity) of monomers was higher than that of dimers, but overall their concentrations remained on the same order of magnitude (Fig. 1a, inset). The concentration of trimers was much lower than that of monomers and dimers. The relative contributions of monomers, dimers, and trimers evolved in time due to the changing concentration of each HOM species. Comparing the contributions of various classes of HOM in period 1 with those in periods 1–6 reveals that the relative contribution of monomers increased with time, especially that of 2N-monomers, while the contribution of dimers decreased. This trend is attributed to the larger wall loss of dimers compared to monomers because of their lower volatility and also to the continuous formation of second-generation monomers, mostly 2N-monomers. Overall, the relative contribution of total HOM monomers decreased immediately after isoprene addition, while the contribution of HOM dimers increased rapidly (Fig. S15), which was attributed to the faster increase in dimer intensity due to their rapid formation. Afterwards, the contribution of monomers to total HOM gradually increased and that of dimers decreased, which was partly due to the faster wall loss rate of dimers and to the continuous formation of second-generation monomers.

3.6 Yield of HOM

The HOM yield in the oxidation of isoprene by NO₃ was estimated using the sensitivity of H₂SO₄. It was derived for the first isoprene addition period to minimize the contribution of multi-generation products and to better compare with the data in the literature, thus denoted as primary HOM yield (Pullinen et al., 2020), and was estimated to be 1.2 %${}_{-\mathrm{0.7}\mathit{\%}}^{+\mathrm{1.3}\mathit{\%}}$. The uncertainty was estimated as shown in Supplement Sect. S1. Despite the uncertainty, the primary HOM yield here was much higher than the HOM yield from the ozonolysis and photooxidation of isoprene (Jokinen et al., 2015). The difference may be attributed to the more efficient oxygenation in the addition of NO₃ to carbon double bonds. Compared with the reaction with O₃ or OH, the initial peroxy radicals contain five oxygen atoms when isoprene reacts with NO₃, while the initial peroxy radicals contain only three oxygen atoms when reacting with OH, and the ozonide contains three oxygen atoms in the case of O_3.

4 Conclusion and implications

HOM formation in the reaction of isoprene with NO₃ was investigated in the SAPHIR chamber. A number of HOM monomers, dimers, and trimers containing one to five nitrogen atoms were detected, and their time-dependent concentration profiles were tracked throughout the experiment. Some formation mechanisms for various HOM were proposed according to the molecular formula identified and the available literature. HOM showed a variety of time profiles with multiple isoprene additions during the reaction. First-generation HOM increased instantaneously after isoprene addition and then decreased, while second-generation HOM increased gradually and then decreased with time, reaching a maximum concentration at the later stage of each period. The time profiles provide additional constraints on their formation mechanism besides the molecular formula, suggesting whether they were first-generation products or second-generation products or a combination of both. 1N-monomers (mostly C₅) were likely formed by NO₃ addition to a double bond of isoprene, forming monomer RO₂, followed by autoxidation and termination via the reaction with HO₂, RO₂, and NO₃. Time series suggest that some 1N-monomer could also be formed by the reaction of first-generation products with NO₃ and thus be of second generation. 2N-monomers were likely formed via the reaction of first-generation products such as C5-hydroxynitrate with NO₃ and are thus second-generation products. 3N-monomers likely comprised peroxy/peroxyacyl nitrates formed by the reaction of 2N-monomer RO₂ with NO₂ and possibly nitronitrates formed via the direct addition of N₂O₅ to the first-generation products. HOM dimers were mostly formed by the accretion reactions between various HOM monomers RO₂, either first-generation or second-generation or with the contributions of both, and thus showed time profiles typical of either first-generation products, second-generation products, or a combination of both. Additionally, some dimer peroxy radicals (dimer RO₂) were formed by the reaction of NO₃ with dimers containing a C=C double bond. HOM trimers were proposed to be formed by accretion reactions between the monomer RO₂ and dimer RO₂.

Overall, both HOM monomers and dimers contribute significantly to total HOM, while trimers only contributed a minor fraction. Within both the monomer and dimer compounds, a limited set of compounds dominated the abundance, such as C₅H₈N₂O_n, C₅H₁₀N₂O_n, C₁₀H₁₇N₃O_n, and C₁₀H₁₆N₂O_n series. 2N-monomers, which were second-generation products, dominated in monomers and accounted for ∼34 % of all HOM, indicating the important role of second-generation oxidation in HOM formation in the isoprene + NO₃ reaction. Both RO₂ autoxidation and “alkoxy–peroxy” pathways were found to be important for 1N- and 2N-HOM formation. In total, the yield of HOM monomers, dimers, and trimers accounted for 1.2 %${}_{-\mathrm{0.7}\mathit{\%}}^{+\mathrm{1.3}\mathit{\%}}$ of the isoprene reacted, which was much higher than the HOM yield in the oxidation of isoprene by OH and O₃ reported in the literature (Jokinen et al., 2015). This means that the reaction of isoprene with NO₃ is a competitive pathway of HOM formation from isoprene.

The HOM in the reaction of isoprene with NO₃ may account for a significant fraction of SOA. If all the HOM condense on particles, using the molecular weight of the HOM with the least molecular weight observed in this study (C₅H₉NO₆), the HOM yield corresponds to a SOA yield of 3.6 %. Although SOA concentrations were not measured in this study, Ng et al. (2008) reported a SOA yield of the isoprene + NO₃ reaction of 4.3 %–23.8 %. Rollins et al. (2009) reported a SOA yield of 2 % at low organic aerosol loading (∼0.52 µg m⁻³) and 14 % if the further oxidation of the first-generation products is considered in the isoprene + NO₃ reaction. Comparing the potential SOA yield produced by HOM with SOA yields in the literature suggests that HOM may play an important role in the SOA formation in the isoprene + NO₃ reaction.

The RO₂ lifetime is approximately 20–50 s in our experiments, which is generally comparable to or shorter than the lifetime of RO₂ in the ambient atmosphere at night, varying from several tens to several hundreds of seconds (Fry et al., 2018), depending on the NO₃, HO₂, and RO₂ concentrations. Assuming a HO₂, RO₂, and NO₃ concentration of 5 ppt, 5 ppt (Tan et al., 2019), and 300 ppt (Brown and Stutz, 2012), respectively, the RO₂ lifetime in our study is comparable to the nighttime RO₂ lifetime (50 s) found in urban locations and areas influenced by urban plume. In areas with longer RO₂ lifetime such as remote areas, the autoxidation is expected to be more important relative to bimolecular reactions. This may enhance HOM yield and thus enhance SOA yield. However, on the other hand, at lower RO₂ concentration and thus longer RO₂ lifetime, reduced rates of RO₂+RO₂ reactions producing low-volatility dimers can reduce the SOA yield by reducing dimer yield (McFiggans et al., 2019; Pullinen et al., 2020). The RO₂ fate in our experiments is dominated the reaction RO₂+NO₃ with significant contribution of RO₂+RO₂, which can also represent the RO₂ fate in the urban areas and areas influenced by urban plume. Our experiment condition cannot represent the chemistry in HO₂-dominated regions such as clean forest environments (Schwantes et al., 2015).

We observed the second-generation products formed by the reaction of first-generation products. The lifetime of first-generation nitrates in the ambient atmosphere, according their rate constants with OH and NO₃ (Wennberg et al., 2018), are ∼5 and ∼1.3–4 h, respectively, with respect to the reaction with OH and NO₃ assuming a typical OH concentration of 2 × 10⁶ molec. cm⁻³ (Lu et al., 2014; Tan et al., 2019) and a NO₃ concentration of 100–300 ppt in urban areas (Brown and Stutz, 2012). Therefore, they have the chance to react further with OH and NO₃ at dawn. In our experiments, the lifetimes of these first-generation nitrates with respect to OH and NO₃ are comparable to the aforementioned lifetime due to comparable OH and NO₃ concentrations with these ambient conditions. Therefore, our findings on the second-generation products are relevant to the ambient urban atmosphere and areas influenced by urban plumes. Some of these products such as C₅H_8,10N₂O₈ and multi-generation nitrooxyorganosulfates have been observed in recent field studies in polluted megacities in eastern China (Hamilton et al., 2021; Xu et al., 2021).