The data presented here was measured in two campaigns in 2019 (SOA19b) and 2021 (SOA21a) covering 213–313 K in the Aerosol Interaction and Dynamics in the Atmosphere (AIDA) aerosol and cloud simulation chamber at the Karlsruhe Institute of Technology (KIT). The chamber is an 84.5 m³ aluminium vessel equipped with a LED solar radiation simulator and with precisely controlled temperature, humidity, and gas mixtures. A fan allows all components to be mixed well within 90 s (Saathoff et al., 2009). Details about the AIDA chamber are given by previous studies (Möhler et al., 2003; Vallon et al., 2022; Wagner et al., 2006).

Two types of SOA were generated in batch mode from dark oxidation of: (1) sole α-pinene at 273 K (SOA_ap-273), (2) isoprene mixed with α-pinene at 213, 243, 273, 298, and 313 K (SOA_213 K, SOA_243 K, SOA_273 K, SOA_298 K, SOA_313 K), respectively. The experimental conditions are summarized in Table 1. Well defined amounts of isoprene and α-pinene were added to the AIDA chamber with a flow of 10 L min⁻¹ of synthetic air. Ozone was injected subsequently after the biogenic VOC were mixed well inside the chamber, followed by the continuous addition of tetramethyl ethylene (TME) generating OH radicals by its reaction with ozone. The OH concentrations were (0.8–1.5) × 10⁷ molecules cm⁻³ in all experiments. The initial concentration ratios of isoprene to α-pinene were kept at 1.0±0.1 for all two-precursor experiments, while the ratios of O₃ to α-pinene were 14±3 among all experiments with the exception of Exp 1 at 213 K (O₃: α-pinene = 38). At 213 K, the initial concentrations of isoprene and α-pinene of 6.7 ppb led to a relatively small amount of SOA mass. To generate sufficient SOA mass for the longer warming experiment we generated more SOA mass in a second oxidation step with about twice the VOC concentrations of 13.5 ppb. We note that the two times of injections of precursors may have impact on the chemical regimes during the SOA formation at 213 K compared to other experiments. Seed particles and OH scavengers were not used in this work. Additionally, to investigate the cross-dimers formed from the oxidation of α-pinene and isoprene, we used ¹³C-labelled isoprene (> 98 %, Merck) in Experiments 6 and 7 (Table 1). This isotopic labelling enabled us to identify products with a shift of one nominal mass-to-charge unit (i.e., m/z+1), which unambiguously marks those dimers containing one skeleton from the labelled isoprene.

The initial reaction lasted 90 min, then the VOC precursors were depleted. The subsequent course of the experiment consisted of one hour of photochemical aging by illumination and then 14 h of warming the entire chamber at a constant rate. The increment of temperature before and after warming is shown in Table 1. To evaluate the effect of dilution, we injected CO₂ which is a chemistry bystander before warming. The loss of CO₂ was less than 4 % for all experiments after 14 h of warming. Therefore, the dilution effect is neglectable.

The concentrations of VOC and semi-volatile organic particles were measured by a Proton-Transfer-Reaction-Time-of-Flight-Mass-Spectrometer coupled with a Chemical Analysis of Aerosol Online (CHARON-PTR-ToF-MS, Ionicon Analytik GmbH) particle inlet.

Bulk SOA was online detected by a high-resolution time-of-flight Aerosol Mass Spectrometer (HR-AMS, Aerodyne Inc.), while the particle-phase chemical composition of SOA at molecular level was detected by a chemical ionization mass spectrometer (CIMS) coupled with a filter inlet for gas and aerosols (FIGAERO) using iodide (I⁻) as reagent ions with 1 Hz time resolution (Lopez-Hilfiker et al., 2014; Lee et al., 2014). The CIMS data presented in this work stems from offline analysis. The filter samples were analyzed using a FIGAERO-iodide-CIMS. We also note that the sensitivity of FIGAERO-iodide-CIMS is highly dependent on the functionalities of the organic compounds and can vary by orders of magnitudes (Lopez-Hilfiker et al., 2016; Lee et al., 2014; Riva et al., 2019). Therefore, the results shown in this work are based on signal intensities but not mass concentrations. The detailed description of instruments, filter sample collection, and data analysis are described in Sect. S1 and Fig. S1 in the Supplement.

O₃ was detected by a gas monitor (O₃41M, Environment SA). Particle size distributions and number concentrations were measured by a scanning mobility particle sizer (SMPS) utilizing a differential mobility analyzer (DMA, 3071 TSI Inc.) connected to a condensation particle counter (CPC, 3772, TSI Inc.). The total particle number concentrations were monitored by two condensation particle counters (CPC, 3776 and 3022A, TSI Inc.).

Typically, background measurements for both gas and particle phase are done before and after the addition of VOC to identify any contaminations inside the chamber. Gas background confirms that there were no significant gas-phase contaminations for all the experiments. Most of the particle background signals were coming from filter matrix contaminations mainly due to fluorinated constituents of low relevance. Please note that the background in all experiments was measured in the same way as described previously (Gao et al., 2022).

The large number of organic compounds detected in the particle phase are presented in a one-dimensional volatility basis set (1D-VBS) (Donahue et al., 2006), based on the effective saturation concentration (Csat, µg m⁻³). In this work, 298 K Csat (Csat,298K, µg m⁻³) values of individual compounds are determined according to their measured elemental formulas applying a parameterization using molecular corridors (Li et al., 2016). The saturation concentration of species at other temperatures (Csat,T, µg m⁻³) can be derived from Csat,298K according to the Clausius-Clapeyron relation: 1Csat,T=Csat,298KexpΔHvapR1298-1T where T is the experimental temperature in K; ΔHvap is the evaporation enthalpy in kJ mol⁻¹, which can be estimated based on Csat,298K by Stark et al. (2017) 2ΔHvap=-5.7×log⁡10Csat,298K+129 In the volatility basis set, we use the following volatility classes: ultra-low VOC (ULVOC, log10Csat<-8.5), extremely low VOC (ELVOC, -8.5<log⁡10Csat<-4.5), low VOC (LVOC, -4.5<log⁡10Csat<-0.5), semi VOC (SVOC, -0.5<log⁡10Csat<2.5), intermediate VOC (IVOC, 2.5<log⁡10Csat<6.5), and VOC (log10Csat>6.5).Based on the same dataset as the volatility prediction, the glass transition temperature (Tg) of CHO compounds is estimated by the parameterization method expressed by the Eq. (3) (DeRieux et al., 2018): 3Tg=nC0+ln⁡nCbC+ln⁡nHbH+ln⁡nCln⁡nHbCH+ln⁡nObO+ln⁡nCln⁡nObCO where nC, nH, nO are the number of molecular C, H, O atoms, respectively; nC0 is the reference carbon number; bC, bH and bO refers to the contribution of each atom to Tg; and bCH and bCO are coefficients reflecting contributions from carbon–hydrogen and carbon–oxygen bonds, respectively. The values of all parameters used can be found in the published paper (DeRieux et al., 2018).

The simulation chamber results are implemented to PMCAMx (Murphy and Pandis, 2009), a chemical transport model (CTM) which utilizes the SOA volatility bases set approach (Lane et al., 2008) to simulate the formation of secondary aerosol from biogenic and anthropogenic VOCs. A brief description of PMCAMx is provided in Sect. S2 of the Supplement. The model-incorporated stoichiometric yields are based on the molecular composition of the particles measured by FIGARO-CIMS. The volatility of the produced aerosol is determined following the approach described in Sect. 2.3, however, to minimize the computational cost the species are re-distributed to four VBS bins (10⁰, 10¹, 10², 10³ µg m⁻³) rather than using the whole volatility range. The stoichiometric yields of both isoprene and α-pinene are temperature dependent based on the parameterization of Exp 1–5. Specifically: T<243 K, parameters based on Exp 1 (213 K); 243 K ≤ T<273 K, parameters from Exp 2 (243 K); 273 K ≤T<298 K, parameters from Exp 3 (273 K); 298 K ≤ T<313 K, parameters from Exp 4 (298 K); T≥313 K, parameters from Exp 5 (313 K). For the partitioning of the secondary organic species between the gas and the aerosol phase, PMCAMx assumes that there is equilibrium between the two phases and that the organic compounds form a pseudo-ideal solution. Specifically, in the model the partitioning of the organics between the gas and the aerosol phase depends on two parameters, the temperature and the total OA concentration of the simulated cell. Therefore, the model can replicate the concentration changes that occur in the atmosphere due to both warming and cooling. Utilizing the experimental data after warming rather than before warming commenced inside the chamber would result in the same predicted SOA concentrations by PMCAMx. Nevertheless, the warming stage of the experiments is better represented in the model by adopting the mass-stoichiometric yields derived from the initial temperatures. Values for the Base and New cases are provided in Table S1 and S2 in the Supplement. Utilizing the stoichiometric yields of Table S2, Fig. S2 depicts the secondary organic aerosol mass fraction derived as a function of the total organic aerosol mass together with the experimentally measured values.

The period considered in this model application is 5 June–8 July 2012 (PEGASOS campaign) in a European domain (5400×5832 km², Figs. S3 and S4) with 36×36 km grid resolution, and 14 vertical layers extending up to 7.5 km above ground. The temperature together with other metrological parameters are provided by the Weather Research and Forecasting meteorological model (WRF). Biogenic emissions are calculated by the MEGAN model (Guenther et al., 2006), while anthropogenic and wildfire emissions are based on the GEMS (Visschedijk et al., 2007) and IS4FIRES (Sofiev et al., 2008) inventories, respectively. In our application, the domain average concentrations of isoprene and terpene in the simulated European domain are 0.15 and 0.04 ppb, respectively, with maximum predicted values of 2.8 and 0.5 ppb. The spatial distributions of their average ground-level concentrations over Europe are showed in Fig. S3.

In each experiment, the molecular composition of fresh SOA particles was characterized by FIGAERO-iodide-CIMS using iodide as the reagent ion. The evolution of trace gases as well as particle mass and size distribution for the oxidation of isoprene α-pinene mixture at all temperatures are shown in Fig. 1. The beginning of the ozone addition is considered time zero for each experiment. The addition of ozone and the subsequent production of OH radicals, resulted in the complete depletion of the initial α-pinene and isoprene. The SOA particle diameters increased typically to 65–100 nm and the mass concentrations of the newly formed SOA ranged between 33–133 µg m⁻³ (mass yield: 9 %–52 %) depending on temperature. Subsequently, the fresh SOA was exposed to simulated solar radiation for 1 h. This photochemical aging resulted in no significant chemical change (cf. Fig. S9). This aging age was followed by 10–12 h of warming, which will be discussed in Sect. 3.2.

We present first the identified cross dimers formed from concurrent oxidation of isoprene and α-pinene (hereafter “ISO-AP dimers”) at 273 K. By comparison of the particle-phase chemical composition among the experiment for sole α-pinene (Exp 0), α-pinene and isoprene mixture at an equal concentration (Exp 3), and α-pinene and ¹³C labelled isoprene mixture at an equal concentration (Exp 6) shown in Table 1, we identified ISO-AP dimers such as C₁₅H₂₀O_3–7, C₁₅H₂₂O_3–9, C₁₅H₂₄O_4–9, C₁₅H₂₆O_5–9, C₁₅H₂₈O_5–9, C₁₄H₂₀O_6–8, C₁₄H₂₂O_5–9, and C₁₄H₂₄O_6–8. The identification of these cross dimers with 3–9 oxygen atoms completes the list of highly oxygenated cross dimers with 9–13 oxygen atoms, which were previously identified by a CIMS using nitrate as the regent ion (McFiggans et al., 2019; Heinritzi et al., 2020). Among all identified ISO-AP C_14–15 cross dimers in Exp 3, C₁₅H₂₄O_4–9 and C₁₄H₂₂O_5–9 contribute most to the total signals (21 %), followed by C₁₅H₂₆O_5–9, C₁₅H₂₈O_5–9, and C₁₅H₂₂O_3–9 with signal fractions of 16 %, 11 %, and 11 %, respectively. The relative abundances of these cross dimers in Exp 0 and Exp 6 are given in Figs. S5–S6. Due to the scavenging of OH and RO₂ radicals in the presence of isoprene, the relative contribution of solely α-pinene derived C₁₈₋₂₀ dimers from ozonolysis increases, while the contribution of dimers formed via OH radical reactions decrease (Fig. S7). This is qualitatively consistent with previous studies (McFiggans et al., 2019; Heinritzi et al., 2020; Wang et al., 2021) performed at ∼298 K.

As shown in Fig. 2, particle-phase C_14–15 ISO-AP cross dimers show higher signal fractions at lower temperatures (in all detected compounds, 16 % and 11 % in total for 213 and 243 K, respectively) compared to those formed at higher temperatures (<4 % for 273, 298, and 313 K). For the dimers formed from α-pinene oxidation alone (C_18–20, hereafter “AP-AP dimers”), including those from self- (i.e., both RO₂ involved in the dimerization originate either from O₃ oxidation or from OH oxidation.) and cross-dimerization (i.e., between the two RO₂ radicals involved in the dimerization, one originates from O₃ oxidation, while the other originates from OH oxidation) of RO₂ derived from α-pinene oxidation initiated by both O₃ and OH radicals, lower temperatures exhibit slightly higher fractions with 8 %–9 % at 213–243 K compared to 4 %–6 % at 273–313 K, consistent with previous observations (Zhang et al., 2015). Most interestingly, the ratio of ISO-AP dimers to AP-AP dimers is 3.5 times higher at 213 K (the ratio is 2) than that at 273–313 K (the ratios are 0.6, Fig. 2f). This indicates that the production of ISO-AP dimers plays a progressively more important role in SOA formation at lower temperatures. Shown as Figs. 2g and 1h, the higher ratio of ISO-AP dimers to AP-AP dimers at 213 K than 313 K is mainly contributed by the greater formation of C_14–15 compounds. The volatility (expressed by the saturation concentration at 298 K, C298K*) of ISO-AP dimers (C298K*: 10^−3.6–10^2.2 µg m⁻³) is generally higher than that of AP-AP dimers (C298K∗: 10^−4.8–10^0.6 µg m⁻³), indicating that ISO-AP dimers are more volatile than AP-AP dimers when formed at the same low temperatures. The difference in volatility between both groups of dimers is also shown by their desorption temperature of maximum signal in the FIGAERO thermograms (hereafter “Tmax”) (Lopez-Hilfiker et al., 2014), which is an independent and qualitative indicator of effective volatility compared to the volatility estimated by the parameterization approach (Li et al., 2016) used in this work (Sect. S3, Fig. S8).

Figure 3 shows the comparison of the particle volatility distribution at different temperatures. This comparison integrates two approaches: gas- and particle-phase measurements at each temperature (i.e., C*=COAGiPi (Gkatzelis et al., 2018)) and the Clausius–Clapeyron equation. C_14–15 dimers span in the less volatile bins from Clausius-Clapeyron equation at temperatures below 273 K, exhibiting a strong temperature dependence, compared with the volatility based on the measured organic mass. This dependence is suggested to be chemistry-driven rather than governed solely by phase partitioning. We interpret this as follows. First, the gas-phase production rates of the two types of dimers may be temperature dependent due to the temperature-affected concentrations of RO₂ radicals. The gas-phase dimer formation rate via the bimolecular termination of RO2+ R^′O2→ ROOR^′ rises strongly with temperature (Quéléver et al., 2019). At lower temperatures, the lower rate coefficient of α-pinene + O₃ (Khamaganov and Hites, 2001; Bernard et al., 2012) and higher rate coefficient of isoprene + OH (Campuzano-Jost et al., 2000; Campuzano-Jost et al., 2004; Dillon et al., 2017) lead to higher differential between the concentrations of C₁₀ RO₂ from α-pinene and C₅ RO₂ from isoprene. Therefore, at lower temperatures, higher [C₅ RO₂][C₁₀ RO₂] results in larger production of ISO-AP dimers compared with less formation of C₂₀ AP-AP dimers due to lower [C₁₀ RO₂][C₁₀ RO₂]. Besides, the other well-established dimer formation pathway for α-pinene derived dimers, condensed-phase combination of acetyl peroxy radicals yielding diacyl peroxides and their subsequent decomposition (Zhang et al., 2015) to produce esters, carboxylic acids, and alcohols, is affected by temperature as well (Leffler and More, 1972; Lamb et al., 1965). Our observation suggests that the formation of ISO-AP dimers via the diacyl peroxides pathway may be faster than that of AP-AP dimers at lower temperatures. Second, previous studies (Trump and Donahue, 2014; Morino et al., 2020) have shown that the decomposition rates of dimers depend on temperature and the type of dimers. Therefore, we cannot exclude that AP-AP dimers decompose faster than ISO-AP dimers at lower temperature, leading to higher condensed-phase ratios of C₁₄₋₁₅ / C₁₈₋₂₀.

It should be noted that the sensitivity of iodide chemical ionization exhibits substantial variability in detecting organic compounds with different functional groups. As a result, signal-based analyses may not accurately represent the actual abundances of these species. Nevertheless, comparing signal fractions across different experiments can provide valuable insights into product distributions and underlying reaction mechanisms.

Overall, the nonmonotonic temperature dependence (Fig. 2f) of the ratio of C_14–15 to C_18–20 dimers between 213–313 K highlights the importance of the AP-AP dimer suppression by the ISO-AP cross dimers. This is particularly relevant for biogenic particle formation and growth in the real atmosphere especially at lower temperatures (Fu et al., 2009; Andreae et al., 2018).

To study the influence of temperature change on SOA formed at a specific temperature, we warmed the fresh SOA particles up by 1.4–2.4 K h⁻¹ over 10–12 h, which resembles the ambient temperature changing rate (∼0.1–2 K h⁻¹) in the real atmosphere (Hansen et al., 2006). The illumination has no significant effect on the bulk O : C, H : C and OS_C (Fig. S9). The molecular chemical composition and volatility of fresh particles before warming are described in the Sect. S3. Most interestingly, by warming, SOA particles formed initially at different temperatures showed distinct increments and/or decrements in bulk O : C and H : C ratios as well as oxidation states (OS_C) as measured by HR-AMS (Figs. 4, S10, and Table S3). It indicates these SOA particles underwent distinct aging processes including water uptake and evaporation when being warmed up.

We observed a clear increase of O : C ratios (from 0.36 to 0.54 from HR-AMS measurements, from 0.5 to 0.6 from FIGAERO-iodide-CIMS measurements) of fresh SOA particles formed between 243 and 313 K (Fig. 4). One exception is the particles formed at 213 K. The O : C ratio of the fresh SOA_213 K (0.45 from HR-AMS measurement, 0.55 from FIGAERO-iodide-CIMS measurement) is higher than that of SOA_243 K, contrary to the lower O : C ratios of particles formed at lower temperatures. This may result from the higher ratios of initial O₃ to VOCs concentrations (∼19) in Exp 1 at 213 K compared to other experiments (∼7) (details in Method).

According to the HR-AMS measurements, the bulk O : C and H : C ratios of SOA particles formed at 243 K (SOA_243 K) increases from 0.36 to 0.4 and from 1.69 to 1.82, respectively, during gradual warming to 273 K (SOA_{243→273 K}). Although the incremental O : C change is small, the online HR-AMS measurements showed a significant trend during the warming process (Fig. 4). The ratio (= 3.25) of the H : C increment and O : C increment in the Van-Krevelen diagram indicates hydration reactions during warming (Schilling Fahnestock et al., 2015; Heald et al., 2010). Correspondingly, the oxidation state (OS_C) of bulk SOA_243 K decreases from -0.97 to -1.02 for SOA_{243→273 K} (Fig. S10), while the organic particle mass decayed 17 % as measured by HR-AMS. According to the FIGAERO-iodide-CIMS measurements, 18 % fraction of the particle-phase C_xH_yO_z signals are lost during warming of SOA from 243 K (SOA_243 K) to 273 K (SOA_{243→273 K}) (Fig. 5d). The loss of oxygenated organic compounds mainly involves C₅, C_8–10, and C_14–15 compounds (Fig. 5h), which are identified as monomeric products from sole isoprene and sole α-pinene, and their ISO-AP dimers, respectively. However, the loss of these oxygenated organic compounds leads to no significant change in the H : C ratio (from 1.63 to 1.62) and O : C ratio (from 0.50 to 0.50) of the particle-phase C_xH_yO_z measured by FIGAERO-iodide-CIMS. Therefore, the increase in bulk O : C and H : C ratios of SOA measured by HR-AMS indicates not only hydration reactions (Schilling Fahnestock et al., 2015; Heald et al., 2010) but also potential losses of more oxidized compounds with low H : C ratios. The bulk SOA aging towards higher H : C and O : C ratios during warming is likely due not only to sample evaporation but also to the change in the particle phase state.

Similar changes of O : C and H : C ratios were observed for SOA_213 K warmed to SOA_{213→243 K}. Therefore, the SOA_213 K warmed to SOA_{213→243 K} seems to undergo similar aging processes like SOA_243 K being warmed to SOA_{243→273 K}.

We characterized the viscosity of SOA particles by using the glass transition temperature, Tg which is defined as the temperature at which an amorphous material transitions from a liquid-like or semi-solid state to a glassy solid state. As the ambient temperature approaches or drops below the Tg of a particle, its viscosity increases dramatically, often by several orders of magnitude. Therefore, the phase state and viscosity of SOA can be inferred by characterizing the Tg values. Tg was calculated for all detected organic compounds by FIGAERO-iodide-CIMS using a parameterization approach (DeRieux et al., 2018). In this study, SOA_243 K is estimated to be in a glassy solid state with a Tg of 289 K, comparable to the Tg values for sole isoprene- or α-pinene-derived SOA reported in previous studies (DeRieux et al., 2018; Ladino et al., 2014). We note that the Tg values may be underestimated, as the water content in the particles was not taken into account due to a lack of measurements. The high viscosity at low temperature kinetically inhibits the diffusion of water and large organic molecules within the particle. Upon warming, the particle transitions from a glassy to a semi-solid or liquid state, which facilitates the uptake and internal mixing of water. This process can promote aqueous-phase reactions (e.g., hydrolysis, oxidation) that alter the organic composition, increasing the H : C and O : C ratios. Therefore, water uptake and the potential change of particle hygroscopicity (Shiraiwa et al., 2017; Pajunoja et al., 2015; Shiraiwa et al., 2011) may contribute to increasing H : C and O : C ratios of bulk SOA_243 K during warming from 243 to 273 K.

In contrast, from the HR-AMS measurement, the bulk SOA_273 K loses 75 % of mass, and show a significant increase of OS_C (from -0.87 to -0.75) and O : C ratios (from 0.44 to 0.48) but a decrease of H : C ratios (from 1.76 to 1.73) during warming to 298 K (Fig. 4). This tendency is consistent with the changes of O : C ratios and H : C ratios for the oxygenated constitutes measured by FIGAERO-iodide-CIMS. During warming of SOA_273 K to 298 K, 72.5 % of all particle-phase C_xH_yO_z compounds are lost, with OS_C increasing from -0.52 to -0.41, O : C from 0.54 to 0.57, and H : C ratios decreasing from 1.60 to 1.55. This indicates that evaporation is the main loss process with higher losses of less oxidized compounds. This is consistent with the analysis of HR-AMS spectra before and after warming (Fig. S11) The Tg we estimated for SOA_273 K is 278 K, which is in between the temperatures of warming at the start (273 K) and at the end (298 K). Therefore, the diffusion and evaporation of organic molecules are gradually less hindered when particle phase state transits from solid/semi-solid to liquid.

For the bulk SOA_298 K, its estimated Tg is 283 K, which is evidently lower than the temperatures during warming from 298 to 313 K. This indicates that the SOA_298 K remain in the liquid phase during the whole warming process. As illustrated in Fig. 4, warming of all SOA compounds formed at 298 K leads to lower H : C (from 1.63 to 1.57) and O : C ratios (weekly from 0.53 to 0.52), resulting in slightly higher OS_C values (from -0.57 to -0.53). During warming from 298 to 313 K, 40.2 % of all particle-phase C_xH_yO_z compounds and 71 % of organic particle mass were lost, by substantial evaporation. However, the evaporation induces only small changes of O : C ratio from 0.60 (SOA_298 K) to 0.59 (SOA_{298→313 K}), H : C ratio from 1.51 to 1.49, and OS_C from -0.31 to -0.32 for oxygenated organics, even though the trend is clear as shown in Fig. 4. As the reduction in H : C ratio is around 2 times higher than the reduction in O : C ratio for bulk SOA_298 K particles during the warming to 313 K, we infer that there might be water evaporation due to the potential particle-phase dehydration reactions involving elimination of H₂O.

As illustrated in Fig. 5, before warming, volatility indicated by the Tmax of the fresh particles showed a non-monotonic trend. This is similar with previous findings in the β-caryophyllene system (Gao et al., 2023), which is due to favoured condensation or oligomerization reactions at lower temperature and less production of low volatile HOMs which show larger fractions at warmer temperatures. During warming, the volatility of the particles is influenced by changes in their chemical composition as the gas-particle equilibrium is re-established through phase partitioning. As the temperature increases, more volatile organic compounds evaporate from the particle phase. Consequently, the particle composition becomes enriched in the remaining lower-volatile organic species. This is corroborated by the higher Tmax values observed in the thermograms: SOA_{243→273 K} (78 °C) compared to SOA_243 K (68 °C), SOA_{273→298 K} (71 °C) compared to SOA_273 K (57 °C), and SOA_{298→313 K} (124 °C) compared to SOA_298 K (77 °C), as illustrated in Fig. 5b–d. The results indicate that the overall effect of warming on the SOA particle volatility is governed by the initial temperature-dependent chemical composition and the corresponding glass transition temperature.

Further support comes from the distribution of volatility groups estimated by the parameterization approach (Li et al., 2016) based on measured numbers of molecular carbon, hydrogen, and oxygen atoms. During warming, evaporation leads to compositional changes that enrich the relatively lower-volatility compounds. Concurrently, rising temperatures shift the entire VBS toward higher apparent volatility, following the Clausius-Clapeyron relation. For instance, despite the evaporation of some volatile components during warming from 243 to 273 K, the resulting SOA_{243→273 K} particles exhibit higher overall apparent volatility, containing only 35 % of LVOC/ELVOC/ULVOC (Figs. S12 and 6). Similarly, in the warming experiment from 273 to 298 K, the fraction of LVOC/ELVOC/ULVOC decreased slightly from 16 % to 15 %, and from 18 % to 14 % in the case of SOA_{298→313 K} compared to SOA_298 K. These results underscore the significant role of ambient temperature on the apparent volatility of SOA particles.

It should be noted that the FIGAERO-iodide-CIMS exhibits higher sensitivity toward moderate oxygenated compounds (e.g., 2–9 oxygen atoms) (Riva et al., 2019), which may introduce bias in the VBS. Nevertheless, comparisons of signal-weighted VBS distributions across different experimental conditions remain indicative of the effects of temperature and warming on particle volatility and the related chemical processes. Here, we note that the precursor concentrations used in this study are substantially higher than typical atmospheric levels. While such conditions are typical in chamber experiments to generate sufficient particle mass for instrument detection and > 10 h aging by warming, they may influence the underlying chemical processes. Specifically, elevated VOC and O₃ concentrations can enhance the rates of bimolecular reactions, potentially favoring radical–radical recombination, accelerating oligomer formation (Zhao et al., 2023), and increasing SOA yields relative to ambient conditions. These conditions may also shift the partitioning of semi-volatile species toward the particle phase. Consequently, the volatility distributions reported here likely represent an upper bound of reactivity and should be interpreted with caution when extrapolating to atmospheric conditions.

Please note, that other condensed-phase chemical reactions may play a role during warming process as well, e.g., dimers may decompose due to their chemical instability (Pospisilova et al., 2020; Surdu et al., 2024), and the formation and condensation of molecules such as peroxyhemiacetal and aldol has been found to be reversible and temperature-dependent. However, it requires further studies to address this question systematically.

Furthermore, the oxidation states (OS_C) of SOA particles after warming were lower than that of the particles formed directly at these temperatures. As mentioned above, increasing temperatures during warming facilitate the evaporation of more volatile compounds. This results in the organic components remaining in the particles being generally less volatile and higher oxidized corresponding to a higher oxidation state of bulk SOA as measured by the HR-AMS.

However, it cannot compensate for the composition difference (e.g., due to autoxidation (Bianchi et al., 2019)) between SOA_243 K and SOA_273 K caused by different reaction pathways and product distributions at the different formation temperatures. For example, the saturation concentrations of the same compounds in SOA_{243→273 K} and SOA_273 K systems are the same because they are both at 273 K. We compared the molecular chemical composition of SOA_{243→273 K} and SOA_273 K (Fig. S13c and g). The C_11–20 products make up a higher signal fraction in SOA_{243→273 K} (66 %) compared to the corresponding compound groups in the SOA_273 K (43 %), and vice versa for C_4–10 products. Higher mean OS_C values are found for dimeric groups of C_13–15 as well as C₂₀, and other products of C₆ and C₁₆ in SOA_273 K, leading to higher OS_C for bulk SOA particles. Thus, we emphasize that, besides promoting the condensation of condensable components, lower temperatures chemically enhance the formation of ISO-AP cross dimers, while higher temperatures may favor the formation of higher oxidized products, e.g., via the autoxidation mechanism (Bianchi et al., 2019).

For instance, SOA_{298→313 K} has OS_C values of -0.53 (HR-AMS) and -0.31 (FIGAERO-iodide-CIMS), much lower than those of SOA_313 K (-0.49 by HR-AMS and -0.27 by FIGAERO-iodide-CIMS). By comparing the molecular chemical composition of both particles at 313 K (Fig. S13a and e), the higher mean OS_C values for carbon groups of C_4–10 in SOA formed directly at 313 K cause the increase of overall OS_C of oxygenated products. This confirms again that higher temperatures favour the formation of higher oxidized products.

In addition, C₈₋₁₀ compounds (mean formula C_8.4H_12.4O_5.0) in SOA_{298→313 K} have a Tmax of 100 °C. However, C_8–10 compounds have a similar mean formula (C_8.5H_12.5O_5.3) in SOA_313 K but have a lower Tmax of 82 °C. This implies that C_8–10 compounds consist of varying monomeric isomers with significantly different volatilities, being less volatile in SOA_{298→313 K} and more volatile in SOA_313 K.

Besides, although SOA_{273→298 K} has the largest OS_C increment (-0.75 for bulk, -0.41 for oxygenated constitutes) from its initial particles before warming among all particles discussed, its oxidation state is still significantly lower than SOA_298 K (-0.56 for bulk, -0.31 for oxygenated constituents). This is consistent with the somewhat higher volatility of SOA_{273→298 K} (Tmax of 71 °C) than SOA_298 K (Tmax of 77 °C, Fig. 5b and c) observed. All compound groups remaining after warming have higher mean OS_C except for C₄ (Fig. S13). This means that the compounds in most compound groups are more oxidized when formed at 298 K. Thus, we conclude that besides promoting the evaporation of particle-phase compounds, higher temperatures also enhance the formation of higher oxidized products in SOA from oxidation of α-pinene and isoprene mixtures.

The relevance of these findings is corroborated by model simulations that incorporates the new VBS parameterization derived below, including mixed dimers. The results discussed above are based on experiments with equal initial amounts of α-pinene and isoprene. However, in the natural atmosphere, the α-pinene to isoprene ratios can vary substantially for different temperatures (seasons, day / night) and in different regions, e.g., boreal forest, tropical forest, and temperate regions. The averaged ratio of isoprene to terpenes (including other monoterpene compounds) over Europe during the simulation period is predicted to be 3.75 (Fig. S3). With α-pinene representing terpenes, simulations using the PMCAMx chemical transport model (Tsimpidi et al., 2010; Fountoukis et al., 2011; Murphy and Pandis, 2009) show that when the C_14–15 ISO-AP dimers are considered under different temperatures, the predicted mass concentration of organics over Europe is significantly enhanced. The mean ground-level PM₁ biogenic SOA mass concentrations over Europe for the simulated period are found to increase by 47 % from 0.23 µg m⁻³ with the original setup (Base case, Table S1) to 0.41 µg m⁻³ by utilizing the new VBS parameterization including the temperature dependent C_14–15 ISO-AP cross dimers (New case, Table S2) (Fig. 7a, b, c). The contribution of biogenic SOA to the total OA mass increased from 9 % to 14 % (Fig. 7d, e). Specifically, in the New case, the predicted ground-level OA mass concentrations are on average higher by 0.6 µg m⁻³ for four measuring stations located in Italy (Fig. S4), as shown in Fig. S14.

During the simulated period, the isoprene emissions are greater over Croatia than other European areas. As a result, the difference in monthly averaged ground-level biogenic SOA concentrations between the two simulations is larger in Croatia (0.9 µg m⁻³) than the domain average (0.4 µg m⁻³). Figure S15 shows the correlation between isoprene concentrations and the enhancement of biogenic SOA mass predicted in the New case compared to the Base case over Croatia. In addition, due to the synergetic effect of relatively high concentrations of biogenic precursors and higher temperatures (Fig. 7g–h), the simulated biogenic SOA concentrations at the site of Monte Cimone (2165 m a.s.l.) show a better fit with the observed values compared to the Base case (Fig. 7f).