Pascal Renard

Sabrine Tlili

Sylvain Ravier

Etienne Quivet

Anne Monod
email: anne.monod@univ-amu.fr

Aqueous phase oligomerization of alpha,beta-unsaturated carbonyls and acids investigated using ion mobility spectrometry coupled to mass spectrometry (IMS-MS)

Keywords: photooxidation, oligomer formation, oligomer characterization, mass spectrometry, traveling wave ion mobility spectrometry

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Introduction

Organic aerosols (OA) are well known to play a significant role in many atmospheric processes resulting in an important impact on climate and human health. Secondary organic aerosols (SOA) represents almost 80% of OA [START_REF] Spracklen | Aerosol mass spectrometer constraint on the global secondary organic aerosol budget[END_REF], and its formation and growth mechanisms are not well understood. SOA formation is widely attributed to the oxidation of volatile organic compounds (VOCs) in the dry gas phase, leading to the formation of less volatile species that subsequently partition into the condensed phase (Claeys et al., 2004;Donahue et al., 2011;[START_REF] Hallquist | The formation, properties and impact of secondary organic aerosol: current and emerging issues[END_REF][START_REF] Herrmann | Tropospheric Aqueous-Phase Chemistry: Kinetics, Mechanisms, and Its Coupling to a Changing Gas Phase[END_REF][START_REF] Kanakidou | Organic aerosol and global climate modelling: a review[END_REF][START_REF] Kroll | Chemistry of secondary organic aerosol: Formation and evolution of low-volatility organics in the atmosphere[END_REF]. However, under realistic conditions of humidity, the condensed phase contains liquid water with highly variable mass concentrations as theoretically predicted (Carlton and Turpin, 2013;[START_REF] Meng | Contribution of Water to Particulate Mass in the South Coast Air Basin[END_REF][START_REF] Meng | On the Source of the Submicrometer Droplet Mode of Urban and Regional Aerosols[END_REF][START_REF] Pilinis | Water content of atmospheric aerosols[END_REF] and measured [START_REF] Nguyen | Trends in particle phase liquid water during the Southern Oxidant and Aerosol Study[END_REF][START_REF] Tsai | PM aerosol water content and chemical composition in a metropolitan and a coastal area in southern Taiwan[END_REF].

Therefore, the polar compounds formed during the oxidation of VOCs can readily partition into the aqueous phase [START_REF] Blando | Secondary organic aerosol formation in cloud and fog droplets: a literature evaluation of plausibility[END_REF]Epstein et al., 2013;Ervens et al., 2011a;[START_REF] Herrmann | Tropospheric Aqueous-Phase Chemistry: Kinetics, Mechanisms, and Its Coupling to a Changing Gas Phase[END_REF]. Their subsequent chemical reactivity in this phase leads to the formation of organic acids or higher molecular weight products which can remain at least in part in the condensed phase when water evaporates. These aqueous processes lead to additional SOA formation (aqSOA) that can be very different from those in the gas phase, with likely very different physical and chemical properties [START_REF] Brégonzio-Rozier | Gaseous products and secondary organic aerosol formation during long term oxidation of isoprene and methacrolein[END_REF]Carlton et al., 2009;Ervens et al., 2014a;[START_REF] El Haddad | In-cloud processes of methacrolein under simulated conditions-Part 2: Formation of secondary organic aerosol[END_REF]Ortiz-Montalvo et al., 2012;[START_REF] Renard | Aqueous-phase oligomerization of methyl vinyl ketone through photooxidation -Part 1: Aging processes of oligomers[END_REF][START_REF] Smith | Secondary Organic Aerosol Production from Aqueous Reactions of Atmospheric Phenols with an Organic Triplet Excited State[END_REF].

In general, α,β-unsaturated carbonyls >C=C-C(=O)-and conjugated dienes >C=C-C=C< are extremely efficient precursors for radical oligomerization (e.g. initiated by • OH radicals) in the liquid phase (Clayden et al., 2012;[START_REF] Odian | Volatility and Yield of Glycolaldehyde SOA Formed through Aqueous Photochemistry and Droplet Evaporation[END_REF][START_REF] Smith | March's advanced organic chemistry: reactions, mechanisms, and structure[END_REF], but these processes have been only scarcely studied under atmospheric conditions (Ervens et al., 2014a;Ervens et al., 2014b;Kameel et al., 2013a;[START_REF] Liu | Oligomer and SOA formation through aqueous phase photooxidation of methacrolein and methyl vinyl ketone[END_REF][START_REF] Renard | Aqueous-phase oligomerization of methyl vinyl ketone through photooxidation -Part 1: Aging processes of oligomers[END_REF][START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF].

The authors have shown that the oligomerization proceeds via external • OH-addition to a C=C bond, leads to the formation of a hydroxyalkyl radical (HO-R • ) that is stabilized by the resonance effect with the adjacent unsaturation (Figure S1). This HOR • radical has a planar configuration, providing extremely low steric hindrance for further addition [START_REF] Gilbert | Kinetic and structural EPR studies of radical polymerization. Monomer, dimer, trimer and midchain radicals formed via the initiation of polymerization of acrylic acid and related compounds with electrophilic radicals (˙OH, SO 4 -˙ and Cl 2 -˙)[END_REF]. Thus, in competition with O 2 addition, HOR • radical can easily add to the C=C bond of another precursor molecule, and quickly propagate the monomer units in this manner, until the termination step (Figure S1). This termination step is a reaction between two radicals, by coupling or by disproportionation, thus yielding a series of oligomers, each series being initialized by a specific radical, depending on the initial • OH-attack (Kameel et al., 2013b;[START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF]. [START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF]2015) have studied the effects of the precursor initial concentrations for methyl vinyl ketone (MVK) under initially aerated solutions, and they concluded that oligomerization prevails over functionalization for precursor initial concentrations of 2 mM or higher. In wet aerosol, this concentration range may be reached by the sum of the unsaturated water soluble organic compounds (UWSOC) [START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF].

However, to our knowledge, the reactivity of mixtures of different atmospherically relevant UWSOC has never been studied.

The ion mobility spectrometry (IMS) is a method to separate and characterize ions based on their gas-phase transport in electric fields. For roughly 50 years, this technique has been combined with mass spectrometry (MS) by inserting the IMS separation after ionization e.g. by electrospray (ESI) and prior to the mass spectrometry step. This combination of an IMS separation (typically occurring within milliseconds) and MS detection (typically occurring within microseconds) allows an additional separation step on a MS time-frame, in addition to liquid chromatography, without compromising the speed of MS detection [START_REF] Lapthorn | Ion mobility spectrometry-mass spectrometry (IMS-MS) of small molecules: Separating and assigning structures to ions[END_REF][START_REF] Shvartsburg | Fundamentals of Traveling Wave Ion Mobility Spectrometry[END_REF].

Although the IMS-MS has been used in different scientific fields (such as structural polymer chemistry, or biological analyses to fractionate complex mixtures prior to the MS step), it has only recently been applied for "small molecules" such as those found in the 100-500 amu [START_REF] Lapthorn | Ion mobility spectrometry-mass spectrometry (IMS-MS) of small molecules: Separating and assigning structures to ions[END_REF]. This technique is thus very well suited to analyze atmospheric oligomers, but, to our knowledge, it has not yet been used in this field.

The aim of this work is to investigate aqueous phase oligomerization of several atmospheric UWSOC through their • OH-oxidation using IMS-MS. The efficiency of the technique is shown on oligomers that were previously described by [START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF], i.e. derived from MVK photooxidation. The results are then compared to other oligomers, derived from other individual biogenic UWSOCs and mixtures of these compounds. The suitability of the technique for the detection of oligomers in complex chamber and/or field samples is finally discussed.

Experimental

A photoreactor was used to simulate the aqueous phase • OH-oxidation of UWSOC. • OH radicals were generated from H 2 O 2 photolysis. Liquid samples were collected at specific reaction times, and analyzed using ultra-performance liquid chromatography (UPLC) coupled to ion mobility spectrometry and mass spectrometry (IMS-MS). The oligomerization of the investigated UWSOCs was studied for each individual species, and in mixtures.

Oligomer precursors

Eleven atmospheric relevant UWSOCs (Table 1) were investigated, they were all purchased from Sigma-Aldrich. The initial reactant concentrations were chosen to scale in the range of those for which oligomerization was observed previously with MVK [START_REF] Renard | Aqueous Phase Oligomerization of Methyl Vinyl Ketone by Atmospheric Radical Reactions[END_REF][START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF] or isoprene (Kameel et al., 2013a). For all experiments, the initial concentration of H 2 O 2 was 200 mM. The oligomerization of each individual precursor was examined for an initial concentration of 10 mM, and the mixtures of precursors were studied starting from a total UWSOC initial concentration of 10 mM. For the solution mixtures, two control experiments were performed (in the dark; and under irradiation with no H 2 O 2 ) and revealed no oligomer formation. The chosen precursor concentrations correspond to initial carbon mass concentrations ranging from 480 to 1200 mgC L -1 , depending on the compound (from C 4 to C 10 ). These concentrations are higher than the total concentrations of WSOC in cloud and fog droplets, which culminate at approximately 200-300 mgC L -1 [START_REF] Herckes | A review of observations of organic matter in fogs and clouds: Origin, processing and fate[END_REF]. However, they are much lower than the estimated WSOC concentrations in wet aerosols. Ervens et al. (2011) estimate that these concentrations scale inversely with the volume of the particles, resulting in typical concentrations of ~M in wet aerosols. Considering that UWSOC represent 2-20% of WSOC concentrations [START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF], the chosen 10 mM initial concentration may represent the total concentration of all UWSOCs in wet aerosol.

The eleven UWSOC investigated were chosen among a wide range of atmospheric relevant compounds, such as oxygenated isoprenoids and terpenoids, but also green leaf volatiles (GLV), Leaf-Wound Oxygenated Compounds (LWOC) and dicarboxylic acids (Table 1).

Table 1: List of the eleven studied atmospheric relevant UWSOC. 1 the investigated compounds include oxygenated isoprenoids (isop.) and terpenoids (terp.), oxygenated biogenic VOC (OBVOC), green leaf volatiles (GLV), Leaf-Wound Oxygenated Compounds (LWOC) and secondary dicarboxylic acids (sec.). 2 uns. = unsaturated 3 the maximum degree of oligomerization corresponds to the number of monomer units reached at the maximum m/z of the most intense oligomer series. Oligomerization is considered to occur for a maximum degree of oligomerization > 2.

MVK, methacrolein (MACR) and methacrylic acid (MA) are key oxidation products of isoprene, which is the most abundant emitted VOC with a global emission of 500-750 Tg yr -1 (Claeys et al., 2004;[START_REF] Guenther | Estimates of global terrestrial isoprene emissions using MEGAN (Model of Emissions of Gases and Aerosols from Nature)[END_REF]. Linalool is a major oxygenated monoterpene [START_REF] Geron | Seasonal monoterpene and sesquiterpene emissions from Pinus taeda and Pinus virginiana[END_REF]. GLV, containing 5 or 6 carbon atoms are initiated by the lipoxygenase enzymes within plant cells [START_REF] Jardine | Green leaf volatiles and oxygenated metabolite emission bursts from mesquite branches following light-dark transitions[END_REF]. GLV and LWOC emissions [START_REF] Arneth | Terrestrial biogeochemical feedbacks in the climate system[END_REF][START_REF] Mentel | Secondary aerosol formation from stress-induced biogenic emissions and possible climate feedbacks[END_REF][START_REF] Richards-Henderson | Aqueous oxidation of green leaf volatiles by hydroxyl radical as a source of SOA: Kinetics and SOA yields[END_REF]. We investigated several GLV that were observed in the atmosphere, such as cis-3-hexenal, cis-3-hexen-1-ol and 2-methyl-3-buten-2-ol (MBO) (Brilli et al., 2012;[START_REF] Jardine | Green leaf volatiles and oxygenated metabolite emission bursts from mesquite branches following light-dark transitions[END_REF][START_REF] Richards-Henderson | Aqueous oxidation of green leaf volatiles by hydroxyl radical as a source of SOA: Kinetics and SOA yields[END_REF] and LWOC, such as ethyl vinyl ketone (EVK) [START_REF] Jiménez | Photooxidation of Leaf-Wound Oxygenated Compounds, 1-Penten-3-ol, ( Z )-3-Hexen-1-ol, and 1-Penten-3-one, Initiated by OH Radicals and Sunlight[END_REF], MACR and MVK [START_REF] Ruuskanen | Eddy covariance VOC emission and deposition fluxes above grassland using PTR-TOF[END_REF].

Methyl chavicol is a biogenic oxygenated aromatic compound (Bouvier-Brown et al., 2009a ;Bouvier-Brown et al., 2009b;[START_REF] Pereira | Secondary organic aerosol formation and composition from the photo-oxidation of methyl chavicol (estragole)[END_REF], its atmospheric mixing ratios were reported to be strongly correlated with those of MBO.

We also studied three atmospheric unsaturated acids. In addition to methacrylic acid, we tested two isomers, fumaric and maleic acids. These dicarboxylic acids are secondary reaction products of both biogenic and anthropogenic precursors. They are highly water soluble and mostly present in particles, they may be involved with cloud condensation processes [START_REF] Sempéré | Trans-hemispheric contribution of C 2 -C 10 α, ωdicarboxylic acids, and related polar compounds to water-soluble organic carbon in the western Pacific aerosols in relation to photochemical oxidation reactions: dicarboxylic acids in western pacific aerosols[END_REF].

Photoreactor

The photoreactor set-up used was based on the one described in [START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF]. It is a 450 cm 3 Pyrex thermostated photoreactor, equipped with a 1000 W xenon arc lamp (LSH 601, Oriel) and a glass filter (AM 0, ASTM 490) to reduce the lamp intensity, in particular in the infrared range (800 -1100 nm).

All experiments were performed at 25°C. They started with irradiation of aerated UHQ water (18.2 MΩ cm, Millipore), then H 2 O 2 (50 %, stabilized, Acros) was introduced, and after 10 min of H 2 O 2 photolysis, the UWSOC was introduced (individually or as a mixture) at time 0. All experiments were performed in aerated UHQ water, i.e. with initial saturated O 2 concentrations.

For all experiments, the initial ratio

[H2O2]0

[UWSOC]0

= 20 was chosen in order to favor • OH reaction toward UWSOC over its reaction with H 2 O 2 by more than 80 %. Under these conditions, we estimate that the • OH concentrations were approximately 10 -14 -10 -13 M, in the range of the estimated values for fog droplets to wet aerosol conditions [START_REF] Arakaki | A General Scavenging Rate Constant for Reaction of Hydroxyl Radical with Organic Carbon in Atmospheric Waters[END_REF]Ervens et al., 2014b;[START_REF] Herrmann | Tropospheric Aqueous-Phase Chemistry: Kinetics, Mechanisms, and Its Coupling to a Changing Gas Phase[END_REF][START_REF] Herrmann | Tropospheric Aqueous-Phase Free-Radical Chemistry: Radical Sources, Spectra, Reaction Kinetics and Prediction Tools[END_REF].

IMS-mass spectrometry analyses

Aliquots of the solution sampled from the photoreactor were analyzed for oligomers using an ultra-high performance liquid chromatographic system (UPLC, Waters) coupled to a hybrid quadrupole -time of flight (Q-TOF) mass spectrometer (Synapt-G2 HDMS, Waters)

fitted with an electrospray source (ESI). This instrument incorporates a traveling wave ion mobility spectrometry (TWIMS). This latter system has been widely described by [START_REF] Shvartsburg | Fundamentals of Traveling Wave Ion Mobility Spectrometry[END_REF]. Briefly, ions are propelled into a chamber containing a buffer gas and a series of stacked ring electrodes, where a voltage pulse is passed from one to the next, creating a voltage wave in repeating sequences. The height and the speed of the travel wave constitute the main internal parameters of this ion mobility cell. Ions with different collision cross sections (CCS), (i.e., molecular shapes), travel through this ion mobility cell with different velocities, leading to their mobility-based separation [START_REF] Lapthorn | Ion mobility spectrometry-mass spectrometry (IMS-MS) of small molecules: Separating and assigning structures to ions[END_REF] which can be quantified using the ion mobility K given by Equation 1.

K= 3q 16N 2π µk b T 1 Ω Eq. 1
Where K is the ion mobility, q is the ionic charge [C], N is the buffer gas density, µ is the reduced mass of the buffer gas and the ion

[kg], k b is the Boltzman constant [kg m 2 s -2 K -1 ], T is the temperature [K],
and Ω is the collision cross-section (CCS, [Ų]).

The drift time (DT) of each ion in the cell is inversely proportional to the ion mobility [START_REF] Kim | Structural Characterization of Unsaturated Phosphatidylcholines Using Traveling Wave Ion Mobility Spectrometry[END_REF][START_REF] Shvartsburg | Fundamentals of Traveling Wave Ion Mobility Spectrometry[END_REF]. This technique thus allows for an additional separation, especially for large ions, with long carbon chains. The instrument thus provides for each chromatographic peak, 3D spectra: Ion intensity -m/z -drift time.

The chromatographic separations were carried out on an UPLC column (HSS T3 C18, 2.1 × 100 mm -1.8 µm; Waters) at 40°C. The mobile phases consisted in (A) 0.1 % formic acid in water (Biosolve, 99 %) and (B) acetonitrile (Biosolve, ULC/MS). The gradient elution was performed at a flow rate of 600 µL min -1 using 5 to 95 % of B within 7 min and held at 95 % of B for 1.5 min. Some contaminant oligomers, e.g., polyethylene glycols (PEG, (Eckers et al., 2007), appear very often at the end of the run (mostly after 5 min), hence, the detection peak was systematically performed at retention times ranging from 0 to 4 min.

The sample injection volume was 10 µL. The optimum ESI conditions found were as follows: 0.5 kV capillary voltage, 40 V sample cone voltage, 450°C desolvation temperature, 120°C source temperature, 20 L h -1 cone gas flow rate and 800 L h -1 desolvation gas flow rate. Trap and transfer collision gas flows were set at 2.0 mL min -1 (0.02 mbar for Ar cell pressure). Helium cell gas flow was set at 180 mL min -1 , and IMS gas flow (N 2 ) was set at 90 mL min -1 and 3.0 mbar for IMS cell pressure. Travel wave height and velocity were set at 40

V and 650 m s -1 , respectively. Data acquisition and mass spectra treatments were provided by the MassLynx software (v.4.1, Waters). Finally, the DriftScope software (v.2.1, Waters) was used for the treatment of m/z vs. drift-time maps, and provided 2D IMS-MS spectra. Using this software, the selected peak detection parameters were the minimum drift time peak width (0.05 ms), the drift time range (0 to 10.8 ms), the MS resolution (18000) and the minimum intensity threshold (5000 counts).

Results

Using the IMS-MS technique, we studied aqueous phase oligomerization by • OHoxidation of each individual UWSOC listed in Table 1, starting with MVK, for which oligomerization processing was previously discussed in detail [START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF]. The results were then compared to other oligomers, derived from the other studied individual UWSOCs. Finally, the technique was applied to different mixtures of UWSOCs. For each experiment, the solution was analyzed after 50 min of UWSOC photooxidation, roughly corresponding to the maximum of oligomer formation for each solution, as observed using UPLC-ESI-MS. 1, the ion mobility increases (i.e. the drift time decreases) with q. This explains why double charged ions show a shorter characteristic drift time than simply charged ions. In the negative mode, the 2D IMS-MS spectrum of the MVK-oligomers (Figure 2a) also 2 shows a linear correlation between the drift time and m/z (Table 2), which characterizes the 3 MVK-oligomer system in the negative mode. The same kind of observations was performed 4 for all the other individual UWSOCs and mixtures. Thus, we further discuss and compare the 5 results obtained under exactly the same experimental and analytical conditions using the 6 negative mode only, as this mode scarcely shows double charged ions. 7 8 The 2D IMS-MS spectra obtained for each UWSOC that exhibit oligomerization upon • OH-oxidation in the aqueous phase, are shown in Figure 2. The maximum degree of oligomerization (reported in Table 1 andTable 2) (Pearce, 1998) corresponds to the number of monomer units reached at the maximum m/z of the most intense oligomer series observed.

Oligomerization of individual precursors evidenced by IMS-mass spectrometry

The precursors are considered to oligomerize under our experimental conditions when the obtained maximum degree of oligomerization is higher than 2.

Table 1 clearly shows that precursor compounds bearing only one unsaturation or two non-conjugated unsaturations do not provide oligomerization (i.e. maximum degree of oligomerization < 2). Among these compounds, cis-3-hexenal and linalool undergo only dimerization: the former is a α,γ-unsaturated carbonyl, and the latter is a non-conjugated diene. Their dimerization can be the result of radical recombination without propagation.

These results thus confirm the importance of the precursor's chemical structure on the oligomerization process, and especially the great ability of conjugated unsaturated compounds to provide oligomer formation under simulated atmospheric conditions.

Out of the eleven tested compounds, the six compounds bearing a α,β-unsaturated conjugation undergo oligomerization (Table 1). Figure 2 shows that, in the same manner as for MVK, for all these compounds, the m/z and the ion mobility are strongly correlated.

However, important differences are observed from one precursor to the other on the maximum degree of oligomerization, on the number of oligomer series, or on the drift. MVK and EVK show the highest maximum degree of oligomerization ( 14). This result is consistent with the fact that these two compounds have very similar chemical structures, and thus they oligomerize in the same way. This is further confirmed by the fact that the linear correlations between the drift and m/z of their oligomers exhibit the same slope for both precursors, within the experimental uncertainties (Table 2).

The IMS-MS technique also evidences substantial differences between the oligomers arising from MVK and MACR (Figures 2a and2c) although these two precursors are isomers. The lower DT-m/z slope obtained for MACR-oligomers (Table 2) indicates that they oligomerize in different ways. Compared to MVK-oligomers, MACR-oligomers also show a significantly more clustered shape of the 2D IMS-MS spectra (Figure 2), with more scattered data points, a lower correlation coefficient and a lower maximum degree of oligomerization (Table 2). These differences can be due to a more complex oligomer system [START_REF] Kim | Structural Characterization of Unsaturated Phosphatidylcholines Using Traveling Wave Ion Mobility Spectrometry[END_REF] with MACR precursor, as discussed further hereafter. Methacrylic acid (Figure 2d) is one of the reaction products of MACR photooxidation in the aqueous phase [START_REF] Liu | In-cloud processes of methacrolein under simulated conditions-Part 1: Aqueous phase photooxidation[END_REF]. Its oligomers exhibit statistically the same slope as those arising from MACR (Table 2). These observations can be the result of common oligomer series arising from both MACR and methacrylic acid, and thus can explain in part the more complex oligomer system observed from MACR than from MVK.

Fumaric and maleic acids are conformers (Table 1), the former one being produced from the natural photolysis of the latter one under atmospheric conditions [START_REF] Fu | Organic molecular composition of marine aerosols over the Arctic Ocean in summer: contributions of primary emission and secondary aerosol formation[END_REF].

Although the IMS-MS technique is commonly used to distinguish between oligomers arising from isomers [START_REF] Li | Resolving Structural Isomers of Monosaccharide Methyl Glycosides Using Drift Tube and Traveling Wave Ion Mobility Mass Spectrometry[END_REF], maleic and fumaric acids exhibit oligomers with similar trends in the 2D IMS-MS spectra (Figures 2e and2f) and statistically the same slope (Table 2).

However, the slopes obtained are significantly lower than those observed from the oligomers arising from the other precursors. for complex mixtures, the maximum degree of co-oligomerization corresponds to the maximum m/z reached by the most intense series, divided by the average molar mass of the mixture.

Co-oligomerization of precursor mixtures evidenced by IMS-mass spectrometry

In order to examine more complex mixtures, i.e. closer to atmospheric conditions, we investigate in this section IMS-MS analyses of different mixtures of the six compounds bearing a α,β-unsaturated conjugation that individually undergo oligomerization, as shown in the previous section. The aim is to observe oligomerization or co-oligomerization of mixtures containing the same initial total concentration as that used for each individual precursor (10 mM). Due to the different oligomer properties evidenced for the individual precursors, the IMS-MS is a valuable technique to examine if these precursors can undergo cooligomerization when mixed together. Co-oligomerization is the formation of an oligomer derived from more than one species of monomer. Such co-oligomers, in which there is an irregular distribution of different monomers, mainly follows the Bernoulli Law [START_REF] Odian | Volatility and Yield of Glycolaldehyde SOA Formed through Aqueous Photochemistry and Droplet Evaporation[END_REF]. In this case, co-oligomers can theoretically also be statistically characterized by the slope of the 2D IMS-MS linear regression fit formed by the detected peaks.

Figure 3 shows that this phenomenon is observed for the four different mixtures of precursors investigated. Such mixtures show extremely complex mass spectra, from which interpretation is arduous if not impossible (see for example Figure S3), whereas IMS-MS spectra exhibit a linear correlation between the m/z and the drift time which proves indubitably co-oligomerization. For the mixture of MVK + MACR (5 mM each), the 2D IMS-MS spectrum (Figure 3a) shows a linear regression fit with an intermediate slope value between those arising from MVK and MACR individually (Table 2).

This result confirms that we do not obtain two different oligomer systems, but rather one co-oligomerization system. The maximum degree of co-oligomerization is smaller than those arising from each individual precursors (Table 2). However, the number of series is likely higher (Figure 3a), certainly due to the enhanced complexity of the system.

For the mixture of maleic and fumaric acids (5mM each), the 2D IMS-MS spectrum (Figure 3b) shows statistically the same slope as those obtained from each individual acid (Table 2). It is thus not possible to determine if any co-oligomerization is occurring in this case.

For the mixture of maleic, fumaric and methacrylic acids (3.33 mM each) (Figure 3c), we observe one intermediate slope between the value obtained for the previous mixture (Figure 3b) and that obtained for methacrylic acid alone (Table 2). The system becomes more complex, with likely more oligomer series as denoted by the more clustered shape of the 2D IMS-MS spectra and a lower maximum degree of co-oligomerization (Table 2). Note that, in this case where co-oligomers contain various monomers of various molecular masses, the maximum degree of co-oligomerization is only an estimated value as it corresponds to the maximum m/z reached by the most intense series observed, divided by the average molecular mass of the initial mixture.

For the final mixture of the six α,β-unsaturated conjugated compounds (1,67 mM each), the 2D IMS-MS spectrum also shows a highly correlated linear plot (Figure 3d) with an intermediate slope between the six individual compounds (Table 2), with a likely more complex oligomer system, and more oligomer series.

Conclusions and atmospheric implications

One of the current essential issues to unravel our ability to forecast future climate change and air quality, implies a better understanding of natural processes leading to SOA formation, and in particular the formation and fate of macromolecules. The presence of macromolecules in the atmosphere has previously been monitored by ultrahigh resolution mass spectrometry techniques which have revealed the presence of organic molecules containing up to 35 carbon atoms (C 35 ) in aerosol [START_REF] Kourtchev | Molecular composition of biogenic secondary organic aerosols using ultrahigh-resolution mass spectrometry: comparing laboratory and field studies[END_REF][START_REF] Leclair | Fragmentation Analysis of Water-Soluble Atmospheric Organic Matter Using Ultrahigh-Resolution FT-ICR Mass Spectrometry[END_REF][START_REF] Mazzoleni | Identification of water-soluble organic carbon in non-urban aerosols using ultrahigh-resolution FT-ICR mass spectrometry: organic anions[END_REF][START_REF] Rincón | Seasonal differences of urban organic aerosol composition -an ultra-high resolution mass spectrometry study[END_REF], in fog [START_REF] Mazzoleni | Water-Soluble Atmospheric Organic Matter in Fog: Exact Masses and Chemical Formula Identification by Ultrahigh-Resolution Fourier Transform Ion Cyclotron Resonance Mass Spectrometry[END_REF] and in rain [START_REF] Mead | Characterization of CHOS compounds in rainwater from continental and coastal storms by ultrahigh resolution mass spectrometry[END_REF][START_REF] Mead | Insights into dissolved organic matter complexity in rainwater from continental and coastal storms by ultrahigh resolution Fourier transform ion cyclotron resonance mass spectrometry[END_REF].

Evidence that condensed-phase reactions contribute to SOA has been obtained from laboratory and smog chamber studies [START_REF] Hallquist | The formation, properties and impact of secondary organic aerosol: current and emerging issues[END_REF][START_REF] Hall | Oligomer Formation Pathways in Secondary Organic Aerosol from MS and MS/MS Measurements with High Mass Accuracy and Resolving Power[END_REF][START_REF] Herrmann | Tropospheric Aqueous-Phase Chemistry: Kinetics, Mechanisms, and Its Coupling to a Changing Gas Phase[END_REF][START_REF] Zhao | Investigation of Aqueous-Phase Photooxidation of Glyoxal and Methylglyoxal by Aerosol Chemical Ionization Mass Spectrometry: Observation of Hydroxyhydroperoxide Formation[END_REF]. From these studies, it seems that a substantial amount of SOA is composed of oligomers. The latter are small polymers containing less than 30 monomers. The difficulty in characterizing such molecules is to discern between large oxygenated molecules from series of oligomers containing repeated small monomers of diverse structures [START_REF] Nozière | The Molecular Identification of Organic Compounds in the Atmosphere: State of the Art and Challenges[END_REF].

In the present study, taking advantage from previously established radical vinyl oligomerization of MVK in the aqueous phase [START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF] where relatively simple oligomers containing up to 14 monomers were observed, we have investigated the same reactivity on several other UWSOCs and on a few mixtures of these precursor compounds.

The technique used to characterize the formed oligomers was a traveling wave ion mobility spectrometry coupled to a hybrid quadrupole -time of flight mass spectrometer (IMS-MS) fitted with an electrospray source and UPLC. The technique allows for an additional separation, especially for large ions, containing long carbon chains. The technique is currently widely used in polymer chemistry, or biological analyses, it has only recently been applied for "small molecules" such as those found in the m/z 100-500 range. This technique is thus very well suited to analyze atmospheric oligomers, but, to our knowledge, it has not yet been used in this field.

We have shown in this study the efficiency of the IMS-mass spectrometry technique on oligomers derived from MVK photooxidation in the aqueous phase. The results were then compared to other oligomers, derived from ten other individual biogenic UWSOCs: methacrolein, ethyl vinylketone, methacrylic acid, fumaric and maleic acids, cis-3-hexenal, linalool, cis-3-hexen-1-ol, 2-methyl-3-buten-2-ol and methyl chavicol. The technique allowed distinguishing between different oligomers arising from different precursors. It also clearly showed that compounds bearing a non-conjugated unsaturation did not provide oligomerization. Finally, it was shown that the IMS-mass spectrometry technique, applied to mixtures of unsaturated conjugated precursors, exhibited the ability of these precursors to cooligomerize, i.e. forming only one complex oligomer system bearing monomers of different structures.

These observations demonstrate the effectiveness of using IMS-mass spectrometry in the study of atmospheric oligomer systems. IMS-mass spectrometry has significant advantages for the analysis of very complex mixtures. It provides rapid identification of complex oligomer systems, when mass spectra are extremely difficult to interpret. In this way, the technique can be regarded as an excellent complement to the ultrahigh resolution mass spectrometry techniques when long chain complex oligomer series are suspected to be formed, as previously demonstrated on crude oil analyses by [START_REF] Fernandez-Lima | Petroleum Crude Oil Characterization by IMS-MS and FTICR MS[END_REF].

Thus, there should be a growing interest in the use of IMS-mass spectrometry in atmospheric studies to assist in the deconvolution of complex chamber and field samples. Brilli, F., Hörtnagl, L., Bamberger, I., Schnitzhofer, R., Ruuskanen, T.M., Hansel, A., Loreto, F., Wohlfahrt, G., 2012. Qualitative and Quantitative Characterization of Volatile Organic Compound Emissions from Cut Grass. Environ. Sci. Technol. 46, 3859-3865. doi:10.1021/es204025y Carlton, A.G., Turpin, B.J., 2013. Particle partitioning potential of organic compounds is highest in the Eastern US and driven by anthropogenic water. Atmospheric Chem. Phys. 13, 10203-10214. doi:10.5194/acp-13-10203-2013Carlton, A.G., Wiedinmyer, C., Kroll, J.H., 2009. A review of Secondary Organic Aerosol (SOA) formation from isoprene. Atmospheric Chem. Phys. 9, 4987-5005.

Claeys, M., Wang, W., Ion, A.C., Kourtchev, I., Gelencsér, A., Maenhaut, W., 2004. Formation of secondary organic aerosols from isoprene and its gas-phase oxidation products through reaction with hydrogen peroxide. Atmos. Environ. 38, 4093-4098. doi:10.1016/j.atmosenv.2004.06.001 Clayden, J., Greeves, N., Warren, S., 2012. Organic

Figure 1

 1 Figure1shows the 3D (Intensity / Drift time / m/z) and 2D IMS-MS spectra (in the positive mode) of the oligomers derived from MVK after 50 min of aqueous phase • OHoxidation. Generally, each oligomer series is characterized by a recurrent mass (corresponding to the one of the propagating monomer) and a drift time. In the present example, the oligomerization is only due to the propagation of one monomer (i.e. MVK), with a few number of different series, each one corresponding to a different radical initiator[START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF]. The oligomers thus bear highly related structures. As a result, the 2D IMS-MS spectrum shown in Figure1exhibits a linear correlation between the m/z and the drift time for all these structure related oligomer series, in good agreement with the observations by[START_REF] Kim | Structural Characterization of Unsaturated Phosphatidylcholines Using Traveling Wave Ion Mobility Spectrometry[END_REF] and[START_REF] Fernandez-Lima | Petroleum Crude Oil Characterization by IMS-MS and FTICR MS[END_REF] for very different kinds of molecules (i.e. phosphatidylcholines and crude oils respectively). Its linear regression fit, derived over four replicate experiments (drift time = 941 (± 16) × 10 -5 m/z + 0.209 (±0.040) characterizes the MVK-oligomer system in the positive mode. In Figure1, the highlighted red dots label the most intense oligomer series (see the corresponding mass spectrum in FigureS2). Between two subsequent red dots, one can determine the oligomer series' characteristic mass (70.0419 amu corresponding to the molecular mass of MVK) and characteristic drift time (0.659 ms). Figure1also shows the double charged ions (green dots),

Figure 1 :

 1 Figure 1: (a) 3D (Intensity / Drift time / m/z) and (b) 2D IMS-MS spectra of MVK after 50 min of photooxidation in the aqueous phase, in the positive mode. The most intense series is highlighted in red, with its characteristic MVK mass and MVK drift time. Double charged ions are highlighted in green; they are not included in the linear regression calculation.

Figure 2 :

 2 Figure 2: 2D IMS-MS spectra (in the negative mode) of different UWSOCs after 50 min of photooxidation in the 9

Table 2 :

 2 acids DT = 671 (± 12) × 10 -5 m/z + 0.488 (± 0.121) 4 Fumaric + Maleic + methacrylic acids DT = 734 (± 13) × 10 -5 m/z + 0.430 (± 0.106) 5 a MVK + MACR + EVK + Fumaric + Maleic + methacrylic acids DT = 891 (± 15) × 10 -5 m/z + 0.165 (± 0.041) 8 a Linear regression of the drift time (DT) as a function of m/z; and maximum degree of oligomerization obtained from the investigated oligomer precursors: six individual α-β unsaturated UWSOCs and four mixtures, by means of IMS-MS in the negative mode. The statistical data were derived over 1 to 4 replicate experiments. a

Figure 3 :

 3 Figure 3: 2D IMS-MS of four different mixtures of α-β unsaturated carbonyls and acids after 50 min of photooxidation in the aqueous phase, in the negative mode, with the equations of drift time (standard deviations are in table 2) arising from aqueous phase photooxidation of (a) MVK + MACR (5 mM each), (b) fumaric + maleic acids (5 mM each), (c) fumaric + maleic + methacrylic acids (3.33 mM each), (d) MVK + MACR + EVK + Fumaric + Maleic + methacrylic acids (1.67 mM each).

Figure S1 :Figure S2 :

 S1S2 Figure S1: Vinylic oligomerization of an α, β-unsaturated carbonyl in the aqueous phase, initiated by • OHoxidation, n is the degree of oligomerization i.e. the number of monomers (adapted from[START_REF] Renard | Radical mechanisms of methyl vinyl ketone oligomerization through aqueous phase OH-oxidation: on the paradoxical role of dissolved molecular oxygen[END_REF].

Figure S3 :

 S3 Figure S3: Typical mass spectrum obtained using UPLC-ESI-MS of a solution mixture of methyl vinylketone, methacrolein, ethyl vinylketone, methacrylic acid, fumaric and maleic acids (1.67 mM each) after 50 min of photooxidation in the aqueous phase (a) in the positive mode; (b) in the negative mode

Acknowledgements. We thank the National Research Agency ANR (project CUMULUS ANR-2010-BLAN-617-01), AXA insurances. The authors thank Jean-Louis Clément (Aix Marseille Université CNRS, ICR UMR7273, 13397, Marseille, France) for valuable discussions on the reactivity of the different various compounds studied.