On the similarities and differences between the products of oxidation of hydrocarbons under simulated atmospheric conditions and cool-flames.

. Whereas the kinetics of oxidation of limonene has been extensively studied and mechanisms for its oxidation by OH and/or ozone have been proposed, more studies are required for better understanding its oxidation pathways. The oxidation of limonene-oxygen-nitrogen mixtures was studied using a jet-stirred reactor at elevated temperature and atmospheric pressure. Samples of the reacting mixtures were collected and analyzed by high resolution mass spectrometry (Orbitrap) after direct injection or after separation by reverse-phase ultra-high-pressure liquid chromatography and soft ionization by (+/-) HESI and 15 (+/ - ) APCI. The results indicate that among the 1138 detected products, many oxygenates found in earlier studies of limonene oxidation by OH and/or ozone are also produced under the present conditions. Other highly oxygenated products and oligomers were also detected in the present work. The results are discussed in terms of reaction pathways involving the initial formation of peroxy radicals, isomerization reactions yielding keto-hydroperoxides and other oxygenated intermediates and products up to C 25 H 32 O 17 . The possible occurrence of the Waddington mechanism and of the Korcek mechanism are also discussed. The 20 present work demonstrates similarities between the oxidation products and oxidation pathways of limonene under simulated atmospheric conditions and in those encountered during the self-ignition of hydrocarbons at low temperatures, which should stimulate future interactions between communities of atmospheric chemistry and combustion chemistry to improve current chemical models. 42 mL JSR to avoid oxidation before reaching the injectors (4 nozzles of 1 mm I.D.) providing stirring. The flow rates of nitrogen and oxygen were controlled by mass flow meters. Good thermal homogeneity along the vertical axis of the JSR was recorded (gradients of < 1 K/cm) by thermocouple measurements (0.1 mm Pt-Pt/Rh-10% wires located inside a thin-wall silica tube). The oxidation of 1% limonene (C 10 H 16 ) under fuel lean conditions (equivalence ratio of 0.25, 56 %O 2 , 43 %N 2 ) was studied at 590 K, atmospheric pressure, and at a residence time 85 of 2 s. A low-pressure sonic probe was used to freeze the reactions and take samples. To measure low-temperature oxidation products ranging from hydroperoxides, ketohydroperoxides (KHPs), to highly oxidized molecules, the sonic probe samples were bubbled into cooled acetonitrile (UHPLC grade ≥99.9, T= 0°C, 250 mL) for 90 min. The resulting solution was stored in a freezer at - 30°C. Analyses were performed by direct sample instillation (FIA - HESI/APCI settings sheath gas 12 a.u. auxiliary gas flow 0, capillary temperature 120°C, spray voltage 3.8 kV, flow injection of 3μL/min recorded for 1 min for data averaging) in the ionization chamber of a high resolution mass spectrometer (Orbitrap® Q-Exactive from Thermo Scientific, mass resolution of 140,000 and mass accuracy <0.5 ppm RMS). Mass calibrations in positive and negative HESI were performed using Pierce TM calibration mixtures (Thermo Scientific). Ultra-high pressure liquid chromatography (UHPLC) analyses were performed using an analytical column at a controlled temperature of 40° C (C 18 Phenomenex Luna, 1.6μm, 100 Å, 100x2.1

Korcek mechanism (Jensen et al., 1981) through which γ-ketohydroperoxides are transformed into a carboxylic acid and a carbonyl compound can occur too. The formation of carboxylic acids and carbonyl products via the Korcek mechanism has already been postulated by Mutzel et al. (Mutzel et al., 2015) whereas it is frequently considered in recent kinetic combustion 65 modeling (Ranzi et al., 2015). This work aims at characterizing the oxidation products of limonene, which has higher tendency to form HOMs by simulated 70 atmospheric oxidation than more abundant monoterpenes (e.g., α-pinene and β-pinene) (Jokinen et al., 2015) and compare the results with literature data obtained under atmospheric oxidation. To this end, we studied the oxidation of limonene-oxygennitrogen mixtures in a jet-stirred reactor (JSR) at atmospheric pressure, large excess of oxygen, and elevated temperature. Our results are compared to literature data obtained under tropospheric relevant conditions where terpenes are oxidized by OH and/or ozone. For sake of clarity, the present oxidation experiments will be called "auto-oxidation" in the following sections. 75

Experiments
The present experiments were carried out in a fused silica jet-stirred reactor (JSR) setup presented earlier (Dagaut et al., 1986) and used in previous studies (Dayma et al., 2011;Dagaut and Lecomte, 2003;Dagaut et al., 1998). As in earlier works (Thion et al., 2017;Dayma et al., 2011) limonene (R)-(+) (>97% pure from Sigma-Aldrich) was pumped by an HPLC pump (Shimadzu LC10 AD VP) with an online degasser (Shimadzu DGU-20 A3) and sent to a vaporizer assembly where it was diluted by a 80 nitrogen flow. Limonene and oxygen were sent separately to a 42 mL JSR to avoid oxidation before reaching the injectors (4 nozzles of 1 mm I.D.) providing stirring. The flow rates of nitrogen and oxygen were controlled by mass flow meters. Good thermal homogeneity along the vertical axis of the JSR was recorded (gradients of < 1 K/cm) by thermocouple measurements (0.1 mm Pt-Pt/Rh-10% wires located inside a thin-wall silica tube). The oxidation of 1% limonene (C10H16) under fuel lean conditions (equivalence ratio of 0.25, 56 %O 2 , 43 %N 2 ) was studied at 590 K, atmospheric pressure, and at a residence time 85 of 2 s. A low-pressure sonic probe was used to freeze the reactions and take samples. To measure low-temperature oxidation products ranging from hydroperoxides, ketohydroperoxides (KHPs), to highly oxidized molecules, the sonic probe samples were bubbled into cooled acetonitrile (UHPLC grade ≥99.9, T= 0°C, 250 mL) for 90 min. The resulting solution was stored in a freezer at -30°C. Analyses were performed by direct sample instillation (FIA-HESI/APCI settings sheath gas 12 a.u. auxiliary gas flow 0, capillary temperature 120°C, spray voltage 3.8 kV, flow injection of 3μL/min recorded for 1 min for data averaging) 90 in the ionization chamber of a high resolution mass spectrometer (Orbitrap® Q-Exactive from Thermo Scientific, mass resolution of 140,000 and mass accuracy <0.5 ppm RMS). Mass calibrations in positive and negative HESI were performed using Pierce TM calibration mixtures (Thermo Scientific). Ultra-high pressure liquid chromatography (UHPLC) analyses were performed using an analytical column at a controlled temperature of 40°C (C 18 Phenomenex Luna, 1.6μm, 100 Å, 100x2.1 mm) for products separation after injection of 3 μL of sample eluted by water-acetonitrile (ACN) at a flow rate of 250 μL/min 95 (gradient 5% to 90% CAN, during 14 min). Both heated electrospray ionization (HESI) and atmospheric chemical ionization (APCI) were used in positive and negative modes for the ionization of products. APCI settings were: vaporizer temperature of 120°C, sheath gas flow of 55 a.u., auxiliary gas flow of 6 a.u., sweep gas flow of 0 a.u., capillary temperature of 300°C, corona current of 3μA. In HESI mode, we used a spray voltage of 3.8 kV. Because oxidation of analytes in HESI has been reported previously (Pasilis et al., 2008;Chen and Cook, 2007), we verified that no significant oxidation occurred in the HESI and APCI 100 ion sources by injecting a limonene-ACN mixture. HESI source is suitable for the detection of high masses, but also HOMS and the presence of salt adducts remains insignificant (Kourtchev et al., 2020). To determine the structure of limonene oxidation products, MS-MS analyses were performed at collision cell energy of 10-30 eV. 2,4-Dinitrophenylhydrazine (DNPH) was also used to characterize carbonyl compounds. As in previous work (Wang et al., 2017b;Belhadj et al., 2020), the fast OH/OD exchange was used to prove the presence of hydroxyl or hydroperoxyl functional groups in the products. We 105 added 300 μL of D2O (Sigma-Aldrich) to 1.5 mL of sample. The resulting solution was analyzed by flow injection and HESI/APCI mass spectrometry.

Data Processing
High-resolution mass spectrometry (HR-MS) generates a significant amount of data that is easier to interpret with two-or three-dimensional visualization tools (Nozière et al., 2015;Wang et al., 2017a;Walser et al., 2008;Tu et al., 2016). In this study, 110 we used Kendrick's mass analysis, double bond equivalent (DBE), van Krevelen diagrams, and carbon oxidation state (OS c ).
Kendrick's mass analysis (Sleno, 2012;Hughey et al., 2001;Kune et al., 2019) allows representing in two dimensions and in a new reference frame, a complex mass spectrum of an organic mixture. This reference frame is based on a mass defect calculated from structural units (CH 2 , O, CHO, ...). In a Kendrick representation, the homologous series (constructed by the repeated addition of structural units CH 2 , O, CHO, ...) are aligned on the same horizontal line. This mass defect is calculated by the 115 difference between the Kendrick mass and the nominal mass. In this study, CH 2 was chosen as the structural unit.
In Kendrick's plots, the X-axis represents the Kendrick Mass ( ) = * , and the Y-axis represents the Kendrick Mass Defect 120 The belonging of unknown chemical compounds to an homogeneous series of compounds can be used for their identification.
The number of double bond equivalent (DBE) represents the sum of the number of unsaturation and ring present in a compound (Nozière et al., 2015). The decrease in the number of hydrogen atoms increases its value, but it is independent of the number 125 of oxygen atoms. It can be used to identify certain groups of chemical compounds or reaction mechanisms (Kundu et al., 2012).
The decimal values of this number were not taken into account in this study. The van Krevelen diagram (Kim et al., 2003;Van Krevelen, 1950) shows the evolution of the H/C ratio as a function of O/C for a set of identified molecules. In a complex organic mixture, it allows classifying the chemical products according to their degree of oxidation or their degree of reduction/saturation. This type of representation allows the identification of classes of compounds such as aliphatics, aromatics, 130 or highly oxidized compounds (Fig. 3).
The oxidation state of carbon allows the degree of oxidation of organic species (alcohols, aldehydes, carboxylic acids, esters, ethers, and ketones, but not peroxides) (Kroll et al., 2011) to be measured. It is defined by the simple equation: This data can be used together with the atomic ratios of van Krevelen's diagrams to identify families of organic compounds (Tu et al., 2016;Wang et al., 2017a;Bianchi et al., 2019). In the case of HOMs, three families of compounds can be distinguished according to their oxidation state and the O/C and H/C ratios: O/C ≥ 0.6 and OSc ≥ 0 (Region 1, highly oxygenated and highly oxidized) O/C ≥ 0.6 and OS c < 0 (Region 2, very oxygenated and moderately oxidized) 140 OS c ≥ 0 and H/C ≤ 1.2 (Region 3, moderately oxygenated and highly oxidized)

Results and discussion
The oxidation of 1% limonene (C 10 H 16 ) was studied at 590 K, atmospheric pressure, and at a residence time of 2 s. Under these conditions, the fuel conversion is moderate but formation of low-temperature oxidation products is maximized.
To study the nature of the chemical products formed and the particularity of auto-oxidation, we compared our results with 145 those obtained by ozonolysis and OH-initiated photooxidation of limonene. This comparison was carried out using visualization methods adapted to large intrinsic data sets of high resolution and high sensitivity reached with current mass spectrometry. At this scale, these tools allow differentiating families of compounds or chemical processes that are hardly perceptible at the level of a few individuals (chemical species).
The comparison of the oxidation modes of limonene (auto-oxidation and ozonolysis/photooxidation) was based only on the 150 nature of the chemical formula of products, without considering the quantitative, sensitivity, or ionization aspects that are difficult to exploit given the diversity of chemical products formed in this study (i) of the analytical methods, and (ii) the large number of instruments involved in this comparison.
To carry out this comparison, and in order to obtain the greatest representativeness of the oxidation of limonene by ozonolysis and OH-initiated photooxidation, we have selected nine previous studies for their diversity of oxidation and characterization 155 processes. Table 1 presents the main experimental parameters of these studies.  (Jokinen et al., 2015) Ozonolysis online flow glass tube 6.1-6.9 x10 11 molec.cm -3 of ozone 1-10000 x10 9 molec.cm -3 of limonene chemical ionization These nine experimental studies yielded a first set of 1233 molecules for an inventory which, although incomplete, gives a 160 broad representativeness of the chemical products resulting from limonene ozonolysis and OH-initiated photooxidation.
The second set was obtained using the chemical formulae observed here during limonene auto-oxidation. For the identification phase, we favored direct injection for its sensitivity. We used UHPLC for its capacity of isomers separation and advanced isomers identification through MS-MS analysis. For direct injection, we have chosen a HESI source operating in negative mode (3.8 kV, sheath gas :12, T capillary vaporizer temperature: 120°C, mass range between 50 and 1000 Da) for its wide 165 range of polar molecule ionization. After verification of the absence of oxidation induced by the ionization source (Pasilis et al., 2008;Chen and Cook, 2007) and elimination of the ions common to the reference, attribution rules were made on the basis of molecules composed solely of carbon, hydrogen and oxygen, respecting a deviation of less than 3 ppm by mass over the range 50-1000 Da. Chemical formula with relative intensity was less than 1 ppm were not considered. Following these rules, we identified 1138 chemical formula in our oxidized limonene sample, which we split into three groups centred on the number 170 of monomers, i.e. a limonene molecule with different degrees of oxidation: I (50<m/z<300); II (300<m/z<500) and III (500<m/z<700) (Kundu et al., 2012;Leungsakul et al., 2005;Nørgaard et al., 2013).
These groups are identified in Figure 1 which shows the mass spectrum of oxidized limonene. Generally speaking, these groups are built around one or more monomers and a few families of chemical reactions. Group I corresponds to compounds resulting from multiple oxidation reactions including fragmentation and condensation. Groups II and III correspond to higher molecular 175 masses, resulting from addition and condensation reactions including, in the case of ozonolysis reactions of (i) The two sets obtained from each oxidation mode were merged, forming a new set of 1600 molecules. In this set, ~50% of the chemical formulae (771) are common to both oxidation modes, while 462 molecular formulae are obtained solely by 185 ozonolysis/ photooxidation and 367 are produced in auto-oxidation experiments only.
All the molecular formulae were represented in a Kendrick diagram (based on a CH2 structural unit) associated with the DBE number (Fig. 2). The representation of Kendrick highlights the families of compounds, the addition of a third dimension makes it possible to study the reaction mechanisms linking these different families (Bateman et al., 2009);(Kundu et al., 2012).

195
The chemical formulae are distributed into 11 XY planes according to their DBE number. The representation of each of these XY plans is given in the S1 supplementary material. This representation immediately highlights the origin of the chemical formulae, i.e. those specific to auto-oxidation, common to the three modes of oxidation, or specific to ozonolysis and photooxidation. The chemistry of these chemical species can then be read graphically on the axes: the X-axis represents the extent of the family, the Y-axis represents oxidation and the Z-axis denotes addition and condensation reactions. This is 200 illustrated in Figure S1 of the Supplementary material.
Unexpectedly, the distribution of chemical formulae is homogeneous and forms a continuum between oxidation by autooxidation and by ozonolysis/photooxidation.
In auto-oxidation, the above mentioned pathways, probably constrained by short oxidation time (residence time of 2 s), seem to extend the molecular weight growth of products up to ~300 Da, favor splitting (decrease of DBE), additions or condensation 205 (increase of DBE) of unsaturated chemical groups. Ozonolysis and photooxidation experiments, performed over longer periods of time (several seconds < t < few hours), promote, in addition to the previous reactions, the appearance of oligomers and an increase of products molecular weight (Zhao et al., 2015).
In the Kendrick diagram (Fig.2), the DBE=3 XY plane containing limonene includes chemical formulae of products deriving from the early oxidation steps. In this case, the breaking of unsaturation, double bond, and ring are counterbalanced by the 210 formation of carbonyls or ozonides, keeping DBE constant. In this XY plane, 83% of the chemical formulae of products obtained by auto-oxidation are identical to those formed by ozonolysis/photooxidation, although ozone is most likely absent from JSR auto-oxidation experiments. Many of the chemical formulae of products described in previous ozonolysis/photooxidation works involve reaction mechanisms based on ozonides and Criegee intermediates. These chemicals can be primary products, i.e. weakly oxidized (Bateman et al., 2009) (Witkowski and Gierczak, 2017;Jokinen et al., 2015;Walser et al., 2008;Kundu et al., 2012;Fang et al., 2017;Nørgaard et al., 2013;Bateman et al., 2009;Warscheid and Hoffmann, 2001;Hammes et al., 2019). 220 These families are built on the basis of a simple difference in alkyl groups (CH 2 basic unit of the Kendrick diagram).
The decrease of DBE from 3 to 2 and then to 1 reflects a greater reactivity on double bonds and on the limonene ring. This reactivity on unsaturated sites is accompanied by a fragmentation of the C-C bonds and a decrease in molecular weight. The new molecular formula of products, specific to auto-oxidation, are located at the extremities of the DBE=2 plane or on almost the entire DBE=1 plane. They are characterized by a lower O/C ratio, which can be explained by less advanced oxidation, and 225 certainly by fragmentation. The observation of these new chemical formulae of products, compared to previous studies, can be explained, in addition to the short oxidation time and the elevated temperature in the JSR experiment, by a termination in the radical chain process or by bimolecular reactions (Rissanen et al., 2014;Walser et al., 2008).
The increase in DBE from 3 to 11 characterizes the increase in double bonds and degree of unsaturation obtained by the addition or condensation of limonene oxidized species. In the case of ozonolysis/photooxidation, this increase is usually 230 explained by reactions between Criegee radicals (Criegee intermediate) and acids or alcohols, by hemiacetal formation, aldolization, or esterification (Bateman et al., 2009;Docherty et al., 2005). Each of these reactions is associated with an increase in DBE (hemiacetal: +2; aldolization: +3). For example, in the case of aldol condensation between two aldehydes (limonoaldehyde + 7-OH-limonoaldehyde), the DBE increases from 3 to 6. The emergence of new chemical formulae of products with DBE=9 is mostly observed for molecular weights between 200 and 500 Da. These molecules probably 235 correspond to the addition or condensation of several oxidized limonene compounds (condensation/addition of several cycles) favored, under short time oxidation, by the elevated experimental temperature (590 K).
In general, the new molecular formulae of products observed in auto-oxidation, compared to ozonolysis (Tu et al., 2016), have a lower molecular weight and are better found in group I (m/z < 300, 52%) associated with addition or splitting reactions around the limonene skeleton (monomer channel). 240 In ozonolysis/photooxidation, the products which molecular formulae are rather located in groups II and III can easily oligomerize. This process is highly time-dependent in the presence of ozone (Kundu et al., 2012).
In addition to the identification of chemical families by Kendrick's analysis, it is possible to specify the nature of the chemical products using a van Krevelen diagram.  In the limonene oxidation process, observable from the left to the right on this figure, the first oxidation steps concern both the products resulting from JSR auto-oxidation and those from ozonolysis/photooxidation.

Characterization of KHPs
Oxidation, at the initial stage, forms compounds with number of carbon atoms varying from 7 to 11, number of hydrogen 255 atoms ranging from 12 to 16, and number of oxygen atoms increasing to 9. These chemical compounds are globally in the (d) area. In ozonolysis/photooxidation studies, initial oxidation phase, by ozone and/or the radical OH˙ have been widely described (Walser et al., 2008;Kundu et al., 2012;Nørgaard et al., 2013;Librando and Tringali, 2005). Although the experimental conditions and the associated reaction mechanisms are different, it is observed, similarly to Fang et al (Fang et al., 2017), many common products of these different oxidation modes. In the case of auto-oxidation, in the absence of ozone, H-abstraction by 260 the radical OH˙ initiates further oxidation steps yielding ROO˙ radicals and hydroperoxides.
RH + OH  R˙+ H2O ; R˙+ O 2  ROO˙ ; ROO˙ + RʹH  ROOH + Rʹ These reactions will themselves lead to the formation of, among others, KHPs, diketones, or will proceed further (see Section 265 1) and lead to the formation of HOMs (Jokinen et al., 2014b;Wang et al., 2019;Wang et al., 2016). In the initial stage of this autooxidation, we studied the formation of the compounds C 10 H 14 O 3 , C 10 H 12 O 2, C 10 H 16 O 2, C 10 H 14 O 5-11 corresponding respectively to the global formulae of KHPs, diketones, oxyhydroxides, and HOMs. Experiments were carried out using UHPLC-Orbitrap coupling in tandem mode in order to isolate these molecules and fragment them with an HCD at energy ranging from 10 to 30 eV. Considering a mass range of initial molecules detected in auto-oxidation lower than 700 Da, we 270 used an APCI source in positive mode, well suited to this mass range.
For the KHPs (C10H14O3), whose mechanisms of formation from limonene are described in the Supplementary material S4 (with example of reaction mechanisms of KHP formation and probable sites of attack of OH radicals), the analyses by high resolution mass spectrometry confirm the presence of 12 isomers among the compounds formed, compared to a maximum of 18 potentially produced (S5). 275 Among these 12 isomers, MS/MS fragmentation allowed the identification of three groups of compounds presented in Figure   4. The limits of separation and detection of these chemical compounds made it impossible to specify the position of the functional groups in these isomers. In order to verify the presence of carbonyl groups, 20 µl of a mixture containing DNPH (20 µl of H 3 PO 4 (85%) in ACN with 20 µl of 2,4-DNPH) were added to 1 ml of sample. This mixture was allowed to react for 4 hours before analysis.
Characterization, at different reaction times (0.5, 1, and 4 hours), was performed by UHPLC-MS APCI ( -) in tSIM mode 285 following 361.1153 Da mass of the C 16 H 18 O 6 N 4 compound (Fig. S6). One could note an increase in the intensity of the signal (inset Fig. S6). Nearly 12 isomers were observed, with an elution time that is longer and consistent with the initial retention time of the KHPs, thus confirming the presence of carbonyl groups. However, the fragmentation carried out on all these chromatographic peaks did not make it possible to complete the chemical speciation of all the isomers. Nevertheless, for the first time, this study confirms the formation of KHPs initiated by the OH˙ radical during the oxidation of limonene. 290 The difficulty for characterizing KHPs lies in the fact that these products are unstable and transform according to different mechanisms. One of the instabilities described in the literature consists in spontaneous dehydration of KHPs to give diketones https://doi.org/10.5194/acp-2020-1070 Preprint. Discussion started: 8 December 2020 c Author(s) 2020. CC BY 4.0 License. (Herbinet et al., 2012). Analysis of the data confirms the presence of a diketone (C 10 H 12 O 2 ). It shows that diketones are detected both by elution of oxidized limonene (7.79 and 8 min), and systematically in the chromatogram of KHP isomers. This means that this spontaneous transformation can occur in the spectrometer without questioning the presence of diketones in the initial 295 sample. Figure S7 in the Supplementary material compares the two profiles of diketones resulting from the fragmentation of KHPs and by elution.
Other transformation pathways of KHPs are possible, e.g., via the Korcek mechanism (Mutzel et al., 2015) where δ-KHPs decompose into carbonyl compounds and carboxylic acids. Among the 18 proposed KHPs (Supplementary material S5), 4 isomers (#4, 11, 15, and 18) could react via the Korcek mechanism, but only the #4 isomer is likely to form a cyclic peroxide 300 between a carbonyl group and a hydroperoxide group. The other three isomers will give, after ring opening, isomers of the compound C10H14O3. For the #4 isomer, the Korcek mechanism leads to the formation of a carbonyl compound, C 9 H 12 O, and the formic acid CH 2 O 2 (Fig. 5). UHPLC analyses confirm the presence of products with chemical formula C 9 H 12 O in the form of two isomers (Fig. 5), but only the peak located at 5.64 minutes shows a C 8 H 12 fragment consistent with the transformation of the initial KHP. 305  KHPs can also give rise to branching reactions that will generate radicals promoting autoxidation by OH˙ (Wang et al., 2016).
Otherwise, if the H-atom transfer in the OOQOOH intermediate does not involve the H-C-OOH group but another H-C group, 315 then no ketohydroperoxide is formed and a third O 2 addition to HOOQ'OOH yielding OOQ'(OOH) 2 can occur. If oxidation proceeds further following this pathway, it can lead to the formation of HOMs.

Characterization of HOMs
Different strategies were considered for tracking the production of HOMs. Because of higher sensitivity and difficulty in 320 separating isomers, FIA was preferred. The compounds C 10 H 14 O 5 , C 10 H 14 O 7 , C 10 H 14 O 9, C 10 H 14 O 11 (Fig. 3, area (d)) were detected by FIA (APCI positif, vaporizer temperature =120°C, sheath gas flow of 12 a.u., auxiliary gaz flow of 0 a.u.; sweep gas flow of 0 a.u., capillary temperature of 300°C, corona discharge current of 3 µA, flow of 8 µl/min). Nevertheless, the diversity of reaction pathways, associated with the increasing number of chemical compounds, makes it difficult within a population of several hundred chemical compounds to identify all HOMs. 325 We have therefore again used the van Krevelen diagram, which allows following the evolution of the oxidation of the first HOMs and to identify them according to definitions that seem to be consensus (Walser et al., 2008;Tu et al., 2016;Nozière et al., 2015;Wang et al., 2017a). To this end, we used the average carbon oxidation state OS c which allows distinguishing three regions according to the nature of the functional groups: Region 1 (O/C ≥ 0.6 and OS c ≥ 0) consists of highly oxygenated and highly oxidized compounds (acids and carbonyls), Region 2 (O / C ≥ 0.6 and OS c <0), consists of highly oxygenated and 330 moderately oxidized compounds (alcohols, esters and peroxides), finally, Region 3 (OS c ≥ 0 and H/C ≤ 1.2) includes compounds with a moderate level of oxygen, but strongly oxidized (Tu et al., 2016).
It can be seen from Figure 3 that auto-oxidation enhances the development of HOMs, compared to ozonolysis/photooxidation, and that the majority of these new products are found in Regions 1 and 3 of the inset of Figure 3. Thus, further oxidation can go on. We observed products of addition of up to 17 oxygen atoms yielding C 25 H 32 O 17 . 335 Considering the presence of the radicals OH˙, we also searched for chemical compounds resulting from the Waddington mechanism (Li et al., 2020). This mechanism, through which oxidation of alkenes can occur, has two reaction pathways in the case of limonene. The first pathway leads to the formation of a C 9 H 14 O ketone and formaldehyde via oxidation of the exocyclic double bond. The second, involving the endocyclic double bond of limonene, gives the compound C 10 H 16 O 2 . For each pathway, we obtained three isomers on the chromatograms (Fig. 6). 340 The fragmentation of these isomers did not allow their identification. However, in order to confirm the presence of carbonyl groups, we added 20 µl of a mixture containing DNPH (Same experimental condition as above) to 1 ml of sample, and let this mixture react for 4 hours before analyses. In order to facilitate the detection of isomers and their addition compounds, we used the APCI(-) mode for UHPLC analyses. Only the compound C16H20O5N4 (C10H16O2 + DNPH) was detected. The second carbonyl compound (yielding C22H24O8N8) could not be confirmed (Supplement SI fig. 8). Moreover, the addition of D2O, 350 in order to test the presence of -OH or -OOH groups, gave no results for the two chemical compounds. Recent modelling work on Waddington mechanism (Lizardo-Huerta et al., 2016) has shown that structural parameters have an impact on the energy barriers associated with the β-scission step. There, a decrease in the activation energy is observed when the substitution of the carbon atom carrying the peroxyl function increases. According to that study, this effect is amplified by the degree of substitution of the carbon atom carrying the hydroxy group. These results are in agreement with the preferential detection of 355 the compound C 10 H 16 O 2 whose carbon atoms, with the peroxy groups, is the most substituted. Beyond the complete identification of the isomers, this study confirms the presence of chemical compounds which could well result from the Waddington mechanism during limonene auto-oxidation in JSR.

Complementary method of screening
Further study of the oxidation of chemical compounds and their reaction mechanisms is limited by the complexity of the 360 exponential increase of chemical reactions, chemical species, and their isomers. Nevertheless, monitoring the evolution of these complex mixtures is possible by correlating the OSc to the number of carbon atoms (n c ). We have reported in Figure 7 our measurements and have associated to these results the different biogenic VOCs families defined in the literature (Lowvolatility oxygenated organic aerosol (LV-OOA), semi-volatile oxygenated organic aerosol (SV-OOA), hydrocarbon-like organic aerosol (HOA), and biomass burning organic aerosol (BBOA) corresponding to particulates (Kroll et al., 2011;An et 365 al., 2019)). The development of advanced oxidation, specific to auto-oxidation, is confirmed with an OS c close to 1. As it stands, it is difficult to make hypotheses on the evolution of these new chemical products and, in the absence of speciation, to assess their environmental impact. Finally, it is also possible to further exploit the van Krevelen diagram by introducing reaction mechanisms. Until now this diagram has been used to identify reaction pathways or families of compounds (Kim et al., 2003;Wu et al., 2004). One can refine this identification by associating to a reaction mechanism a vector whose amplitude and direction will allow linking 375 reagents and products. By applying this method to all the experimental data points, one scans the space of the possibilities of formation of a compound or its isomers.
If this method is applied to the formation of C10H14O3 (KHPs and isomers), the vector is defined by the loss of two hydrogen atoms and the gain of three oxygen atoms. By focusing only on molecules composed of 10 carbon atoms, 31 C 10 H 14 O 3 isomers were identified, 17 of which are new chemical formulae detected in auto-oxidation only. This is an exhaustive inventory of the 380 possibilities of formation of these compounds based on the experimental data points and not on thermodynamic and kinetic considerations. Applying the same method to the search for keto-dihydroperoxides (-2H; +5O) and di-ketohydroperoxide (-2H; +7O), we observed the formation of 24 and 23 compounds, respectively. All these results are presented in Figure 8. Thanks to all the tools used in this work, especially the last one, the screening of selected classes of compounds is considerably simplified, and the mesh constituted by the reaction vectors becomes a new method for evaluating the nature of a mixture of oxidation products.

Conclusion and perspectives 390
Numerous studies on the ozonolysis of limonene have allowed characterizing the reaction mechanisms of its oxidation by describing a large fraction of chemical products. In these mechanisms, the formation of a Criegee intermediate has often been described as the major pathway for the formation of oxidized compounds, associated with the more restricted formation of the OH˙ radical.
Among these studies, some have shown that despite these differences in oxidation mechanisms of ozonolysis, many of the 395 products were similar. Moreover, it appears that these similarities are extended to photooxidation.
In the present study, where the comparison of oxidation modes is extended to auto-oxidation, we find, in the case of limonene, similar chemical products (nearly 50%). It appears that in the absence of ozone, the oxidation by the OH˙ radical, common to ozonolysis, gives similar results. Nevertheless, this study has allowed us to highlight auto-oxidation specific processes, such as formation of KHPs and diketones, occurrence of the Korcek and Waddington reaction mechanisms. 400 Analysis at the molecular level was complemented by observation at chemical family scale using Kendrick and van Krevelen visualization tools, necessary to compare and identify features in large data sets. Indeed, the formation of new HOMs and the development of combustion-related auto-oxidation are perfectly perceptible using these tools. The same is true for the oligomerization, which is not very important in auto-oxidation, in favor of addition and/or condensation reactions on limonene that are prompt to increase the DBE. As it stands, the meshing within these chemical families according to reaction, 405 thermodynamic, or kinetic criteria remains sketchy, but will certainly develop in the light of all the available experimental and theoretical inputs. Further studies involving others terpenes are underway. They should confirm the results presented here.