The experiment-averaged mass spectra for each MT system showed very different peak distributions (Fig. ). Here, we explore the relative ratios of experiment-averaged ion abundance from categories of products. For comparison, we normalized the integrated area of each peak by the total integrated area of all organic peaks in the mass spectrum. The general formula CwHxNyOz was used to create categories of reaction products that correspond to specific predicted mechanistic pathways that are summarized in Table , with the representative mechanisms for each pathway shown in Fig. . The carbon number provides an indication of fragmentation caused by C–C bond cleavage for any carbon number that is not equal to 10 (for monomers) or 20 (for dimer formation from peroxy or alkoxy radical additions, e.g., RO2 + RO2). The hydrogen number informs us about the terminal functional group and the associated bimolecular reactions leading to them. The nitrogen number can indicate secondary double bond generation or NO2 + RO2 chemistry from residual NO2 in the chamber. Structure–activity relationships (SARs) and rate constants were found in the literature for relevant pathways , but proposed mechanisms were not explicitly modeled for this study. The oxygen number and O:C ratio provide insights into how much autoxidation chemistry occurred, increasing the O:C ratio of the products. While we cannot completely explain the origin of every observed compound, the observed differences provide valuable information regarding the most important pathways that lead to these low-volatility products. The ratio distributions for all of the MT systems are summarized in Fig. . Complete peak lists for each MT system can be found in Sect. S8 in the Supplement. Note that the β-pinene system ratios are the average of an 8 ppb experiment and a 70 ppb experiment (39 ppb average). The full comparison of results from both experiments can be found in Sect. S7 in the Supplement.

The relative abundance of dimers compared with monomers (Fig. ) correlates with observed particle formation (Sect. S3 in the Supplement) for each MT system, with the exception of α-thujene, for which we observed substantial dimer formation without significant particle formation. We predict that the first alkyl radical formed from NO3 addition onto the α-thujene double bond can potentially rearrange to form a new double bond while opening the strained three-membered ring, forming a six-membered ring and new tertiary alkyl radical (Fig. ). That structure can then undergo further oxidation to form highly oxygenated, lower-volatility compounds, including dimers. Our observations of highly oxygenated products for α-thujene shows that, under these experimental conditions, there is an additional pathway for the first-generation alkoxy scission (Fig. ) that is competitive with the formation of thujenaldehyde.

Figure  summarizes the monomer carbon number distributions, which provide insights into fragmentation pathways. Detailed schemes for each MT system are shown in Sect. S5 in the Supplement. In general, alkoxy decomposition pathways (C7, C9) are predicted to be competitive with H migration when leaving groups become highly substituted . For three of the MT systems studied (Δ-3-carene, β-pinene, and α-thujene), terminal sites that are available in the α position to alkoxy radicals become oxidized and lead to fast alkoxy decomposition (Fig. b). For the α-pinene system, however, such a terminal site is not available. Another possible pathway for fragmentation is alkyl radical rearrangement that leads to ring opening. For C7 compounds, radical rearrangement creates new alkyl radicals at tertiary isopropyl sites (Fig. c). Oxidation of the alkyl radical site to an RO2 radical and bimolecular reaction to form an RO radical allows alkoxy decomposition to occur, generating a new alkyl radical . For C9 compounds, ring opening and NO3 radical addition creates a new alkyl radical in the α position to a CH3ONO2 group. If the alkyl radical is again oxidized (forming RO2) and decomposed (forming RO), alkoxy scission with an ONO2 group on the α carbon would not have a smaller energy barrier than a site with OH or OOH α substitution, but this barrier would still be smaller than an alkyl-substituted site.

Although observed a substantial C7 contribution for a Δ-3-carene + NO3 experiment with the same instrument, we observed a negligible C7 contribution. The conditions of the two experiments were different in that the ratio of MT to oxidant was lower in our experiment (0.004 vs. 0.012) and the residence time for our experiment was longer (33 min vs. 23 min). These differences can lead to different chemistry inside the chamber that could result in different observed reaction product distributions. We plan future studies to further explore the source of these differences. A large C7 contribution was observed for both the α-pinene and β-pinene systems. One possible formation mechanism is shown by the R1 arrow in Fig. c, in which the initial alkyl radical formed from NO3 addition rearranges to open the four-membered ring (C7–C8 cleavage), forming a new tertiary alkyl radical. This early alkyl radical rearrangement was proposed by for the β-pinene + NO3 system. However, O2 addition to the initial alkyl radical is expected to be fast under our experimental conditions and in the ambient atmosphere , so we expect this alkyl radical rearrangement not to be significant. R2 in Fig.  shows an alkyl radical rearrangement that opens the four-membered ring and generates a new tertiary alkyl radical (C7–C8 cleavage). This specific ring-opening reaction is not currently supported by quantum chemical modeling, so we cannot currently comment on its competitiveness. Another possibility is that this C7 compound comes from the first-generation alkoxy scission of the C2–C7 bond (Fig. c). While predicted to be a minor pathway for α-pinene, this C2–C7 scission is expected to be equally, if not more, competitive with the other two first-generation alkoxy scission (C2–C1 and C2–C3) for β-pinene . This branching ratio may be somewhat reflected in the relative yields observed from the NO3- CIMS. The C7 product yield from the α-pinene system is roughly half that of the β-pinene system. This early left-side C2–C7 scission makes a secondary radical on the four-membered ring, which is less stable than an acyclic analog because of ring strain . R3 in Fig. c shows the proposed mechanism for this newly generated compound. In abundant O2, this alkyl radical will be oxidized to an RO2 radical. Because this new RO2 radical is confined by the rigid structure of the ring, autoxidation could be slow, while in the presence of other radical species (NO3, RO2), bimolecular decomposition from a peroxy radical (RO2) to an alkoxy radical (RO) could be faster. Few cyclic RO2 H migration computational studies exist for relevant systems , but bimolecular rate constants with NO3, NO2, and HO2 have recently become better defined for RO2 radicals . Once the RO radical is formed, it is possible that decomposition of a C–C bond (thus opening the strained ring and leading to formation of a ketone and a tertiary alkyl radical) could be fast, with a predicted energy barrier of 0.6 kcal mol-1 from SARs . In this position, the tertiary radical resembles the structure predicted for Δ-3-carene in and could lead to the loss of the isopropyl group from C5–C8 cleavage and formation of a C7 fragment. This pathway is only available for the β-pinene and α-pinene systems, and a significant contribution from C7 compounds is only observed from these two systems.

Instead of abundant C7 compounds, we observe a large contribution from C9 compounds for the Δ-3-carene system and smaller C9 signal for the rest of the MT systems. A possible pathway for C9 formation is through the generation of a secondary double bond and subsequent NO3 addition (Fig. b). The CH3ONO2 leaving group could quickly fragment into CH3O and NO2 but is assumed to be more stable than a CH3 radical formed from any other terminal site on the molecule in this case. The most abundant C9 compound for the Δ-3-carene system contains two nitrogen atoms (C9H14N2O12). From our predicted pathway, the resulting product may contain one or two nitrogen atoms because, even if the second ONO2 group is expected to be part of the leaving group, a radical site remains on the molecule, making the RO2 + NO2 pathway possible via reaction with residual NO2 in the chamber. For the α-thujene system, a C9 compound is predicted to be formed in an analogous pathway to the Δ-3-carene system, as terminal double bonds may be generated. For the α-pinene system, C9 formation would be possible if an alkyl radical rearrangement occurred on the four-membered ring, generating a terminal double bond. Finally, for the β-pinene system, a terminal site is available after the initial right-side alkoxy scission (C2–C3), but alkyl radical ring opening could also be possible if a left-side scission (C2–C7) were to occur.

As previously mentioned, the hydrogen number is an indication of the bimolecular termination pathway and the presence of the subsequent terminal functional group for RO2 and RO radicals. For C10 compounds with a single nitrogen atom (Fig. a), H15 closed-shell compounds indicate aldehyde groups created from hydrogen abstraction on a carbon atom in an α position to an alkoxy radical or by other RO2 + RO2 pathways described by . C10H16NOz compounds are radicals – most likely peroxy radical compounds, as the lifetimes of alkoxy and alkyl radicals are very short. C10H17NOz compounds are closed-shell compounds, and they contain hydroxy or hydroperoxy terminal groups formed from abstracting a hydrogen atom from a different molecule. C10H16NOz radical compounds were the most abundant for the Δ-3-carene, β-pinene, and α-pinene systems. In contrast, C10H15NOz aldehyde-/ketone-containing compounds were the most abundant for the α-thujene system and were mainly distributed among two compounds (C10H15NO9 and C10H15NO10). If one assumes that the concentration of bimolecular reaction partners is similar for each MT system, it appears that the reaction products generated in the α-thujene system included structures with especially labile hydrogen atoms in an α position to possible alkoxy radical sites. In that case, this bimolecular hydrogen abstraction reaction would be fast and would lead to a high ratio of C10H15NOz compounds relative to the C10H16NOz and C10H17NOz compounds. Additionally, a moderate C10H15NOz contribution was observed for the β-pinene system from a species with the same formula (C10H12NO10).

Analogously, C9 radical compounds with a single nitrogen atom will contain 14 hydrogen atoms if they are formed from the loss of a methyl group, whereas closed-shell C9 compounds will contain 13 or 15 hydrogen atoms (Fig. b). For the β-pinene system, hydroperoxy or hydroxy C9H15NOz compounds were most abundant. The dominant C9 species in the α-thujene system was a C9H16NOz species; it is not currently clear how C9H16NOz products can be formed. Surprisingly, the most abundant C9 compounds for the rest of the MT systems do not fall into this C9HxNOz category, although some of these types of compounds make up a fraction of the overall C9 signal. C9 dinitrogen compounds were the most abundant for the Δ-3-carene (C9H14N2O12) and α-pinene (C9H14N2O10) systems, with 14 hydrogen atoms indicative of the formation of peroxy radical intermediates or an RO2NO2 group. Finally, C7 radical compounds with a single nitrogen atom are predicted to have 10 hydrogen atoms if formed by the loss of an isopropyl group, whereas closed-shell C7N1 compounds will have 9 or 11 hydrogen atoms (Fig. c). The most abundant C7 compound (C7H9NO8), observed for both the β-pinene and α-pinene system, was a closed-shell compound, and its formula is consistent with the mechanism that we present in Fig. c, but a large radical contribution from C7H10NO9 was also measured in the β-pinene system.

Monomer compounds with a single nitrogen dominate all MT systems, although with varying abundance. The initial addition of NO3 radical leads to the formation of these single nitrogen-containing compounds. The α-pinene system had much higher contributions from N0 and N2 compounds compared with the other MT systems, but it is expected that the majority of products detected for the α-pinene system come from minor pathways; therefore, unusual pathways that are normally considered to be slow can potentially be competitive and lead to the observed ratios of nitrogen-containing compounds. We are not currently certain what those pathways are. The α-thujene system had a 10 % greater contribution from single nitrogen-containing compounds, compared with the Δ-3-carene and β-pinene systems, and a corresponding 10 % smaller contribution from dinitrogen compounds. α-Thujene and Δ-3-carene both contain strained three-membered rings that can make a ring-opening alkyl radical rearrangement reaction faster than the MTs with less strained four-membered rings (β-pinene, α-pinene) . Therefore, it is not possible to know for certain how many nitrogen atoms have been lost by a molecule in the process of oxidation. It is also not possible to attribute a product containing a single nitrogen to the initial NO3 radical addition to the parent α-thujene molecule. This pathway would be available early in the oxidation mechanism for α-thujene, but Δ-3-carene requires one generation of oxidation to pass before the secondary double bond can be generated (Sect. ). Additionally, the Δ-3-carene system has other pathways that can lead to highly oxidized species whereas the α-thujene system is currently predicted to only have one pathway that leads to secondary double bond generation. Dinitrogen compounds can be formed via NO2 + RO2 (from excess NO2 in the chamber), and this can also form a product with two nitrogen atoms. The rate constant for this NO2 + RO2 reaction is highly uncertain, making explicit kinetic modeling of the RO2 fate challenging.

C20 compounds were the most abundant dimers across all MT systems. However, the β-pinene system had a large (22 %) C17 contribution, whereas the other MT systems produced negligible (< 6 %) C17 dimers. Correspondingly, a large C7 monomer contribution was observed for the β-pinene system but not for the Δ-3-carene or α-thujene systems. C19 dimers were produced in all MT systems, but the α-thujene system had an approximately 20 % greater fractional C19 contribution than β-pinene (10 %) and Δ-3-carene (18 %), even though the Δ-3-carene system produced the highest percentage of C9 monomers. Dimers with carbon numbers other than 20 imply that, after alkoxy decomposition and fragmentation of a C10 monomer, the newly generated monomer fragment must contain an active radical site. This can occur through the generation of a secondary double bond within one of the monomer units through alkyl radical rearrangement. Another possibility is that the smaller leaving group is a closed-shell species, leaving the larger fragment with an alkyl radical. A possible example of this rearrangement is shown in Fig. c, in which a C7 radical is generated with acetone as the leaving group in the β-pinene system. That C7 alkyl radical can be oxidized and can possibly form an adduct with a C10 radical, making a C17 dimer that is uniquely observed for the β-pinene system. C19 dimers can potentially be formed through a similar radical rearrangement pathway, as discussed above (Sect. ). It is possible to create a C19 dimer from that C9 fragment, as another active radical site could exist on the molecule after NO3 radical addition to the newly generated double bond. An analogous C9 and C19 dimer could be formed from the α-thujene and β-pinene systems.

Closed-shell C20 compounds formed from two C10H16 compounds (RO2 + RO2) have 32 hydrogen atoms and were the most abundant type of dimers in all MT systems. If C20 compounds have an alternate hydrogen number, it is assumed that a second double bond was generated at some point during the oxidation process, forming a monomer species with both an active radical site and a terminated site (CHO, OOH, or OH). C19N2H30 compounds make up ∼ 80 % of the total observed C19 signal from the Δ-3-carene system and are predicted to form via the addition of a C10H16NOz radical and a C9H14NOz radical. In contrast, the β-pinene system produced C19H32N2Oz compounds with the highest abundance among C19 species, and the α-thujene system produced both C19H30N2Oz and C19H32N2Oz compounds with equal intensity. As with the C9 monomer units, it is uncertain where the extra two hydrogen atoms are gained. For the β-pinene system, C19H26N2Oz molecules were the most abundant C19 species, which is consistent with a C7H10NOz-RO2 monomer fragment combining with a C10H16NOz-RO2 monomer.

For C20 dimers, a nitrogen number of two can correspond to the addition of RO or RO2 radicals with one substituent ONO2 group each. It is expected that products without nitrogen atoms lose them in termination steps. Thus, dimers with two nitrogen atoms cannot be formed by the addition of a dinitrogen monomer and a monomer with no nitrogen atoms unless two radical sites are available on the same molecule and one participates in RO2 + RO2 adduct formation while the other leads to the loss of NO2. This would create a monomer with no nitrogen atoms that is also bonded to another monomer unit. C20 dimers containing two nitrogen atoms are the most abundant across all MT systems. Very small contributions are observed from N3 or N4 C20 species. The α-thujene system has a considerable contribution (13 %) from single nitrogen-containing dimer species. The single nitrogen-containing compounds can possibly be formed by the same combination of monomer units mentioned above for C20N2 compounds, except one of the monomers contains only a single nitrogen atom instead of two. Additionally, it is possible that ozonolysis-RO2 and nitrate-RO2 intermediates engaging in cross-reactions play a role, as the rate constant for α-thujene with ozone or NO3 radical has not been measured.

When comparing the uncorrected (not corrected for wall losses) time series traces for each MT system, a decrease in product signal after the initial increase was observed for the two systems (Δ-3-carene, β-pinene) that exhibited new particle formation (Fig. ). These decreases roughly correspond to the increasing particle number. More quantitative analysis of particle growth rates is beyond the scope of the current study but is planned for future studies. The decrease in gas-phase products over the course of the experiment was not observed for the MT systems that did not produce particles (α-pinene and α-thujene).

Different reaction products have different time series because of different formation rates and sinks, as observed in the Δ-3-carene system. At this time, this analysis is only available for the Δ-3-carene system; however, we expect similar behavior for the products of the other MT systems. By grouping the individual species into the categories detailed in Sect. , insights can be gained into the net formation time (x1/2), which considers wall loss but not loss due to the condensation sink on particles. The time series curves were fitted to sigmoidal curves to determine the time it took for the signal to reach one-half the maximum (x1/2). In general, monomers were found to have faster net formation time x1/2 than dimers (Fig. ). C10H16NOz compounds have the fastest x1/2 and are the most abundant monomer species. Most of these species are also single nitrogen-containing compounds. Within the N1 category, C10H16NOz compounds and C10H17NOz compounds have similar x1/2 times, whereas the C10H15NOz species have a slower x1/2 overall, falling into the same x1/2 regime as the dimer compounds. If one assumes that these C10 compounds all have a similar condensation sink rate, it appears that H16 radicals and H17 hydroxy and hydroperoxy compounds form faster than the H15 carbonyl compounds. C9 compounds have more variable x1/2 times but are, in general, slower than the fastest C10 monomers. Additionally, the most abundant C9 species (C9H14N2O12) has an x1/2 value in the dimer region (note that this compound contains two nitrogen atoms). Additionally, for C10 compounds with one nitrogen atom, there is an almost imperceptible increasing trend relating x1/2 and the effective O:C ratio (Fig. b). A similar slight trend can be observed for C20 compounds. It is possible that, because the formation and sink times cannot be isolated, more highly oxidized molecules take longer to form but also condense more rapidly.