The limonene +NO3 experiment was performed in the atmospheric simulation chamber SAPHIR (Simulation of Atmospheric PHotochemistry In a large Reaction chamber) at the Forschungszentrum Jülich, Germany. SAPHIR is a 270 m3 double-wall cylindrical Teflon chamber with a surface-to-volume ratio of ∼1 m2 m-3. Details of SAPHIR have been described before (Rohrer et al., 2005; Zhao et al., 2015a, b; Zhao et al., 2018) and are only summarized here. Detailed experimental procedures can be found in Fig. 1a. Before each experiment, SAPHIR was flushed for about 4 h at a flow rate of 370 m3 h-1 with high-purity synthetic air (purity >99.9999 % O2 and N2) in order to clean the chamber. To simulate nighttime conditions for the NO3 chemistry, the chamber roof remained closed throughout the experiment. The experiment was performed under dry conditions (RH <2 %) at a temperature of 302±3 K. No seed aerosols were used in the experiments. A fan was used for active mixing in the chamber, leading to a typical mixing time of ∼1 min (Fuchs et al., 2013).

NO3 radicals were generated via the reaction of ozone with nitrogen dioxide: R10NO2+O3→NO3+O2,R11NO2+NO3↔N2O5.

Therefore, O3 and NO2 were first added to the chamber to form N2O5 and NO3 with mixing ratios of ∼2 and ∼0.15 ppbv, respectively. About 20 min later, 5 ppbv of limonene was added to start the organic chemistry. Five more additions of limonene followed, with added concentrations of about 3, 3, 2, 2, and finally 8 ppbv, which divided the experiment into six periods (P1 to P6) (Fig. 1a). For period P3 and P5, NO2 and O3 were also added to compensate for the loss of NO3 and N2O5 (Fig. 1a). The concentrations of NO2 and O3 were maintained around 20 to 70 ppbv throughout the experiment, ensuring the major loss of limonene was by reaction with NO3 rather than with O3 (Figs. S1). In the first 10 min of reaction (named period P1a hereafter, Fig. 1a), NO3 accounted for 86 % of the chemical loss of limonene.

Gas-phase HOM were detected by a chemical ionization time-of-flight mass spectrometer (CI-APi-TOF, Aerodyne Research Inc., USA) with a resolution (m/z)/(Δm/z) of ∼3800 using 15NO3- as the reagent ion, which is capable of detecting organic molecules with high oxygen content (Eisele and Tanner, 1993; Jokinen et al., 2012). The mass spectra were analyzed using the software Tofware (Tofwerk/Aerodyne) in Igor Pro (WaveMetrics, Inc.). Peak identification was conducted by a high-resolution analysis (examples shown in Fig. S2). We observed several peaks which were obviously products from the isoprene +NO3 reaction, such as C5H10N2O8⚫⋅15NO3- at m/z 289. Such peaks were present before the limonene oxidation reaction started, suggesting that these compounds preexisted in the chamber. These isoprene oxidation products were likely formed in an isoprene +NO3 experiment performed 2 d before (Zhao et al., 2021) and released slowly from chamber walls due to their semi-volatile character. Their total concentration is less than 1 ppt. All the isoprene-HOM observed (C5H9NO7,10, C5H8N2O8-10, C5H10N2O8, C5H9N3O9,10) are saturated and do not contain C=C double bond. The isoprene-HOM will not influence the reaction of limonene with NO3 in this study. Therefore, they are not discussed as products from the limonene oxidation in our experiment. (However, we cannot exclude that they were partly generated from fragmentation in the limonene +NO3 reaction.)

A set of instruments were used to measure other gas-phase species, including VOC, NOx, O3, NO3, and N2O5 (Shen et al., 2021). Concentrations of NO3 and N2O5 were measured in situ using a home-built diode laser-based, cavity ring-down spectrometer similar to the instrument described in the work by Wagner et al. (2011). The concentrations of limonene were measured using a proton transfer reaction time-of-flight mass spectrometer (PTR-TOF-MS, Ionicon Analytik, Austria). The SOA number concentration, surface concentration, and size distribution were detected by a scanning mobility particle sizer (SMPS, TSI DMA3081/TSI CPC3786) and a condensation particle counter (CPC, TSI3785). Temperature and relative humidity were continuously monitored throughout the experiment.

HOM concentrations were obtained from the normalized signals to the total signals of the mass spectra (nc, normalized counts) by applying a calibration coefficient (C) of 2.5×1010 molecule cm-3 nc-1. C was determined using H2SO4 as the charging efficiency of HOM and H2SO4 are considered to be equal (Ehn et al., 2014; Pullinen et al., 2020; Shen et al., 2021). The details of determination of the calibration coefficient are shown in Sect. S1 in the Supplement. A mass-independent transmission efficiency was used according to our previous study, which causes an additional uncertainty of 14 % (Pullinen et al., 2020). In this previous study, the transmission efficiency curve of nitrate CI-APi-TOF was determined and found to monotonously decrease with increasing mass of ions but only slightly depend on the mass range (14 % change). As we used the same setting as our previous study, we have included the slight dependence of transmission on m/z in the uncertainties. The concentrations of HOM were corrected for chamber wall losses, which were determined for a number of HOM similar to our previous study (Zhao et al., 2018), with details described in the Supplement. When the chamber is actively mixed, the wall loss was determined to be (2.2±0.2)×10-3 s-1. As the HOM yield was determined during the first 3 min of the experiment, we considered the wall loss rate to be constant (2.2×10-3 s-1) during this period. Sensitivity analysis showed that the HOM yield in this study is not very sensitive to the wall loss rate and is changing by only +0.88 % and -0.44 % if the wall loss rate is varied by +100 % or -50 %.

The HOM yield was calculated as 1Y=HOMVOCr=IHOM⋅CN2O5r, where HOM is the concentration of HOM, IHOM is the total signal intensity of HOM, C is the calibration factor, and VOCr and N2O5r stand for the concentrations of limonene and N2O5 reacted, respectively. We used the reacted concentration of N2O5 rather than the measured reacted limonene concentration as a large fraction of limonene was already reacting away during the VOC injection before it was homogeneously mixed in the chamber. During this part of the experiment, the high limonene concentration resulted in a rapid loss of NO3, such that every NO3 formed from the decomposition of N2O5 reacted with limonene: R12N2O5→NO2+NO3R13limonene+NO3→Products. The initial NO3 concentration before the limonene injection was small compared to the time-integrated loss of N2O5, and other NO3 loss processes were negligible right after the limonene injection, so that the observed decrease in the N2O5 concentration equals indeed the consumption of limonene. The wall loss rate constant of N2O5 in the SAPHIR chamber is 7.2×10-5 s-1 (Fry et al., 2009). As the HOM yield determination is based on the first 3 min, the wall loss of N2O5 can be ignored compared to the loss via the reaction of NO3 with limonene.

The uncertainty of the HOM yield was estimated to be -55%/+117% based on the combined uncertainties of the HOM-ON peak intensities (∼10 %), the limonene concentration (∼15 %), the transmission efficiency (-0%/+14%), and the calibration factor (-52%/+101%) using error propagation (Zhao et al., 2021). The first 3 min after the injection of limonene were used to calculate the HOM yield, when most of the first-generation oxidation products were produced and negligible particles were formed. The HOM yield thus reflects the “primary” HOM yield.

The SOA mass from the condensation of HOM was calculated to evaluate the role of HOM for the SOA mass growth. Detailed estimation methods are described in the Supplement, including the determination of particle wall loss and dilution loss rate (Sect. S2). In brief, the growth rate of SOA through HOM vapor condensation is based on the collision rate of vapor molecules with aerosols in the kinetic regime. The Fuchs–Sutugin approach is applied to describe the correction for transition from the kinetic to the diffusion regime (Fuchs and Sutugin, 1971; Ehn et al., 2014). Based on the volatility of HOM, we considered two scenarios for HOM condensation. In scenario 1, all HOM were assumed to irreversibly condense on the surface of particles leading to particle mass growth. In scenario 2, only the irreversible uptake of LVOC and ULVOC/ELVOC compounds were considered to contribute to the growth of SOA particles in order to examine the role of LVOC and ELVOC while IVOC and SVOC were not included, although they may also contribute to SOA. The calculation of saturation concentration C* (in µgm-3) of each HOM was done based on their molecular compositions using two different parameterizations considering the uncertainties in estimating volatility (R. Wu et al., 2021):

an updated version of the parameterization of Donahue et al. (2011) by Mohr et al. (2019) (scenario 2a): 2log⁡10(C)=25-nC×0.475-nO-3nN×0.2-2nO-3nNnCnC+nO-3nN×0.9-nN×2.5,where nC, nO, nN, and nH are the number of carbon, oxygen, nitrogen, and hydrogen atoms of the compound, respectively.

The RO2⚫ loss pathways were estimated based on MCM simulations (http://mcm.york.ac.uk/, last access: 14 November 2021). The gas-phase reactions of limonene +NO3 under dark condition were simulated using iChamber, an open-source program (https://sites.google.com/view/wangsiyuan/models?authuser=0, last access: 14 November 2021) (Wang and Pratt, 2017). The default chemistry of limonene +NO3 in the MCM was applied in this study (Saunders et al., 2003). Photolysis reactions were excluded by setting the zenith angle to 90∘. Concentrations of O3, NO3, NO2 and N2O5, and temperature and relative humidity were constrained to the experimental data with a time resolution of 1 min. The chamber dilution rate of 1.5×10-5 s-1 was applied to all species. The P1 period was simulated using the above conditions, and the initial concentrations of limonene were added in the model according to the experimental procedures. The sum of all 140 RO2⚫ in the limonene subset of MCM v3.3.1 were used in the usual way to estimate the loss rates of RO2⚫ bimolecular reactions. The reaction rate constants are provided in Table S3 in the Supplement, and calculated loss rates are shown in Fig. S3. We note that the MCM reaction schemes do not include the accretion reactions between HOM-RO2⚫. Berndt et al. (2018a) determined the rate constant of accretion reaction of C10H15O4⚫ formed via α-pinene ozonolysis to be ∼1×10-11 cm3 molecule-1 s-1, which is of the same order as the upper limit for RO2⚫+RO2⚫ reactions used in the MCM schemes for functionalized peroxy radicals such as acyl peroxy radicals (Jenkin et al., 1997; Saunders et al., 2003). However, currently we do not see a reliable updated set of rate coefficients that are applicable to the reaction system in this study. If the rate constants of some RO2⚫+RO2⚫ reactions were higher than those used in MCM, the concentrations of RO2⚫ would be lower and relative importance of RO2⚫+RO2⚫ in RO2⚫ fate would increase. Several simulation results are shown in Fig. S4, including NO3, N2O5, limonene, RO2⚫, reaction rate of limonene with NO3 (k×limonene×NO3), and examples of first- and second-generation RO2⚫.

In the early stage of each period, RO2⚫ mainly reacted with RO2⚫ and NO3, although in the later stage the reaction with NO2 also contributed to a significant fraction of RO2⚫ loss (Fig. S3, showing period P1 as an example). During the period P1a which our peak assignment was based on, the RO2⚫ loss was dominated by RO2⚫+RO2⚫ and RO2⚫+NO3.

After each limonene addition, the concentration of limonene rose first and then rapidly declined, while the concentrations of NO3 and N2O5 rapidly decreased due to the fast reaction between limonene and NO3, and gradually increased when limonene had been consumed (Fig. 1a). About 10 min after the first limonene addition, new particles had already formed and quickly grew in size (Fig. 1b). Therefore, we used the first 10 min reaction time (period P1a) to identify gas-phase HOM products, and the whole experiment to examine the contribution of HOM to SOA.

During period P1, HOM were quickly formed. We identified about 280 HOM compounds, including monomers (C7-C10, ∼ 280–460 Th), dimers (C17-C20, ∼ 490–700 Th), and trimers (C26-C30, ∼ 720–960 Th) (Fig. 2a). Their detailed formulas can be found in Table S1. HOM on the horizontal lines of the Kendrick mass defect plot (O-based) (Figs. 3, S5, and S6) share the same number of C, N, and H atoms, with the number of oxygen atoms increasing from left to right. Such HOM compounds are defined as a family. We notice that most monomer peroxy radical families are each related to two monomer closed-shell product families, with one H atom more or one H atom less, which are the expected termination products of RO2⚫+RO2⚫ reactions, or if HO2⚫ is present, RO2⚫+HO2⚫ termination products. These three related families are defined as a “series”, with the same number of C and N number, such as C10H15-17NO6-14. In total, we identified 6 monomer series (C10H15-17NO6-14, C10H14-16N2O9-15, C10H14-16O7-12, C9H13-15NO7-14, C8H11-13NO6-13, and C7H9-11NO7-11) and 1 monomer family (C10H17N3O12-16), 11 dimer families (C20H31NO10-15, C20H33NO12-16, C20H32N2O9-20, C20H31N3O14-20, C20H33N3O12-20, C20H34N4O15-20, C20H32O13-16, C19H29NO10-13, C19H31NO10-15, C19H30N2O10-18, and C19H31N3O15-19), and 3 trimer families (C30H47N3O18-24, C30H48N4O16-24, and C29H46N4O19-24). The monomer family C10H17N3O12-16 is not classified as series because the supposedly relevant families are not clearly identified. Compounds containing at least one nitrogen atom accounted for more than 90 % of the identified HOM products. We assume that compounds containing nitrogen atoms are organic nitrates, because other N-containing species such as amines or nitro compounds are very unlikely to be formed from the reaction of limonene with NO3. Organic nitrates formed in this study could be alkylnitrates, or (acyl)peroxynitrates formed via the reaction of RO2⚫ with NO2.

During period P1a, in the absence of particles, both HOM monomers and oligomers were observed, including monomers (47 %), dimers (47 %), and trimers (6 %) (Fig. 2a). Concentrations of gas-phase dimers and trimers decreased evidently after particle formation (Figs. 2b, 5, 6), indicating a fast gas–particle condensation and strong tendency of oligomers to condense on particles.

Based on their typical time series (Fig. 1c), products can be classified as first-generation or second-generation products. Generally, the concentrations of first-generation products, which result from the direct reaction of limonene with NO3, are expected to quickly increase after the limonene addition, followed by a steady decline due to wall loss or chemical reactions. Concentrations of typical second-generation products, which result from further reactions of first-generation products, are expected to show a gradually increasing concentration pattern after a limonene addition and reach their maximum concentration later than first-generation products. These general expectations are modified in our case, since the particle concentration increased in our experiment (Fig. 1b) and the condensational sink of HOM products became stronger over time. Thus, an increase in concentration suggests that the increasing condensational sink was exceeded by increasing production with time, i.e., from second-generation pathways.

To sum up, gas-phase HOM formed in the limonene +NO3 system were dominated by HOM monomers and dimers. Time series patterns of the products indicate multiple generations of reaction pathways.

Among dimers, C20 products were the most abundant, followed by C19 products. Among C20 and C19 dimers, the most prevalent families included C20H32N2Ox (x= 9–20), C20H33N3Ox (x= 12–20), C20H31NOx (x= 10–15), C20H31N3Ox (x= 14–20), C20H34N4Ox (x= 15–20), and C19H30N2Ox (x= 10–18) (Fig. S5). The O/C ratio of dimers did not exceed one, while that of monomers was as high as two. This could be due to oxygen atom loss and participation of less oxygenated RO2⚫ in the dimer formation as discussed below. Time series of dimers also showed different behavior compared to monomers. For example, compounds of the C20H32N2Ox family only reached a considerable peak intensity in period P1 and decreased rapidly thereafter, while the signal intensity in periods P2 to P6 were low (Fig. 5). Generally, other dimers showed similar patterns (Figs. S12–S14), though the difference of their concentration between P2-P6 and P1 were not as large as for the C20H32N2Ox family. The time when signals of several dimers (e.g., C20H32N2Ox, C20H33N3Ox, C20H34N4Ox) dropped substantially matched the time of new particle formation (NPF) and the onset of particle growth, indicating that some dimers were likely involved in the early growth of particles. Such a behavior is expected since dimers have a much lower volatility than monomers. This observation is consistent with the limonene +NO3 laboratory study by Faxon et al. (2018) that found a significant fraction of HOM dimer derived in the particle phase.

In general, C20H32N2Ox showed an overlaying time profile of first- and second-generation products (Fig. 5). C20H32N2Ox were likely formed via the accretion reaction between two monomer RO2⚫ (C10H16NOx⚫): R15C10H16NOx1⚫+C10H16NOx2⚫→C20H32N2Ox1+x2-2+O2. Since C10H16NOx⚫ can be first- or second-generation products, the resulting dimers C20H32N2Ox can also be first- or second-generation products. The time series shows that C20H32N2Ox with lower O number presented more of a first-generation product time profile (Fig. 5), while the relative contribution of second-generation formation was observed to increase with oxygen number.

We compared the observed dimer formula with those expected based on accretion reactions of HOM-RO2⚫. x in the C20H32N2Ox observed was ≥9; however, according to the accretion mechanism and the observed C10H16NOx⚫ (x≥6), x in C20H32N2Ox should be ≥10 (6+6-2=10). Moreover, as the most abundant RO2⚫ within the C10H16NOx⚫ family was C10H16NO10⚫ (Table 1), the most abundant C20H32N2Ox would have an oxygen number of 18 if they were exclusively formed by the accretion reaction of HOM RO2⚫. This contradicted the fact that the most abundant molecule among the C20H32N2Ox family was C20H32N2O13. The findings above could only be explained by the participation of less oxygenated RO2⚫ such as C10H16NO5,6⚫ in the accretion reaction (Berndt et al., 2018a, b; McFiggans et al., 2019). C10H16NO5⚫ was not detected by our CI-APi-TOF, which is attributed to the lower detection sensitivity of molecules with O number ≤5 in the NO3--CIMS (Riva et al., 2019). Still, C10H16NO5⚫ is the first RO2 radical formed in the limonene +NO3 reaction (scheme 1a) so a high mass flux has to pass through this RO2⚫. If we assume that the abundance of C10H16NO5⚫ was high, and considering that the concentration of C10H16NO10⚫ was the highest in the C10H16NOx⚫ family, their accretion reaction (R16) could form C20H32N2O13 and support that C20H32N2O13 was the most abundant C20 dimer product: R16C10H16NO5⚫+C10H16NO10⚫→C20H32N2O13+O2. Time series of dimers with different numbers of N atoms were different, indicating different formation pathways. For example, the C20H31NOx family were mainly first-generation products (Fig. S12), which may be formed via the following reaction: R17C10H16NOx1⚫+C10H15Ox2⚫→C20H31NOx1+x2-2+O2. C10H15Ox⚫ were first-generation radicals (Sect. 3.2.4), while C10H16NOx⚫ were mainly second-generation radicals. C10H16NOx⚫ could also be formed via first-generation pathway as discussed above (scheme 1a), but that was not borne out by the time profile, suggesting a fast termination of first-generation C10H16NOx⚫ radicals. Reaction (R17) could be one of the termination pathways of first-generation C10H16NOx⚫ based on the first-generation time profile of C20H31NOx. In the study by Faxon et al. (2018), the formation of 1N-C20 dimers was explained by a mechanism involving two 1N-RO2 radicals which produced HNO3 as a by-product. However, C10 RO2 radicals without nitrogen atoms were identified in our study, which provided a direct formation pathway of 1N-C20 dimers through reaction (R17).

On the other hand, C20H33N3Ox and C20H34N4Ox were mainly second-generation products (Figs. S13, S14). C20H33N3Ox and C20H34N4Ox were likely to be formed via NO3 oxidation of dimers containing less nitrogen atoms, and were thus second-generation products. The related radicals were also detected, such as C20H32N3Ox⚫ (x= 16–19) and C20H31N2Ox⚫ (x= 13–16). Possible formation pathways of dominant oligomer families are displayed in Table 2. We cannot exclude that the formation pathway of C20H33NOx, C20H34N4Ox, and C19H31NOx may also involve limonene oxidation by OH⚫ (Table 2), which can be formed in the ozonolysis of limonene as a minor pathway. In addition, the high abundance of C20H31NOx (x= 10–15) among the dimers may be partly attributed to a contribution of the reaction of limonene with O3.

The initial drop of the products (dimers and monomers) in Figs. 1, S8, and S12 during P1 (the characteristic time of the fastest decay was 15, 10, and 13 min, respectively) is attributed to the balance of their sources via the reaction of limonene with NO3, their wall loss, and their potential loss by the reaction with NO3. The characteristic time of the fastest decay of the HOM over the second limonene addition in Figs. 1, 4, 5, S12, and S13 are 4–8 min. These decays can be explained by the wall loss rate (characteristic time ∼8 min) and condensation sink of vapor loss to particles according to the study of Kulmala et al. (2012) (characteristic time ∼13 min). The characteristic times of the fastest decay of the HOM at the end of P2 in Figs. S12 and S13 are 1.4–3.4 min, which can also be well explained by the updated wall loss rate and condensation sink of vapor loss to particles at the end of P2 (characteristic time ∼1.4 min). In addition, for some HOM (e.g., C10H15NO10, Fig. 1; C10H14N2O10, Fig. 4; C20H33N3O17, Fig. S13; C20H34N4O17, Fig. S14), the times of limonene additions (except for the first time) matched the time when HOM signals dropped rapidly. This phenomenon implies a sudden decrease of the source of these HOM at limonene additions as sinks including the losses to walls and particles were largely invariant in such a short time. The decrease of the source may be attributed to the rapid depletion of NO3 at limonene injections (Fig. 1). As many of these HOM are second-generation products, i.e., formed via the reactions of first-generation products with NO3, the depletion of NO3 could lead to sudden decreases of the source of the second-generation HOM, which accounted for most HOM in the study.

In summary, HOM dimers are likely to be formed via accretion reactions of monomer RO2⚫, and some dimers can undergo secondary oxidation by NO3. Some dimers were likely involved in the early growth of SOA particles.

Trimers (C26-30) were dominated by C30 compounds (Fig. S6, Table S1). To the best of our knowledge, this is the first study that identified gas-phase trimers in the limonene +NO3 reaction. The O/C ratio of trimers was lower than that of monomers and dimers, suggesting possible multiple accretion reactions in their formation pathways, which lose 2 oxygen atoms in each reaction. As each accretion reaction terminates the peroxy radical chain, the observation of trimers also implies that some dimers could further react with NO3, creating dimer RO2⚫. The most prevalent product families were C30H48N4Ox (x= 16–24) and C30H47N3Ox (x= 18, 19, 21, 23, 24), which were likely formed via the most abundant monomer RO2 radicals – C10H16NOx⚫ and the most abundant dimer RO2 radicals – C20H32N3Ox⚫ and C20H31N2Ox⚫. Trimers from other monoterpenes +NO3 have been observed in previous laboratory studies. For example, C30H48N4O16 and C30H47N3O16 were observed in the mass spectra of α-pinene +NO3 SOA by C. Wu et al. (2021), and C30H47N3O13 was identified in β-pinene +NO3 SOA by Claflin and Ziemann (2018).

Similar to their precursors C20H32N2Ox, C30H48N4Ox showed negligible signal except in period P1, and presented an overlaying time profile of first- and second-generation product pattern (Fig. 6). For comparison, gas-phase trimer products were not observed in the β-pinene +NO3 reaction (Shen et al., 2021), and the trimers observed in SOA from β-pinene +NO3 are likely formed via particle phase reactions (Claflin and Ziemann, 2018). An efficient gas-phase trimer production via subsequent accretion reactions between peroxy radicals requires that the precursor dimer has a high enough reactivity to create a dimer RO2⚫, e.g., via NO3 reaction to a double bond. This suggests that the VOC containing at least two double bonds are likely more favorable to form trimers, which is consistent with our previous findings that trimers were formed in the NO3 reaction with isoprene which also contains two double bonds (Zhao et al., 2021), while they were not observed in the reaction of NO3 with β-pinene which contains only one double bond (Shen et al., 2021).

We chose period P1 for the calculation of HOM yields in order to minimize the influence of the condensational sink on HOM concentration. However, both first-generation and second-generation products existed in this period, as discussed in Sect. 3.2 through Sect. 3.4 and supported by the time-behavior of the total HOM concentration (Fig. S15). Period P1 can be roughly divided into three phases based on the trends in HOM concentration. Shortly after the limonene injection, large quantities of HOM were produced (first-production phase) followed by a balanced intermediate phase when HOM concentrations stopped increasing. After the intermediate phase, HOM concentrations began to increase again (second-production phase). The first-production phase overlapped with the time span where limonene, NO3, and N2O5 concentrations decreased, implying the dominance of first-generation HOM production process. During the second production period, wall loss was compensated by second-generation HOM formation, leading to another rise of the total HOM concentrations. Therefore, we use the first-production phase to estimate primary HOM production, determined over the first 3 min of the experiment. The calculated “primary” HOM molar yield is 1.5%-0.7%+1.7%. This value is significantly lower than the HOM yield of 5 % to 17 % in earlier limonene ozonolysis experiments (Ehn et al., 2014; Jokinen et al., 2015; Pagonis et al., 2019). It should be emphasized that second-generation HOM, which contributed greatly to the limonene +NO3 reaction system, is not included in this primary HOM yield.

We observed nucleation and growth of SOA particles in the limonene +NO3 reaction. We calculated the contribution of HOM to SOA formation and particle growth, and compared it to the measured particle growth (Fig. 7a). We assumed different scenarios of HOM uptake on aerosol particles, using the calculation methods described in the literature (Ehn et al., 2014; Seinfeld and Pandis, 2006; Nieminen et al., 2010). The assumption that all HOM irreversibly condense on the particles (scenario 1) resulted in a strong overestimation of particle mass growth (red markers in Fig. 7a). Applying the parameterizations of Mohr et al. (2019) (scenario 2a) or Peräkylä et al. (2020) (scenario 2b) for classification and accounting only LVOC- and ULVOC/ELVOC-HOM for irreversible uptake framed the observed values (blue and yellow markers in Fig. 7a). While scenario 2a agreed quite well with the observations and only slightly overestimated SOA concentrations after 7 h by +11 %, scenario 2b underestimated the SOA concentration at the end by -53 %. The agreement between the modeled and observed SOA concentration suggests that HOM, and particularly LVOC- and ULVOC/ELVOC-HOM, play a major role in growth of SOA particles in this study. This is consistent with the work by Faxon et al. (2018) who found that many of the dimers are ELVOC, which is also supported by our calculation result based on the method of Mohr et al. (2019).

Since neither SO2 nor H2SO4 was added in our experiment, new particle formation (NPF) could be attributed to the nucleation initiated by HOM of low volatility. HOM trimers with as many as 30 carbon atoms were identified in the early stage of this study, and their sudden loss matched the onset of rapid formation of SOA. Trimers identified in our experiment are classified as ULVOC/ELVOC, with much lower volatility than monomers and dimers (Fig. 7b). Therefore, NPF in the current study can more likely be attributed to HOM trimers since they have the strongest potential of initiating nucleation, although we cannot rule out some contributions of dimers in the NPF. In contrast, in an earlier experiment investigating the NO3-initiated oxidation of β-pinene also conducted in the SAPHIR chamber under similar conditions, new particles were barely formed (<20 cm-3) (Shen et al., 2021). As already mentioned above, no trimer HOM products were observed in that study, and only molecules with C ≤20 were detected (Sect. 3.4). Extremely low volatile organic vapors formed in α-pinene ozonolysis have been shown to induce nucleation and drive initial particle growth in the atmosphere (Tröstl et al., 2016; Kirkby et al., 2016). Since our experiment of NO3 oxidation of limonene was performed under near atmospheric conditions, such NPF events induced by the oxidation of limonene by NO3 could also occur in the ambient atmosphere. Although monoterpene concentrations in this study (0–0.92 ppbv) are higher than in most ambient regions, they are still in the range of ambient concentrations (∼ 0.01–1 ppbv) (e.g., Coggon et al., 2021; Wang et al., 2022), especially for forested regions (e.g., Xu et al., 2015; Kontkanen et al., 2016; Janson, 1992). Assuming that dimers react with NO3 at a rate similar to limonene, and that they have a condensation sink similar to H2SO4 (10-3–10-1 s-1) (Dada et al., 2020), the lifetime with respect to NO3 at an NO3 concentration of 5–300 ppt and to condensation on particles are ∼ 0.1–10 and ∼ 0.1–20 min, respectively. Therefore, although aerosols may scavenge HOM dimers in the ambient atmosphere, dimers can still react with NO3 at nighttime, forming trimers. Such reactions are particularly important when the ambient aerosol concentration is low. Several field observations have shown NPF events taking place at nighttime where biogenic emissions dominate (Kammer et al., 2018; Huang et al., 2019). The work by Ortega et al. (2012) demonstrated an important role of monoterpene ozonolysis products in nocturnal NPF events in chamber experiments. In a previous laboratory study, limonene +NO3 appears more effective at initiating nucleation than the limonene +O3 reaction (Fry et al., 2014), which supports that limonene +NO3 can play a significant role in nighttime nucleation. Our study suggests that NO3 oxidation of limonene could contribute to the nighttime NPF via HOM trimer formation. In contrast, we infer that NO3 reactions with other monoterpenes containing only one double bond such as α-pinene and β-pinene are less likely candidates for nighttime NPF, because gas-phase trimers are not observed.