Comparison of computational and experimental saturation vapor pressures of α-pinene + O3 oxidation products

Abstract. Accurate information on gas-to-particle partitioning is needed to model secondary organic aerosol formation. However, determining reliable saturation vapor pressures of atmospherically relevant multifunctional organic compounds is extremely difficult. We estimated saturation vapor pressures of α-pinene ozonolysis derived secondary organic aerosol constituents using FIGAERO-CIMS experiments and COSMO-RS theory. We found a good agreement between experimental and computational saturation vapor pressures for molecules with molar masses around 190 g mol−1 and higher, most within a factor of 3 comparing the average of the experimental vapor pressures and the COSMO-RS estimate of the isomer closest to the experiments. Smaller molecules likely have saturation vapor pressures that are too high to be measured using our experimental setup. The molecules with molar masses below 190 g mol−1 that have several orders of magnitude difference between the computational and experimental saturation vapor pressures observed in our experiments are likely products of thermal decomposition occurring during thermal desorption. For example, dehydration and decarboxylation reactions are able to explain some of the discrepancies between measured and calculated saturation vapor pressures. Based on our estimates, FIGAERO-CIMS can best be used to determine saturation vapor pressures of compounds with low and extremely low volatilities.


and dehydration reactions are significant in FIGAERO measurements for multifunctional carboxylic acids that have more than 4 oxygen atoms, degree of unsaturation between 2 and 4, and maximum desorption temperature (T max ) higher than 345 K.
They found that COSMO-RS (parametrization BP_TZVPD_FINE_C30_1501 implemented in the COSMOtherm program; COSMOtherm (2015)) predicts up to 8 orders of magnitude higher saturation vapor pressures than group-contribution methods, such as EVAPORATION (Compernolle et al., 2011) and SIMPOL.1 (Pankow and Asher, 2008). The COSMOtherm15estimated saturation vapor pressures indicated that the studied highly oxidized monomers derived from the ozonolysis of α-pinene were likely classified as SVOC with saturation vapor pressures higher than 10 −5 Pa (Kurtén et al., 2016). However, 70 the parametrization in COSMOtherm has a large effect on the calculated properties, since the model is parametrized using a set of well-known compounds with experimental properties available. There have been significant improvements since the BP_TZVPD_FINE_C30_1501 parametrization used by Kurtén et al. (2016), especially with better description of the effect of hydrogen bonding on thermodynamic properties. This is an important factor in calculating properties of multifunctional compounds that are able to form intramolecular H-bonds. For example, Hyttinen et al. (2021b) found that with an improved 75 conformer sampling method (recommended by Kurtén et al. (2018)) and a newer parametrization (BP_TZVPD_FINE_19), COSMOtherm-estimated saturation vapor pressures of the two most highly oxygenated α-pinene ozonolysis monomer products studied by Kurtén et al. (2016) are up to 2 orders of magnitude lower than SIMPOL.1 estimates, while COSMOtherm predicted higher saturation vapor pressures than SIMPOL.1 for 15 different α-pinene+OH-derived dimers.
In this study, we investigate the saturation vapor pressures of SOA constituents formed in α-pinene ozonolysis, using both 80 FIGAERO-CIMS experiments and the COSMO-RS theory. We compare saturation vapor pressures derived from both experiments and calculations (different isomers), in order to evaluate the experimental method. Additionally, we investigate the prevalence of thermal decomposition in our experiment.

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The experiments were conducted at a 9 m 3 Teflon environmental reaction chamber. The chamber is located at University of Eastern Finland (Kuopio, Finland). During the experiment, the chamber was operated as a batch reactor, i.e., the experimental conditions were set at the start of the experiment, and after the chemistry was initiated, the proceeding changes in gas and particle phase in the close system were sampled. The chamber is set on a foldable frame which allows the chamber to collapse when deflated, maintaining a constant pressure. The chamber and the instruments were situated inside a temperature-controlled environment (temperature set to 295.15 K). Before the experiment, the chamber was flushed over night with dry clean air, to reduce the impact of evaporation of residues from preceding experiments from the walls.
To prepare the chamber for the experiment, it was first filled with clean air, which was sampled by a proton-transfer-reaction time-of-flight mass spectrometer (PTR-ToF-MS, Ionicon, Inc.), and a Filter Inlet for Gases and AEROsols (FIGAERO) coupled with a Time-of-Flight Chemical Ionization Mass Spectrometer (ToF CIMS) to determine chamber background. The next section 95 will provide a more thorough description of the instruments. After the chamber was filled close to operational capacity (9 m 3 ), α-pinene was introduced into the chamber. This was done by flushing dry purified air through an α-pinene diffusion source and into the chamber until target concentration (11 ppb) was reached. α-Pinene levels were monitored with an online PTR-ToF-MS.
Polydisperse ammonium sulfate seed aerosol (∼ 10 000 # cm −3 , maximum number concentration at ∼ 80 nm) was added to provide condensation nuclei and to prevent possible nucleation during the experiments. Lastly, 30 ppb of externally generated 100 ozone (using an ozone generator with UV lamp of wavelength 185 nm) was introduced into the reaction chamber to start the chemistry. Experiment duration was 8 hours from when the chemistry started (ozone was added). There was practically no change in the chamber size during the experiment, due to the low sampling flows compared to the total chamber volume.

Instrumentation
In this study, we analyzed particle-phase composition measurements performed with a Filter Inlet for Gases and AEROsols 105 (FIGAERO) inlet system coupled with a time of flight chemical ionization mass spectrometer with iodide ionization (I-CIMS, Aerodyne Research Inc.), a system that allows for measurement of both gas-phase and particle-phase compounds with a single instrument , 2015Ylisirniö et al., 2021). In the FIGAERO inlet, the aerosol particles are collected on a Teflon filter (Zefluor 2 µm PTFE Membrane filter, Pall Corp.) while simultaneously analysing gas phase. After a predetermined collection time (here 45 minutes) is finished, the sampled particle matter is evaporated using a gradually heated 110 nitrogen flow with a heating rate of 11.7 K min −1 and the evaporated molecules are carried into the detector instrument I-CIMS. Integrating over the heating time will give the total signal of a particular compound in the sample being processed. The working principle of I-CIMS has been introduced elsewhere Iyer et al., 2017), but in short, oxidized gas-phase constituents are detected by clustering negatively charged iodide anions (I -) with suitable organic compounds. Clustering of the organic molecules and Ihappens in an Ion Molecule Reaction Chamber (IMR), which is actively controlled to be at 10 4 115 Pa pressure.
The particle sampling period was set to 45 minutes, and the particle analysis period consisted of 15 minutes ramping time (when the filter was heated linearly from room temperature to 473.15 K), and 15 minutes of soak period (where the filter temperature was kept at 473.15 K). Thus, there are 45 minutes of gas-phase measurements followed by a 30-minute gap while particle chemical composition is being analysed. Seven particle samples were collected during the 8-hour SOA experiment.

Data analysis
All FIGAERO-CIMS data were preprocessed with tofTools (version 611) running in MATLAB R2019b (MATLAB, 2019), and further processed with custom MATLAB scripts. Saturation vapor pressures of the oxidized organics were estimated based on their thermograms, i.e., signal as a function of temperature along the heating of the particle sample in FIGAERO. We used 20 s averaging in the thermograms. The temperature axis calibration sample was made as described by Ylisirniö et al. (2021), by using an atomizer to produce a particle population with a similar size distribution to the one present in the chamber experiment. Polyethylene glycol (PEGn with n = 6, 7 and 8) with known saturation vapor pressures (see Fig. S1 and Table S1 of the Supplement) were used to produce the calibration particle population. Following the calibration fit, the saturation vapor pressure (p sat in Pa) of a molecule can be calculated from the temperature of the highest signal (T max in K): (1)

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The variation in T max values between 3 calibration runs varies from 0.5 K of the smallest PEG6 (282.3 g mol −1 ) to 7.6 K of the largest PEG8 (370.4 g mol −1 ). With our calibration curve, these differences correspond to a factor of 1.1 and 3.3 variation in the saturation vapor pressures, respectively. Saturation vapor pressures were calculated for multiple α-pinene-derived SOA constituents from 6 different samples, i.e., 6 different subsequent thermal desorptions, during the one 8-hour experiment. The first sample of our experiment was omitted, because the signals were much lower in the first sample than the other samples.

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This was likely caused by lower concentrations of oxidation products in the chamber at the beginning of the experiment. In our experiment, the variation in T max values between the different thermal desorption cycles ranged from 2.0 to 11.1 K. The variation in T max values increases with the increasing molar mass (see Fig. S2 of the Supplement). The 11.1 K variation corresponds to a factor of 5.8 variation in p sat . Most of the studied compounds have saturation vapor pressures within a factor of 4 from the 6 measurement cycles. For our COSMO-RS calculations, we selected conformers containing no intramolecular H-bonds, detailed previously by Kurtén et al. (2018),  and Hyttinen et al. (2021b). This method has been shown to provide more 150 reliable saturation vapor pressure estimates for multifunctional oxygenated organic compounds even if they are able to form intramolecular H-bonds (Kurtén et al., 2018). The conformer search was performed using the systematic algorithm (sparse systematic algorithm for isomers that have more than 100 000 possible conformers) of Spartan'14 (Wavefunction Inc., 2014).
Instead of omitting conformers containing intramolecular H-bonds after running the quantum chemical calculations, as recommended by Kurtén et al. (2018), we removed conformers containing intramolecular H-bonds already after the initial conformer 155 search step, in order to decrease the number of density functional theory (DFT) calculations needed for the input file generation (see Sect. S1 of the Supplement for the details).
The quantum chemical single-point calculations and geometry optimizations were performed using the COSMOconf pro- In COSMOtherm, the saturation vapor pressure (p sat,i ) of a compound is estimated using the free energy difference of the compound in the pure condensed phase (G (l) i ) and in the gas phase (G Here R is the gas constant and T is the temperature.

Saturation vapor pressures
We selected 26 elemental compositions (20 monomers and 6 dimers) from our FIGAERO-CIMS measurements for the compar-180 ison with COSMOtherm-estimated saturation vapor pressures. All elemental compositions that contain up to 10 carbon atoms are assumed to be monomers (containing carbon atoms only from the original reactant α-pinene), while compounds with 11-20 carbon atoms are assumed to be dimers (covalently bound accretion products of two monomers). For COSMOtherm analysis, we selected 1-7 isomer structures that can be formed from α-pinene ozonolysis for each elemental composition. The degree of unsaturation of the studied monomers and dimers is 1-4 and 4-5, respectively, determining how many double bonds or ring structures each isomer must contain.
The structures of the studied monomers were formed based on structures suggested by previous experimental and computational studies (Lignell et al., 2013;Aljawhary et al., 2016;Mutzel et al., 2016;Kristensen et al., 2014;Kurtén et al., 2015;Iyer et al., 2021). pair of monomer isomers with the same elemental composition for each dimerization reaction. For most of the monomers used to form the studied dimers, the best agreement between experimental and computational saturation vapor pressures was found with the isomer that had the lowest COSMOtherm-estimated p sat . We therefore mainly chose the monomer isomers with the lowest p sat to form the studied dimer isomers. Table S3 of the Supplement shows, which monomers were used to form each of the studied dimer isomers.
200 Figure 1 shows COSMOtherm-estimated saturation vapor pressures of the studied isomers, as well as vapor pressures derived from the experimental T max values. The agreement between COSMOtherm-estimated and experimentally determined saturation vapor pressures is good for molar masses higher than 190 g mol −1 . Even with a limited selection of dimer structures, the agreement between COSMOtherm and FIGAERO-CIMS is very good, and even better agreement could likely be found by selecting additional dimer isomers for COSMOtherm calculations.

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The large discrepancy between measured and calculated p sat of the lowest molar mass molecules (light gray bars in Fig.   1) suggests that the measured T max values are related to the thermal decomposition temperatures of larger compounds, rather than saturation vapor pressures of the measured elemental compositions. It is unlikely that COSMOtherm would overestimate saturation vapor pressures by several orders of magnitude using the newest parametrization and improved conformer selection (Kurtén et al., 2018). Additionally, if the low molar mass compounds are IVOCs (p sat > 10 −2 Pa), as predicted by 210 COSMOtherm, they are not likely to contribute to the SOA formation. Conversely, the calibration curve sets a practical upper limit to experimentally derivable p sat based on the experiment temperature and premature evaporation. For example, the upper limit p sat corresponding to the initial temperature of the experiment (T max = 294.15 K) is 1.2×10 −3 Pa. However, the highest experimental saturation vapor pressure among the studied molecules is 8.5×10 −6 Pa, which corresponds to T max = 325 K. This may indicate that the SOA constituents selected for our analysis do not contain SVOCs and the selected elemental

Correlation between monomer and dimer vapor pressures 235
The COSMOtherm calculations of dimers are computationally more demanding than of monomers, due to larger size and higher number of possible conformers. In group-contribution methods, such as SIMPOL.1, saturation vapor pressure of a compound is estimated as the sum of contributions of each of the functional groups in the molecule: We used the same approach to estimate the saturation vapor pressures of dimers and compared those values to saturation vapor 240 pressures estimated using COSMOtherm. However, instead of using the functional groups of the dimer, we used the contributions of the two monomers that formed the dimer. This way, the group-contribution term b k was replaced by COSMOthermestimated saturation vapor pressures of the monomers multiplied with a scaling factor (S n ) to account for the changing functional groups and loss of atoms in dimerization reaction n.
p sat,dimer = S n p sat,monomer1 p sat,monomer2  that were used to form the dimers. We see that the product of monomer vapor pressures is 1-3 orders of magnitude higher than the dimer vapor pressure. There is also a size dependence in the scaling factor, the values of S as a function of dimer size are shown in Fig. S13 of the Supplement. Of the studied acid anhydride dimers, C 13 H 18 O 9 (the smallest dimer) isomers have scaling factors 10 −3 -10 −2 and C 17 H 24 O 10 (the largest dimer) isomers 10 −2 -10 −1 . As a comparison, SIMPOL.1 predicts S = 1.1×10 −2 for the acid anhydride (ketone and ester) formation from two carboxylic acid monomers, with no size dependence.

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The correlation between COSMOtherm-estimated saturation vapor pressures of monomers and dimers can be used to obtain

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A recent study by Yang et al. (2021) proposed two major thermal decomposition pathways for multifunctional carboxylic acids occurring in FIGAERO-CIMS: dehydration (reaction 5) and decarboxylation (reaction 6).  decomposition reactants also fulfill the number of oxygen and degree of unsaturation criteria given by Yang et al. (2021). Other likely decomposition products among the studied monomers are C 4 H 4 O 5 , C 4 H 4 O 6 , C 9 H 12 O 3 , C 10 H 16 O 3 and C 9 H 14 O 4 (see Fig. 1). Figure 3 shows the COSMOtherm-estimated p sat of the studied thermal decomposition product isomers of C 7 H 10 O 4 , 280 C 7 H 10 O 6 , C 8 H 12 O 4 and C 8 H 12 O 6 in red markers. The corresponding reactants are shown in blue markers at the product molar mass, and experimental p sat of the product elemental compositions are given as a range of the six measurement points. The studied thermal decomposition reaction is possible, if the COSMOtherm-estimated saturation vapor pressure of the reactant molecule is lower than the measured saturation vapor pressure of the product elemental composition. Otherwise, the reactant would desorb from the sample before the thermal decomposition reaction has taken place. For example, the elemental compo-285 sition of C 7 H 10 O 4 at 158.15 g mol −1 and its reactants C 8 H 10 O 6 (decarboxylation) and C 7 H 12 O 5 (dehydration) all have higher estimated saturation vapor pressures than the one derived experimentally (though Reactant-1 vapor pressure is close to the experimental one, see Fig. 3). This indicates that the measured C 7 H 10 O 4 is likely not a product of dehydration. The decarboxylation reaction is a possible source of the measured C 7 H 10 O 4 , assuming under-or overestimation of the saturation vapor pressure by our experiments or COSMOtherm, respectively. Another possibility is that the measured C 7 H 10 O 4 is a fragmenta-290 tion product of some other thermal decomposition reaction, where the reactant has an even lower saturation vapor pressure. For C 8 H 12 O 4 , C 7 H 10 O 6 and C 8 H 12 O 6 , some of the studied thermal decomposition reactants have saturation vapor pressures lower than the experimental p sat . This means that the reactant molecules would remain in the sample at the measured T max (= potential thermal decomposition temperature). The measured C 8 H 12 O 4 is more likely a product of decarboxylation than dehydration, because the proposed dehydration reactant has a higher COSMOtherm-estimated saturation vapor pressure than the measured 295 p sat of the product C 8 H 12 O 4 . C 7 H 10 O 6 and C 8 H 12 O 6 have similar estimated and measured saturation vapor pressures and the measured molecules can therefore be either thermal decomposition products or simply relatively low-volatility isomers.
The saturation vapor pressures of the thermal decomposition reactant molecules are 3.3-6.5 (on average 4.7) orders of magnitude lower than the saturation vapor pressures of the corresponding product molecules. The difference between SIMPOL.1estimated saturation vapor pressures of the reactants and products are 4.9 and 3.9 orders of magnitude for the dehydration 300 and decarboxylation reactions, respectively. Based on this, it is unlikely that the detected molecule is formed in either of these specific thermal decomposition reactions, if the COSMOtherm-estimated p sat of the detected molecule is more than 7 orders of magnitude higher than the p sat derived from FIGAERO-CIMS experiments. In those cases, the reactant is likely a larger monomer or even a dimer, that decomposes to form two larger fragments.
It is also possible that other molecules detected in our FIGAERO-CIMS experiments are thermal decomposition products 305 formed during the heating of the sample, though it is impossible to determine if this is true only based on information available from our measurements and calculations. If the decomposition temperature is lower than the T max of the decomposition product molecule, the measured T max values can correspond to the saturation vapor pressures of the decomposition products. However, this possibility was not taken into account when we selected the isomers for the COSMOtherm calculations.

Comparison with previous studies 310
Recently, Thomsen et al. (2021) identified multiple carboxylic acids in SOA formed in α-pinene ozonolysis experiments using an ultra-high performance liquid chromatograph (UHPLC). Out of the compounds included in Thomsen et al. (2021) vapor pressures from previous studies (Bilde and Pandis, 2001;Lienhard et al., 2015;Babar et al., 2020) are given for the specific isomer, while COSMOtherm15 values (Kurtén et al., 2016) are for various other isomers. Pa), the studied monomers with high molar masses (i.e., C 9 -C 10 and O 10 ) may be ELVOCs, while the studied monomers with lower molar masses (around 190 < M w < 275 g mol −1 ) are likely LVOCs (around 10 −9 < p sat < 10 −5 Pa), with the exception of some higher p sat isomers at lower molar masses (M w < 235 g mol −1 ).

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We have shown that COSMOtherm-estimated saturation vapor pressures agree (for M w > 190 g mol −1 ) with those derived from particle-phase thermal desorption measurements of the α-pinene ozonolysis SOA system, taking into account the possibility of thermal decomposition. The measured α-pinene ozonolysis monomer products selected from our SOA sample are mainly LVOCs and dimers are mainly ELVOCs. Molecules with ultra low volatilities are likely not desorbing during the experiments without fragmenting and are not detected by FIGAERO-CIMS. The smaller monomers (M w < 190 g mol −1 ) with the 345 highest saturation vapor pressures (IVOCs) were likely not present in the sample aerosol collected from the chamber, instead, they are likely products of thermal decomposition formed from larger compounds during the experiment.
Comparison between estimated and experimental p sat can provide insight about the possible chemical structures of SOA constituents. Based on our results, the commonly used FIGAERO-CIMS instrument is best suited for measuring saturation vapor pressures of monoterpene-derived highly oxygenated monomers in the LVOC and ELVOC range with M w > 190 g 350 mol −1 . Hence, it is reliable for estimating saturation vapor pressures of oxidation products of monoterpenes, such as α-pinene, keeping in mind that the smallest measured molecules are likely products of thermal decomposition. COSMOtherm can be used to estimate saturation vapor pressures of compounds for which p sat is outside the applicable range of FIGAERO-CIMS experiments, i.e., IVOCs, SVOCs and ULVOCs, if the exact structures of the molecules are known.
In conclusion, this study gives us useful information for studying saturation vapor pressures of multifunctional compounds, 355 and further on gas-to-particle partitioning of the compounds, which is the key when the SOA formation is investigated. Recently, it has been shown that SOA formation has a clear effect on both direct and indirect radiative forcing, highlighting the atmospheric relevance of our study.
Data availability. The research data have been deposited in a reliable public data repository (the CERN Zenodo service) and can be accessed at https://doi.org/10.5281/zenodo.5499485 (Hyttinen et al., 2021a).

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Author contributions. SS, AV and TY designed the study, NH ran the COSMO-RS calculations, IP performed the experiments and wrote the experimental section, NH, IP and AN analyzed the data, NH, SS, AV and TY interpreted the results, NH wrote the manuscript with contribution from all coauthors.
Competing interests. The authors declare that they have no conflict of interest.