Atmospheric simulation chamber experiments of the oxidation of α-pinene, isoprene, and β-caryophyllene were performed at the Paul Scherrer Institute in an 8 m3 Teflon chamber (see Platt et al., 2013), operating at 18–23 ∘C and 58 %–65 % relative humidity (RH) (see Table 1 for an overview of the experiments). Gas-phase instruments included a quadrupole proton transfer reaction mass spectrometer (Q-PTR-MS; Ionicon), an ozone monitor (Thermo 49C), and a NOx monitor (Thermo 42C). Particle-phase instruments included a scanning mobility particle sizer (SMPS; TSI model 3938), a custom-built VTDMA, isothermal evaporation chambers coupled to a custom-built SMPS, and a FIGAERO-CIMS (Aerodyne). Clean air was supplied by a zero-air generator (AADCO) and was used to flush the chamber overnight following every experiment at 50 L min-1 with the chamber volume heated to 30 ∘C.

In the NO3 experiments, the chamber was humidified with milliQ water (resistivity > 18 MΩ cm) until it reached the desired humidity, then the VOC of choice (α-pinene – Sigma Aldrich, 99+ %; isoprene – Sigma Aldrich, 95+ %; or β-caryophyllene – Sigma Aldrich, 99+ %) was injected into the chamber, and finally N2O5 (sampling from the head space above solid N2O5, which was kept chilled in an ice bath) was injected in a short burst (∼ 5 s at ∼ 1 L min-1), and the chamber was stirred by injecting 100 L min-1 of air for 10 s. N2O5 was generated by reacting liquid NO2 with high concentrations (∼ 1 %) of O3 and collecting the N2O5 crystals in a dry ice acetone bath. In the O3 experiments, O3 was generated by photolysis of air. Similar to the NO3 experiments, the chamber was first humidified and then O3 and α-pinene with the desired levels were added to the chamber volumetrically.

To determine the initial N2O5 concentrations, the decay rates of the VOC precursors were modeled with the Master Chemical Mechanism (MCM) using a simple 0-D box model (F0AM; Wolfe et al., 2016). For the β-caryophyllene experiment, its concentration could not be monitored with the PTR-MS because its mass-to-charge ratio (m/z) of 204 Th is outside of the mass transmission range for quantitative measurements; thus we estimated the concentration from the average N2O5 concentrations in the other experiments.

The particle mass concentrations (in µg m-3) were derived from integrated number size distributions from the SMPS and their conversions to mass using an assumed organic aerosol density (1.19 g cm-3; Vaden et al., 2011). They were further corrected for wall losses using a uniform dynamic wall loss rate kwall for the whole size range. The wall loss rate (kwall) was calculated from the exponential decay of the total particle number concentration (cm-3) measured by the SMPS, corrected for coagulation. The particulate wall loss is defined by 1dNdt=-kcoag.N2-kwallN, where N is the particle number concentration and kcoag. corresponds to the coagulation coefficient (5 × 10-10 s-1; Pospisilova et al., 2020). The wall-loss-corrected particle mass was divided by the uncorrected mass to obtain a wall loss correction factor for correction of the signals from the FIGAERO-CIMS.

We assessed the SOA volatility using three methods: (1) a VTDMA (Sect. 2.2.1), (2) an isothermal evaporation chamber (Sect. 2.2.2), and (3) a FIGAERO-CIMS (Sect. 2.2.4). From the first two methods, we observed reduced particle diameters due to heating and dilution, respectively, and calculated the volume fraction remaining (VFR) (see Sect. 2.2.3). With the FIGAERO-CIMS, we obtained thermal desorption profiles of individual compounds as well as the bulk sample. In addition, we also estimated the volatility based on the chemical composition measured by the FIGAERO-CIMS and modeled the temperature- and time-dependent VFR using a kinetic evaporation model (Sect. 2.2.5) for comparison with the VTDMA and the isothermal evaporation chamber, respectively.

An overview of the initial precursor and oxidant concentrations is presented in Table 1, together with the resulting maximal mass load in the particle phase. Prompt particle formation, due to rapid reaction with NO3 or O3, followed by steady particle mass decay due to evaporation, was observed for all three precursors. For the NO3 experiments, the initial particle composition followed primarily from the reactions between peroxy radicals (RO2–RO2) and between RO2 and NO3, resulting in a substantial fraction of oligomers with the dimer-to-monomer ratio increasing with decreasing precursor carbon number (Bates et al., 2022; Bell et al., 2022; C. Wu et al., 2021). According to the FIGAERO-CIMS, the mass fractions of oligomers were 86 %–88 %, ∼ 100 %, and 60 %–63 % for the α-pinene, isoprene, and β-caryophyllene SOA, respectively. Compared to the nitrate systems, the oligomer mass fraction for α-pinene + O3 was lower and in the range of 45 %–60 %. The aerosol particles formed from nitrate oxidation of α-pinene and isoprene were dominated by oligomers with two and three to four nitrate groups, respectively. The β-caryophyllene SOA was dominated by both monomers with one to two nitrate groups and dimers with two to three nitrate groups (C. Wu et al., 2021). The wall-loss-corrected maximum mass concentrations formed were 23–47 µg m-3 for α-pinene + O3, 8–53 µg m-3 for α-pinene + NO3, 9–24 µg m-3 for isoprene + NO3, and 60–464 µg m-3 for β-caryophyllene + NO3. The corresponding SOA yields of 10 %–17 % (α-pinene + O3), 3 %–10 % (α-pinene + NO3), 3 %–9 % (isoprene + NO3), and 111 %–144 % (β-caryophyllene + NO3) are generally in line with the literature (Berkemeier et al., 2020; Ng et al., 2017; R. Wu et al., 2021).

Figure 1 presents the experimental data on the evaporation of α-pinene SOA from oxidation with O3 and NO3, measured as temperature-dependent VFR in the VTDMA (Fig. 1a), time-dependent VFR in the isothermal evaporation chamber (Fig. 1b), and temperature-dependent normalized signal (thermograms) during heating rounds from the FIGAERO-CIMS (Fig. 1c). The VTDMA plots (Fig. 1a) show that particles formed through nitrate oxidation consistently display a lower VRF at given temperatures than the particles from ozonolysis, and hence they have higher bulk volatility. We also compared the VFR data from the α-pinene ozonolysis experiments to available literature data (see, e.g., Tritscher et al., 2011, and references therein) in Fig. S1. The comparison shows general agreement with the previous measurements, with some variation arising from the different experimental conditions such as the residence time within the TD, which ranges from < 1 up to 31.6 s in the data sets included in Fig. S1. With the residence time of 1.9 s, our measurements are at the short end of the range, with correspondingly higher VFR to be expected. The lower VFRs during isothermal evaporation for NO3 oxidation as compared with ozonolysis agree with the VTDMA data, indicating that nitrate oxidation of α-pinene SOA produces more volatile compounds (Fig. 1b). The FIGAERO-CIMS average thermogram also reveals lower maximum desorption temperature, indicating higher bulk volatility for α-pinene + NO3 than for α-pinene ozonolysis (Fig. 1c). The three methods are therefore overall consistent in this regard. The time-dependent VFR for nitrate SOA with different loadings in the isothermal evaporation exhibits a tendency for lower VFR for higher initial mass loadings. This may be related to, e.g., variation in the volatility distributions depending on the precursor and oxidant loadings. However, no significant dependence of the evaporation on the mass loading was observed for the VTDMA results (see Fig. S2).

Figure 2 presents the volatility data from the VTDMA, isothermal evaporation chamber, and FIGAERO-CIMS for the nitrate oxidation of isoprene (Fig. 2a–c) and β-caryophyllene (Fig. 2d–f) in comparison with α-pinene. The isoprene + NO3 SOA has similar bulk volatility as the α-pinene + NO3 SOA. Both the temperature ramp in the VTDMA and residence time in the isothermal evaporation chamber result in slightly higher VFR and hence somewhat lower volatility than for the corresponding SOA from α-pinene oxidation. The effect is not as clear in the FIGAERO-CIMS thermogram, where the peak of the bulk thermogram is observed at slightly lower temperatures than for α-pinene, although with a prominent shoulder at higher temperatures. The temperature-dependent VFRs for the β-caryophyllene system are even higher, and in the isothermal chamber no significant evaporation could be observed. In the FIGAERO-CIMS analysis, the β-caryophyllene data display a bimodal thermogram with one peak (from monomers) at the same temperature as α-pinene, while the dominant peak (from dimers) is located at higher temperatures, in agreement with the higher measured VFRs.

The volatility distributions in the form of VBS resulting from the parameterizations by Mohr et al. (2019), modified Daumit et al. (2013), modified Li et al. (2016), and Peräkylä et al. (2020) (hereafter referred to as MHR, DMT, Li, and PRK, respectively) are presented in Fig. 3 for all the studied chemical systems, including α-pinene ozonolysis. PRK produces the highest volatilities, followed by Li, with MHR resulting in the least volatile compounds for all nitrate systems and DMT resulting in the least volatile compounds for the α-pinene ozonolysis system. The volatility distributions from MHR, DMT, and Li tend to contain a wider range of C* values, while the volatility distributions by PRK are narrower and generally unimodal; the same trend can be observed for all the four systems.

The MHR parameterization predicts the presence of extremely low volatilities for a major part of the nitrate oxidation products of all three different precursors, with β-caryophyllene (Fig. 3d) producing the least volatile compounds, which is qualitatively in line with the observed VFRs (see Fig. 2). For α-pinene and isoprene, MHR predicts the majority of the compounds to fall into the volatility bins located below log10(C*) ∼ -6 and -5, respectively. For β-caryophyllene, MHR predicts two main classes of volatilities: one below log10(C*) ∼ -10 (oligomers) and another, broader peak around log10(C*) ∼ -5.5 (monomers). Comparing the nitrate system with the ozonolysis system, MHR predicts that α-pinene nitrate (Fig. 3b) SOA has lower volatility than α-pinene ozonolysis SOA (Fig. 3a). This result is in contrast with the direct volatility measurements displaying lower VFR, indicating higher volatility, for nitrate oxidation compared to α-pinene ozonolysis (see Fig. 1a). All in all, the MHR parameterization predicts ELVOCs to dominate the composition of the SOA from nitrate oxidation of BVOCs.

The DMT parameterization also predicts a broad range of volatility, similar to MHR. It predicts more ELVOC for the ozonolysis system, with a mean log10(C*) of -5.2, which is lower than the mean log10(C*) of -4.2 by MHR. However, for all nitrate systems, it predicts significantly less ELVOC than MHR, and the mean log10(C*) is also higher than that by MHR.

The other two parameterizations yield narrower distributions that are generally shifted towards higher volatility. PRK results in higher volatilities than Li for all three precursors, with the majority of the species being in the LVOC and SVOC range. With the Li parameterization, the isoprene nitrate products are more volatile than the α-pinene nitrate products, with isoprene peaking around log10(C*) ∼ 0.5 compared to log10(C*) ∼ -2.5 for α-pinene. For the SOA from β-caryophyllene, Li also produces a bimodal distribution, overlapping both the MHR and PRK distributions. The least volatile peak for Li overlaps the most volatile peak in the MHR distribution, at log10(C*) ∼ -7.5, while the more volatile peak appears at log10(C*) ∼ -0.5, instead overlapping with the whole distribution by PRK for β-caryophyllene. Finally, with the PRK parameterization, the VBS distributions of all systems are similar and in a narrow range between -3 to 1, which suggests that this parameterization is the least sensitive. Although the differences in the VBS for the α-pinene nitrate and ozonolysis system are smaller using these two parameterizations, they still predict lower-volatility products of the nitrate system compared to the α-pinene ozonolysis SOA, which is in contrast with the observations. Clearly, the four parameterizations yield different volatility distributions, which are not always in line with the measured evaporation described in Sect. 3.2.

In order to better compare the volatility derived from the chemical composition to the evaporation observed in the VTDMA and isothermal evaporation chamber, the volatility distributions derived from the four investigated parameterizations (Sect. 3.3, Fig. 3) were entered into a kinetic model describing the mass transport to and from the aerosol surface (Riipinen et al., 2010, Sect. 2.2.5). The model results are compared to the experiments in Fig. 4.

The calculated evaporation of SOA from α-pinene ozonolysis in the VTDMA (Fig. 4a) using MHR and DMT reproduces the evaporation well, while the other two parameterizations, Li and PRK, result in lower VFR compared to the measurements. The overall performance is comparable for the isothermal evaporation data (Fig. 4e): i.e., MHR reproduces the evaporation best, while Li and PRK underestimate VFR; however, DMT overestimates the evaporation over time. The α-pinene ozonolysis data set was used to demonstrate the sensitivity of the model to the key input parameters (see Table S1). In this regard, we tested the values of 0.1 and 0.01 for the accommodation coefficient (see, e.g., Riipinen et al., 2010), a fixed value of 70 kJ mol-1 for the vaporization enthalpy (see, e.g., Hong et al., 2017), as well as the effect of estimating the diffusion coefficient based on the molecular composition, which was now directly available from the FIGAERO-CIMS data (see Eq. 13). The results are presented in Fig. S3. While modifying the accommodation coefficient or the vaporization enthalpy can bring the other parameterizations somewhat closer to the observations, it is clear that the MHR parameterization captures the evaporation of this system exceptionally well with the base case assumptions in the model. Including a detailed description of the diffusion coefficient based on the molecular structure had no significant effect on the output of the data for any of the volatility parameterizations.

For the nitrate systems, MHR, in contrast to its good performance for the ozonolysis system, results in too high VFR compared to what is measured with the VTDMA (Fig. 4b, c, and d) and the isothermal evaporation chamber (Fig. 4f and g). PRK, which results in highest volatility (Fig. 3), underestimates the VFR for all cases. The VFR estimates using Li and DMT fall in between. DMT tends to overestimate, and Li tends to underestimate the VFR with the VTDMA (Fig. 4b, e, and d). We simulated the VFR using averaged Li and DMT values in Fig. S7 and it works well for the α-pinene and isoprene systems but not the β-caryophyllene system. For simulating the VFR with the isothermal evaporation chamber, their performance is different and depends on individual systems: DMT and Li both overestimate the VFR for the α-pinene system, DMT overestimates the VFR and Li underestimates the VFR for the isoprene system, and both underestimate the VFR for the β-caryophyllene system.

Based on these results, no parameterization can be deemed to be systematically the best for reproducing both the VTDMA and the isothermal evaporation chamber data. This is understandable, since these experimental techniques are sensitive to different volatility ranges given the different operating temperatures. Combining these results with the volatility distributions (Fig. 4) suggests that the material contributing to the VFRs from the VTDMA setup consists of species with volatilities at the low end of the spectrum (log10(C*) values of about -5 and lower), while the species that remain in the particle phase in the isothermal evaporation chamber seem to have log10(C*) values below about -2. This is especially clear for the isoprene simulations, with both the TD and isothermal evaporation simulations being very sensitive in the volatility range between log10(C*) ∼ -5 to -2 (see Figs. 3 and 4).

It is worth noting that with the FIGAERO-CIMS, subtraction of the thermal decomposition compounds may also induce uncertainties. Thermal fragmentation contributed 5 %–27 %, 1 %–4 %, and 10 %–23 % of the total organic signal of the isoprene, α-pinene, and β-caryophyllene nitrate SOA, respectively, and 3 %–13 % for α-pinene ozonolysis SOA. Since thermal decomposition due to dehydration or decarboxylation reactions normally occurs at temperatures higher than 120 ∘C (Buchholz et al., 2020; Stark et al., 2017) and the parent compounds of the decomposing molecules have an even higher thermal desorption temperature, we can conclude that the compounds we remove are of very low volatility. Unfortunately, their volatility could not be identified with the parameterization based on the formula of the thermal decomposition compounds, as they are much smaller than the parent compounds and thus have much higher volatilities. We subtracted these compounds for the further calculation of the bulk volatility and the simulation of evaporation, but we also note that it may lead to decreases in the simulated VFR in the higher temperature range (> 120 ∘C) in the VTDMA; thus it could be a potential reason for the discrepancies between the calculated VFR and the measured VFR with the VTDMA. In addition, as α-pinene nitrate SOA exhibits much less thermal fragmentation compared to isoprene and β-caryophyllene, it could also explain partly the different performance of parameterization in simulating the evaporation in the VTDMA in different systems.

Taken together, the results from Fig. 4 suggest that the volatility reduction by the nitrate group is considerably overestimated by the MHR parameterization, while PRK tends to systematically overestimate the volatility of the studied systems in the TD and isothermal evaporation setups. This is generally in line with previous findings, particularly the conclusion by R. Wu et al. (2021) for the isoprene + NO3 system, who find that the MHR parameterization gives clearly lower volatilities than that estimated by other parameterizations, e.g., SIMPOL (Pankow and Asher, 2008) and PRK, as well as that obtained by experimental approaches. Furthermore, these results show a substantial contribution of species in the LVOC range in the SOA from both α-pinene + NO3 and isoprene + NO3, and probably the presence of SVOCs, which show considerable evaporation even at room temperature (since the isothermal evaporation is mainly sensitive in this range, as described above). The SOA from β-caryophyllene + NO3 on the other hand seems to consist primarily of species in the ELVOC and LVOC range. Our data present overall lower volatilities of SOA formed from α-pinene + NO3 and isoprene + NO3 compared with the few other existing studies (Berkemeier et al., 2020; Boyd et al., 2015; Ng et al., 2017; R. Wu et al., 2021), while for the β-caryophyllene + NO3 system, no previous data exist. When interpreting these comparisons, however, one should be aware of the somewhat different experimental conditions in the existing studies, remembering, e.g., the fact that our experiments show a substantial contribution from oligomers.

The MHR and Li parameterizations are of similar mathematical form, with the exception that the former subtracts the oxygen atoms from the nitrate groups in the carbon–oxygen non-ideality, while the latter includes all oxygen atoms in the carbon–oxygen non-ideality. In MHR, a nitrate group reduces the saturation vapor pressure of a compound by 2.5 orders of magnitude, instead of 0.7732 orders of magnitude in Li (which is similar to a hydroxyl group). The difference is due to the different training data sets used to create the parameterizations. The MHR and DMT parameterizations are similar in the bN values but different in the way they treat other functional groups containing oxygen atoms. DMT assumes all oxygen atoms except those from -NO3 are from -OH and =O functional groups, while MHR was tuned for -OOH functional groups, and the bO (= 0.2) is much smaller than b-OH (= -2.23) and b=O (= -0.935) in DMT. As MHR works better for the α-pinene + O3 system and DMT works better for the α-pinene + NO3 system, it is possible that the α-pinene + O3 system has more -OOH and the α-pinene + NO3 system has more -OH and =O. However, it is worth noting that, with the assumption in DMT, the level of unsaturation (DBE) arises from carbonyl and nitrate groups. Ring structures (which are highly possible in many α-pinene and β-caryophyllene oxidation products) are treated as the former. This could lead to underestimation of the volatility. The PRK parameterization, on the other hand, is based on experimental methods, specifically on HOMs from α-pinene ozonolysis, and displays a simple dependence on the individual atoms instead of specific functional groups (like the nitrate group). With this in mind, it is not surprising that PRK best captures α-pinene. Finally, the uncertainty of the effect of nitrogen groups on the saturation vapor pressures of organic species is also to be expected, given the lack of quantitative experimental data to use to train the parameterizations (see, e.g., Pankow and Asher, 2008).

Therefore, we investigated the effect of modifying the parameter bN in steps for MHR, DMT, and Li for better reproducing the observations (see Table 2 and Fig. 5). When applying the MHR parameterization, the nitrate-induced reduction in saturation vapor pressure needed to be substantially reduced for all three systems to get predictions closer to the observations. For the isoprene system, bN values between 1.0 and 1.5 provided the best fit to the observations (Fig. 5b), still however indicating a saturation vapor pressure reducing effect of the nitrate group. For the α-pinene and β-caryophyllene systems, however, the bN values needed to be reduced to negative values (from -0.75 to -0.5) to fit the observations (Fig. 5a, c). The negative values would indicate that the nitrate group would increase the volatility. With DMT, a reduction of bN from 2.23 (original) to 1–1.5 would lead a better simulation for the α-pinene and isoprene systems. For the β-caryophyllene system, the original value did the best job. In the case of Li, the original value of bN= 0.7732 already performed exceptionally well for the nitrate oxidation of α-pinene, and hence no adjustment was warranted here (Fig. 5g). For isoprene and β-caryophyllene, the saturation vapor pressure reduction by the nitrate group needed to be increased to 1.8–2.8 orders of magnitude, indicating similar nitrate influence as previously estimated by Pankow and Asher (2008). Since none of the bN values were able to reproduce the data from different precursors for MHR, DMT, or Li, it is clear that simply adjusting the bN value would not resolve the discrepancy we observed between the measured and simulated VFR based on the chemical composition. The logC* is closely related to the other interaction terms, e.g., the carbon–carbon interaction term and the carbon–oxygen non-ideality. This finding indicates complexity of the interactions between different functional groups and warrants further and more detailed studies on nitrate-containing systems.