The EVAPORATION model, developed by Compernolle et al. (2011), is used in this study for the calculation of the temperature-dependent pure component (saturation) vapour pressures of organic compounds in the liquid state. The pure component vapour pressure is important for determining the order-of-magnitude extent to which a component may partition to the particle phases at equilibrium (Barley and McFiggans, 2010; Booth et al., 2010) as a consequence of Eq. (1). EVAPORATION uses a group contribution approach to represent the effects of different functional groups in organic molecules on the pure compound. This approach is similar to other estimation methods, such as SIMPOL.1 (Pankow and Asher, 2008), but, in addition, EVAPORATION also includes a second-order chemical structure describing the parameters in order to take into account the effects of certain intermolecular group–group interactions and to correct for the limitations in the applied first-order functional group additivity assumption. The predicted pure-component liquid-state vapour pressure, pi0(T), which is a function of temperature only, is used to calculate the saturation concentration Ci0 via the following: 3Ci0=pi0MiRT. Here, Mi is the molar mass of the compound, R the universal gas constant, and T the absolute temperature (all expressed in SI units or with the appropriate conversion applied). The level of accuracy obtained for pi0(T) is often important for the calculated total PM mass concentration and related model uncertainties when the component is in the semi-volatile range (O'Meara et al., 2014).

A parameterization for the temperature dependence of pi0 applied in EVAPORATION is given by Compernolle et al. (2011) as follows: 4log⁡10pi0[1atm]=Ai+BiTκ. An optimal value of κ=1.5 has been determined by Compernolle et al. (2011) to account for the vapour pressure of hydrocarbons, with or without heteroatoms, over a wide temperature range; atm denotes the unit pressure scale here (1 atm = 101 325 Pa). For applications in this study, Eq. (4) is solved for the values of Ai and Bi, using pi0 calculated by the online EVAPORATION model (http://tropo.aeronomie.be/index.php/models/evaporation/15-tropospheric/44-evaporation-run, last access: 11 September 2018) at two sufficiently different temperatures (e.g. at 0 and 60 ∘C) for each component i. The component-specific coefficients Ai and Bi can then be used to parameterize pi0 for the system components in the temperature range of interest.

The selection of an SOA-forming set of characteristic chemical components is a key input to our modelling framework. The choice of surrogate components representing isoprene oxidation products is described in the following. The use of a set of surrogate components typically means that the actual system of oxidation products is highly simplified in terms of number and chemical classes of components. Some components will partition mostly to the gas phase and others, to a small or large extent, to the condensed phase. From the perspective of the gas–particle partitioning physics common to the volatility basis set (VBS) and surrogate-based approaches, it is necessary and sufficient to cover different volatility classes by at least one surrogate species. In such a framework, it is then important to approximately match the volatility distribution of the surrogates contributing to the SOA mass, which is achieved by tuning surrogate yields to match observations (as far as the range of measured SOA concentrations allow). As such, knowing the pure-component volatilities of the potential surrogate components matters; we exploit this by selecting a set of low-volatility and semi-volatile surrogate components that will likely contribute to the SOA mass under the given environmental conditions. In addition, higher-volatility components, directly predicted by a gas-phase chemical mechanism, are part of our system and enable the establishment of a scalable link between the yields of those products and the selected lower-volatility surrogate compounds. Aside from surrogate compound volatilities, it is also important to match, approximately, the distribution of functional groups and molecular sizes, such that the resulting SOA hygroscopicity is captured by the AIOMFAC model. This aspect is considered by tuning the surrogate yields to observations taken at substantially different RH levels. A state-of-the-art chemical mechanism for gas-phase reactions, the Master Chemical Mechanism (MCM), version 3.3.1 (Jenkin et al., 2015; http://mcm.york.ac.uk, last access: 22 December 2021), was used to account for the reactions of isoprene with the ozone and OH radicals formed during the reaction process. MCM is useful to predict the formation of stable, volatile, early generation products under given experimental conditions. For conditions mimicking the CLOUD chamber setting, a gas-phase chemistry simulation with the MCM provided the time evolution of the molecular concentrations of reacted isoprene, ozone, and the stable early generation products formed, namely glyoxal, methylglyoxal, methyl vinyl ketone (MVK), hydroxymethacrylate (MACO3H), 2-hydroperoxy-3-hydroxy-2-methylpropanal (MACROOH), and 2-hydroperoxy-3-hydroxy-2-hydroxymethyl propanal (HMACROOH). The major stable products predicted by the MCM for the first/early generations of oxidation are compounds of low molecular mass with relatively low O:C ratios and high vapour pressures (VOC to intermediate VOC, IVOC, class compounds). Hence, these compounds reside predominantly in the gas phase, and organic particulate matter forms only at very low temperatures (low compared to 298 K), at very high relative humidity levels, or at very high (atmospherically irrelevant) concentrations of isoprene reacted (i.e. the isoprene amount oxidized by O3 or OH radicals). In order to validate the amounts of ozone, OH, and isoprene reacted predicted by the MCM, conditions and measurements from the CLOUD 10 and CLOUD 9 chamber experiments, as reported by Fuchs (2017), were used for a comparison with observations, which are further discussed in the following. Based on the MCM predictions, the reaction of isoprene by OH radicals is estimated to have accounted for approximately 30 % of the isoprene oxidation, while the remaining ∼ 70 % were due to oxidation by ozone (under dark, low NOx conditions; see Sect. 3.5.3 of Fuchs, 2017).

Additional components of a semi-volatile and low-volatility nature formed via multi-generation oxidation, which are not fully considered by MCM, need to be included in the partitioning model as part of the isoprene system. Therefore, we introduce a selection of organic surrogate species, included in the model in the form of frequently observed higher-generation oxidation products, to represent wider classes of isoprene-ozonolysis-derived SOA compounds. The selected surrogate components are shown in Fig. 1. Oxalic acid along with compounds such as 2-methyltetrol, 2-hydroxy-dihydroperoxide, 2-methylglyceric acid, and a C5 alkene triol are among the main semi-volatile and low-volatility products that are expected to form after oxidation (by ozone and by OH) of the early generation compounds under low NOx conditions. Oxalic acid formation in the aqueous phase is shown in Carlton et al. (2009); the compounds 2-methyltetrol, 2-hydroxy-dihydroperoxide, and 2-methylglyceric acid are suggested as being surrogate compounds by Couvidat and Seigneur (2011). The C5 alkene triol and the C10-hemiacetal dimer are selected as surrogates, based on the partitioning of IEPOX to aerosols, followed by aqueous-phase reactions described by Surratt et al. (2010). The selected C10-hemiacetal dimer is a compound representing a whole class of potential dimer and oligomer compounds formed by accretion reactions from the above-mentioned five higher generation products. The five SVOC and LVOC compounds, along with the ELVOC dimer, form the set of surrogate species included in our model to account for the gas–particle partitioning of isoprene-derived SOA in this study.

In an aqueous solution, it has been observed that glyoxal and methylglyoxal exist predominantly as their corresponding mono- or dihydrates, whereas MCM predicts the non-hydrated forms of glyoxal and methylglyoxal from the gas-phase chemistry. To account for these different forms of the species, pure compound vapour pressures of the monohydrates of glyoxal and methylglyoxal have been considered to account for partitioning and the dihydrate forms for liquid-phase interactions in the thermodynamic mixing model. Also, monohydrates can further react in aqueous solutions to form hemiacetals, oxidized oligomers, imidazoles, and organosulfate compounds (Ervens and Volkamer, 2010). Moreover, in the presence of aqueous sulfate, glyoxal dihydrates form ELVOC by displacing water molecules in the hydration shell of sulfate ions; this pathway is indicated by the dotted grey arrow in Fig. 1. This gives rise to a salting-in effect on glyoxal (Kampf et al., 2013; Waxman et al., 2015). At the molecular level, these ELVOCs correspond to the formation of glyoxal–dihydrate–sulfate complexes (Kurtén et al., 2015), which are indicated in the upper left of Fig. 2 as a dotted grey range in volatility. Such complexes are presently not covered in the AIOMFAC-based equilibrium partitioning framework. Therefore, in this study, the aqueous chemistry of glyoxal is only partially represented; however, given the relatively low gas-phase yields of glyoxal and methylglyoxal for the reaction conditions of the CLOUD experiments, omitting a more detailed aqueous-phase representation of these species is considered acceptable. Moreover, the scaling parameters β5 and β6 can be considered to account for glyoxal-derived SVOC and ELVOC effects indirectly in the parameterized model (see the discussion of the scaling parameters in Sect. 2.3.4).

Predicted amounts from a MCM-based continuous flow chamber simulation for the two species MACO3 and MACR (abbreviations are the names assigned by MCM) have been lumped into MACO3H. Similarly, the cumulative amounts of MACRO2 and MACROOH have been lumped into MACROOH because of the chemical pathways of the species and the simplifying approach of avoiding chemical species in radical form from the lists of surrogates. We emphasize that the higher-generation surrogate products selected (and shown in Fig. 1) for the model are not formed directly from the (parent) early generation oxidation products; instead, several unresolved steps of chemical reactions take place to arrive at those SVOC compounds. Here the emphasis is not on detailed chemical pathways; we, rather, focus on the characterization of the SOA formation and growth due to the partitioning behaviour of the multi-generation oxidation products. Insights into typical compounds formed from isoprene oxidation gained from laboratory and field experiments were used to assign the set of higher-generation products in the model (Carlton et al., 2009; Couvidat and Seigneur, 2011; Surratt et al., 2010; Kroll et al., 2006). Surratt et al. (2010) proposed a chemical mechanism via the reactive intermediate epoxydiols (IEPOX) pathway leading to the formation of 2-methyltetrols and C5 alkene triols for the oxidation of isoprene by OH. The 2-methyltetrol and C5 alkene triol are part of the current surrogate model system, since OH radicals also form during the ozone-initiated oxidation of isoprene and its products (Zhang et al., 2018).

Figure 2 shows the pure component volatilities as a function of the O:C ratio for all the surrogate components considered in the gas–particle partitioning model (details are described in Sect. 2.3.4).

The CLOUD chamber is a continuous flow chamber in which the ozone-initiated isoprene oxidation process is controlled by reactant inflow, with mixing during the chamber mean residence time and a continuous outflow of reactor components. At steady-state conditions, the rate of reactant inflow and outflow to/from the chamber is the same, and the net variability in the reactant species in the chamber is approximately zero. Therefore, the steady-state organic mass concentrations formed are associated with the amount of isoprene reacted per residence time period in the chamber. This includes the amount of isoprene reacted responsible for subsequently forming the SOA sampled by the instruments. Zhang et al. (2018), among others, proposed a kinetic modelling scheme and steady-state assumptions to understand the evolution of species concentrations in a continuous flow chamber for the interpretation of experimental SOA mass concentration and yield data.

The concentration of isoprene reacted, [ISOPRCT], quantifies the modelled gas-phase concentration of an artificial tracer component added to the MCM simulation. It is the concentration resulting from the cumulative sum of all reactions of isoprene with O3, OH, or NO3, including a correction for chamber dilution. In short, [ISOPRCT] is the difference between the isoprene inflow concentration and its steady-state concentration. This tracer is essential for the calculation of molar yields of system components. We can express [ISOPRCT] by accounting for its reactive formation (rf) via isoprene oxidation, its loss due to dilution (out), its loss due to partitioning to chamber walls (wl), and its loss due to condensation to particulate matter (pm). The variability in [ISOPRCT] at the steady state in the flow chamber is then given by the following: 5d[ISOPRCT]dt=∂[ISOPRCT]∂trf-∂ISOPRCT∂tout-∂ISOPRCT∂twl-∂ISOPRCT∂tpm=0. This definition implies that there is no inflow of [ISOPRCT] into the chamber or the related first-generation products of isoprene oxidation. As a simplification, assuming that there were no wall loss or loss by condensation to particles, Eq. (5) simplifies to (at the steady state) the following: 6∂[ISOPRCT]∂trf=∂[ISOPRCT]∂tout7∂[ISOPRCT]∂tout≈[ISOPRCT]ssVch⋅ΔVchΔt. Here, Vch is the volume of the chamber, and ΔVchΔt is the exchanged chamber volume portion during the discrete time interval Δt due to inflow/outflow. Since ΔVch exchanged during residence time τ is equivalent to Vch, we obtain, from Eqs. (6) and (7), the following: 8ISOPRCTss=∂[ISOPRCT]∂trf⋅τ. To this end, the MCM-predicted molecular concentrations of [ISOPRCT] are averaged over 30 min time periods to account for quasi-steady-state concentrations in the chamber when flow conditions were maintained for an extended time period of at least 1 h (characteristic of the mean chamber residence time). The averaged amounts of isoprene reacted along with the corresponding steady-state mass concentrations of the various organic products formed are used to calculate pseudo-molar yields for the MCM-predicted products. We note that the molar yields of individual MCM-predicted products differed between the simulations of CLOUD 9 and CLOUD 10 cases due to differences in experimental conditions. This is accounted for by means of different sets of input concentration data for the gas–particle partitioning calculations of seeded or seed-free cases when compared to the CLOUD experiments. In the CLOUD 9 (seeded) case, during specific time intervals, cloud droplets were formed by the process of adiabatic expansion, whereby the previously pressurized chamber was depressurized from 220 hPa above ambient pressure back to ambient pressure (approx. 1013 hPa) for a time period of 8 min. After cloud formation, the inflow RH was returned to a subsaturated level and maintained for about 1.5 h; during the first hour, the system relaxed back to near-steady-state conditions. Additional adiabatic expansions were conducted over similar time intervals. Given the pressure, humidity, and temperature variations with the cloud formation cycles during the CLOUD 9 experiments, the corresponding molar yields of the MCM-predicted products were based only on the component concentrations at the times when the chamber had stabilized during subsaturated conditions, i.e. excluding time periods of cloud formation and immediately after.

Details of the MCM box model approach in Fuchs (2017) are as follows: the box model used inputs for the isoprene and ozone inflow concentrations, condensation sink (from SMPS data), inorganic seed concentration, rainout rate constant (quantifies the rate of formation of cloud droplets and the associated mass loss in the cloud), dilution rate constant, aerosol wall loss rate constant, RH, reaction rate constants of isoprene with the OH and O3 oxidants, and the hygroscopic growth factors of inorganic seeds and organics. The virtual tracer, [ISOPRCT], was simulated with oxidation of isoprene as the source and dilution as the only sink (i.e. without wall loss). In each time step, the produced [ISOPRCT] was instantaneously distributed to a volatility basis set distribution. In their comprehensive version of the box model, Fuchs (2017) simulated wall losses, dilution, condensation/evaporation, and hygroscopic growth, assuming internal mixing and using the kinetic partitioning method by Donahue et al. (2006) as a basis for calculating evaporation and the condensation sink to represent gas–particle partitioning.

In this work, we use output from a version of the MCM-based box model by Fuchs (2017) that employs a simpler wall loss correction for generating the evolution of early generation oxidation products. These product concentrations at selected points in time were then used as the input data for our RH-dependent equilibrium partitioning model.

In the absence of a mechanistic, quantitative prediction for the formation of the higher-generation products from the early generation gas-phase oxidation products, their formation is here constrained by the quasi-steady-state molar concentrations of the six MCM-predicted components (the VOCs in Fig. 1). Those components serve as the parent compounds of the less volatile surrogate compounds chosen (see Fig. 1). This establishes a direct constraint in our model on the maximum molar (or mass) amounts of carbon available for the formation of the SOA-relevant SVOC, LVOC, and ELVOC compounds. The estimated molar amounts of surrogate species formed from the VOC precursors at a certain time in an experiment are expressed by a set of dimensionless scaling parameters, βi, further described below.

The yield calculation for each higher generation compound (SVOC and LVOC) is done by constraining them with molar yields of the MCM-predicted gas-phase oxidation products (the early generation products) as follows: 9ni=βi×∑jnj0. Here, ni is the molar concentration (moles per cubic metre of air; hereafter mol m-3) of the SVOC surrogate product, i, formed (2-methyltetrol, 2-hydroxy-dihydroperoxide, 2-methylglyceric acid, or C5 alkene triol), excluding oxalic acid (see Fig. 1); nj0 are the MCM-predicted molar concentrations at the quasi-steady state of the parent products MVK, MACO3H, MACROOH, and HMACROOH, as indicated in the scheme of Fig. 1. Since the concentrations of these parent components decrease in the process of the formation of higher-generation species, a resulting proportional decrease in each of the compounds consumed in Eq. (9) is accounted for by subtracting a mole-fraction-weighted amount of cumulative higher-generation products formed from each of the parent products considered, as follows: 10nj=nj0-xj0×∑ini, with xj0=nj0∑lnl0, where indices j and l cover the parent compounds and index i the SVOC surrogate products formed (excluding oxalic acid). Prior to the calculation of the surrogate yields, a check is carried out to ensure that the sum of the assigned branching ratios does not exceed 1 in order to maintain the carbon mass balance. Equations (9) and (10) describe an empirical scheme for the quasi-instantaneous conversion of a fraction of the early generation products to higher-generation compounds, with the latter being important for the gas–particle partitioning of SOA. This approach is a substantial simplification of the actual chemical system; however, this scheme provides a physical constraint on the molar formation budget of surrogate species. The method used in Eqs. (9) and (10) is also adopted for calculating the amount of oxalic acid formed from the parent products glyoxal and methylglyoxal and their associated decrease in molar concentration.

The molar concentration nk of the surrogate oligomeric species C10 hemiacetal dimer is calculated in a similar way, yet it is based on the cumulative molar amounts of the SVOC surrogate components rather than directly from the early generation products, as follows: 11nk=βk×0.5×∑ini0. Here, βk is the parameter constraining the amount of dimer formed, and the ni0 are the (initial) calculated molar concentrations of its parent compounds, namely 2-methyltetrol, 2-hydroxy-dihydroperoxide, 2-methylglyceric acid, and C5 alkene triol. The sum of the molar amounts of these four species is divided by two, for estimating the molar dimer amount (nk), because the dimer (as a surrogate for a variety of similar C10 dimers) is formed as a result of accretion reactions of certain combinations of parent surrogate products, each of which contains typically half the number of carbon atoms compared to the formed dimer. The corresponding decrease in each parent surrogate's concentration is accounted for by subtracting a mole-fraction-weighted amount of dimer formed from each of the potential parents as follows: 12ni=ni0-xi0nk. Our decision-making process, involved with setting initial scaling parameter values (βi and βk), was informed by the O:C vs. volatility space of all the system components, which is an approach that is also the basis of the two-dimensional volatility basis set approach to describe the formation and growth of organic aerosols (Donahue et al., 2011, 2012). In our simple model, the scaling parameters (branching ratios) are adjustable and are determined iteratively by model–measurement comparison. After the gas–particle partitioning model was used to calculate the equilibrium SOA mass concentration formed at varying levels of reacted isoprene, covering the range observed in the CLOUD chamber experiments, and for high to low relative humidity, the values of the scaling parameters were gradually adjusted in the model to influence the predicted molar amounts of the different higher-generation species formed. In addition, the distinct hygroscopic contributions to the aerosol water content and associated changes in gas–particle partitioning by all organic components also offered some guidance in the optimization of the scaling parameters. The consideration of observed SOA mass concentrations formed at several levels of reacted isoprene, as well as low and high RH levels, makes our scaling parameter determination distinct from the approach taken in more traditional SOA yield parameterizations, such as fitting of a (1-D) VBS to dry conditions data only. Reasonably good agreement was achieved after a few iterations of this optimization process. We note that our set of determined scaling parameters (i.e. the branching ratios) is not unique; other combinations of scaling parameters may provide similar agreement with the observations. The determined scaling parameters for the surrogate species are provided in Table 1.

Measurements from the CLOUD chamber for the seed-free experiments suggest an SOA mass yield of 1 %–2.4 % at 35 % RH and 1.7 %–3.7 % at 85 % RH at a temperature of 5 ∘C. These mass yields reflect the data when a simple, vapour wall loss correction is applied to the measurements, which then indirectly affects the fitted model parameters. We acknowledge that accounting for the actual wall losses is difficult, and may change the stated SOA yields substantially, but this is beyond the focus of this study since we are mainly interested in understanding the partitioning effects at different RH levels. Such relative effects are likely not susceptible to the specific type of wall loss treatment used. However, we note that accounting for a higher actual wall loss of low and semi-volatile species would result in a higher actual SOA mass yield than stated above. The isoprene and ozone mixing ratios for the seed-free experiments in the CLOUD chamber were 275 and 130 ppbv (parts per billion by volume), respectively, for both the low and high RH conditions. A key point in our evaluation of the RH effect is that the same molar yields have been used for the MCM-predicted gas-phase concentrations of the early generation products and the hypothetical model tracer species of isoprene reacted, which covers the modelling of the SOA mass concentrations at all levels of RH.

The SOA mass concentration data used here were reported by Fuchs (2017). The measurements for SOA mass concentration vs. MCM-predicted isoprene-reacted concentration at several points in time in the experiments were compared with the model results obtained for the same conditions using periods for which the quasi-steady-state assumption was applicable. Those data are shown in Fig. 3 and listed in Table S4. The set of pseudo-molar yields of the surrogate components used by the partitioning model are provided in Table S1.

Based on the predicted early generation product yields and the set of determined scaling parameters (β), the effective molar yields of the surrogate components were calculated with the AIOMFAC-based gas–particle and liquid–liquid equilibrium model for a given input level of reacted isoprene. The same scaling parameter values were used at high and low RH. This was done for the following two reasons: (i) the assumption that the chemistry behind the formation mechanism of the SOA products remains the same at low and high RH, since the absolute water vapour concentration at 35 % RH and 5 ∘C is still abundant (for gas-phase chemistry), and (ii) using the same parameters, the model predictions allow for a direct quantification of the role of seed hygroscopicity and associated aerosol water content on the gas–particle partitioning of all SOA components at variable RH.

Figure 3 shows the modelled SOA mass vs. isoprene reacted in agreement with the experimental data at 35 % RH (Fig. 3a) and 85 % (Fig. 3c). This confirms the successful tuning of the scaling parameters β. Figure 3b shows the model–measurement comparison of SOA mass yield vs. SOA mass concentration at 35 % RH. The error bars shown in Fig. 3 represent the range of uncertainty for measured SOA mass concentrations and yields. These error bars are based on an estimated relative error of 50 % in the measured organic aerosol mass concentration (Fuchs, 2017). Figure 3c and d show the model calculations of SOA mass concentration and mass yield in comparison to the measurements at 85 % RH. The SOA mass varies in a non-linear manner with the isoprene-reacted levels, which is in reasonable agreement with the predictions from the model. Nevertheless, the experimental data show some scatter at isoprene-reacted concentrations between ∼ 140 to 175 µgm-3, which the model is unable to reproduce when good agreement at lower isoprene-reacted levels is achieved. Based on the seed-free SOA formation case shown in Fig. 3, the measurements and model predictions reveal a relative humidity effect on the SOA mass concentration.

For example, for an isoprene-reacted level of 150 µgm-3, the predicted SOA mass concentration at gas–particle equilibrium for 35 % RH is about 2 µgm-3, resulting in an organic mass yield of 1.33 %, while the corresponding SOA mass concentration predicted for 85 % RH is ∼ 3.5 µgm-3, a 75 % enhancement, with an SOA mass yield of approximately 2.33 %. For this seed-free system, the model simulation, therefore, suggests that the measured increase in SOA mass yield at 85 % RH compared to 35 % RH can be fully explained by the effect of aerosol water uptake on the equilibrium phase partitioning of all system components. Fuchs (2017) reported average SOA elemental compositions for the CLOUD experiments based on measured desorption profiles from a FIGAERO-CIMS (filter inlet for gases and aerosols chemical ionization mass spectrometer) instrument. For the seed-free case (and low NOx conditions), the determined average O:C for SOA ranged from 0.62–0.67 at low RH (∼ 35 % RH) and up to 0.69 at high RH (∼ 85 % RH), i.e. indicating only a small change in the average O:C between low and high RH conditions (Fuchs, 2017; see Sect. 3.6.1 therein). The measured average H:C ratios were about 1.48 to 1.50. Our modelled SOA is of higher O:C and H:C ratios on average. At 278 K, for 140 µgm-3 of reacted isoprene (a typical value for comparison with the CLOUD experiments; see Fig. 3), the predicted SOA has the following properties: at 35 % RH, there is 1.77 µgm-3 SOA, O:C of 0.843, and H:C of 2.26; at 85 % RH, there is 3.14 µgm-3 SOA, O:C of 0.844, and H:C of 2.18. The values at RH levels in between are similar. The lower-volatility surrogate species used with the model have individual H:C ≥ 2.0; e.g. the C10 dimer has a H:C ratio of 2.2 and a O:C ratio of 0.7. While this comparison suggests substantial differences between measured and modelled average elemental organic aerosol composition, it remains unclear how different the associated SOA water uptake behaviour is.

The effect of equilibrium partitioning with non-ideal mixing in the liquid phase was further studied using the AIOMFAC-based model over an extended range of RH for a fixed isoprene-reacted steady-state concentration. The different SOA surrogate species are shown to provide distinct contributions to the organic PM mass as RH varies. Figure 4b shows stacked bar graphs of the predicted PM mass concentrations of the organic components for the range from near-zero up to 99 % water activity (equivalent to bulk equilibrium RH). The water content in the form of particle-phase mass fractions is shown in Fig. 4c. These model results were obtained by assuming that all PM-bound organic species remain in a liquid (or an amorphous semi-solid) state regardless of RH (no crystallization allowed), which is an assumption that is considered to be valid for complex multicomponent SOA systems (Marcolli et al., 2004). Furthermore, due to the substantial hygroscopicity of isoprene SOA, as evident from Fig. 4c, and the semi-volatile nature of organic components like the C5 alkene triol and 2-methyl glyceric acid surrogate compounds, a continuous SOA mass and yield enhancement is predicted with increasing RH (compare Fig. 4a and b). The model predicts this RH dependence because of the coupled absorptive water uptake and enhanced gas-to-particle partitioning of the semi-volatile organics in the absence of any potential changes in gas-phase or liquid-phase chemistry with changes in RH. In the case shown in Fig. 4, an SOA mass concentration of ∼ 3.3 µgm-3 (yield of ∼ 2.64 %) is computed for a water activity of 95 %, which is more than double that obtained at 35 % RH. Figure S9 shows the predicted mole-fraction-based activity coefficients of the different system components as a function of water activity. In this seed-free system, without any inorganic electrolytes, several of the SOA surrogates show activity coefficients ranging between 0.3 and 1, especially in the RH range from 40 % to 96 %. This indicates favourable mixing among the liquid-phase components and, compared to an ideal mixing assumption on mole fraction basis, an enhanced SOA mass concentration in that RH range. In the RH range above 96 %, several SOA surrogate components show an increase in their activity coefficients (except for oxalic acid), which is indicative of unfavourable mixing in the presence of a large mass fraction of water.

Since secondary OH radicals form during the ozonolysis of isoprene, quantifying the contribution of OH-reaction-derived SOA mass and the role of radical scavengers is of interest. Sato et al. (2013) discuss the effects of different OH radical scavengers used in sufficient concentrations during smog chamber experiments. They performed experiments using the OH radical scavengers of cyclohexane, carbon monoxide, n-hexane, and diethyl ether in a static 6 m3 environmental chamber at 25 ∘C. For the dark ozonolysis of isoprene without any seed particles, and in the absence of an OH scavenger, Sato et al. (2013) obtained SOA yields in the range from 0.29 % to 2.3 % (after applying a particle wall loss correction) for produced SOA mass concentrations in the range from 2 to 120 µgm-3, i.e. covering a much wider SOA concentration range than that explored in the CLOUD experiments but only at dry conditions and a higher temperature. The initial isoprene and ozone concentrations in the chamber were in the range 0.5–2 ppmv (parts per million by volume; approximately 1400–5500 µgm-3) and 2–4 ppmv at a temperature of 25 ∘C under very dry conditions (RH < 1 %). Using our equilibrium model along with the same reacted isoprene concentration of 5484 µgm-3 and temperature as during the experiments by Sato et al. (2013), an SOA yield of ∼ 1.28 % was calculated for dry conditions of 1 % RH (also ∼ 2.62 % yield at 85 % RH), which is within the range of mass yields observed in the experimental study (see Table 2 and Fig. S1). The same pseudo-molar yields for the early generation products and scaling parameters for the higher-generation products, as for the CLOUD 10 seed-free case, were used for the model calculations. Repeating the model calculation for 5484 µgm-3 of isoprene reacted, but at 5 ∘C, this results in a predicted SOA mass yield of ∼ 2.82 % at 1 % RH (∼ 3.07 % yield at 85 % RH). This indicates that the temperature effect (a difference of 20 ∘C between 5 ∘C in the CLOUD chamber and 25 ∘C in the chamber studied by Sato et al., 2013) increases the pure component volatilities of the surrogate species sufficiently to decrease their partitioning to the aerosol. Since a relatively large fraction of SOA in the model surrogate system is contributed by SVOCs, their gas–particle partitioning is sensitive to changes in temperature.

Experimental studies on the temperature effects of SOA formed from the dark ozonolysis of isoprene conducted by Clark et al. (2016) detected SOA yields as high as 9 % at 5 ∘C under dry conditions (RH < 1 %). Their experiments were conducted in a polytetrafluoroethylene (PTFE; Teflon) chamber at initial isoprene and ozone concentrations of 250 and 125 ppbv and an isoprene-reacted level of 278 µgm-3. Using the equilibrium model to predict isoprene SOA formation for the same conditions as the latter study, an SOA yield of ∼ 1.25 % was predicted for dry conditions of ∼ 1 % RH (see Fig. S2). It is observed that, even though the experimental conditions in the chamber by Clark et al. (2016) resemble the original CLOUD experiment conditions, the measured SOA yield by Fuchs (2017) is lower than the SOA yield reported by Clark et al. (2016). The difference in the measured SOA yields is likely explained by differences in the type and sophistication of the particle wall loss correction procedure used by Clark et al. (2016) compared to the simple vapour wall loss correction applied to the CLOUD data, as referenced in this study. Using the SOA mass measured from the CLOUD 10 experiments, it is predicted that pure compound vapour pressures of the semi-volatile components constituting the SOA are lowered when the temperature decreases from 25 to 5 ∘C (as is expected). Hence, with this temperature effect, the SOA yields during dark ozonolysis of isoprene at 5 ∘C become comparable to those reported for isoprene photooxidation at 25 ∘C (Chhabra et al., 2010; Lambe et al., 2015). The relatively high SOA yield observed in the CLOUD ozonolysis experiments may also partially be due to the absence of an OH radical scavenger.

Among other model–measurement studies on the photooxidation of isoprene, the MCM and SOA partitioning model results for the OH-initiated oxidation of isoprene reported by Chen et al. (2011) are used for comparison with our model predictions for the ozone-initiated oxidation (Sect. S2). For this comparison, a different set of system components, based on components listed by Chen et al. (2011) for the isoprene oxidation system without an inorganic seed, were used with our AIOMFAC-based model to calculate the gas- and particle-phase compositions at different levels of water activity. The SOA yields originally predicted by Chen et al. (2011) range from 1.08 % to 2.69 % at isoprene-reacted concentrations ranging from 134 to 334 µgm-3 at 40 % RH and 25 ∘C. For the Chen et al. (2011) surrogate mixture, as modified by Rastak et al. (2017) (see Table S3), our model predicts the SOA mass to exist in a single particle phase at all RH levels, as shown in Fig. 5. For calibration, we constrained our model input composition in terms of total gas- plus particle-phase molar concentrations such that it predicts the same equilibrium SOA mass concentration as the Chen et al. (2011) model at a reference point of 3.6 µgm-3 SOA at 40 % RH, 25 ∘C and a mean isoprene-reacted concentration of 147 µgm-3. Therefore, the SOA yields predicted both by Chen et al. (2011) and the AIOMFAC-based model are 2.4 % at 40 % RH. At 85 % RH and T=25 ∘C, our model predicts an SOA mass concentration of ∼ 6.2 µgm-3 and an SOA yield of ∼ 4.2 % for the photooxidation case, since significant amounts of SVOCs partition to the PM at high RH levels (> 80 % RH) similar to the hygroscopic growth and coupled enhanced SVOC partitioning determined for the isoprene ozonolysis case.

The effect of RH on the SOA yield enhancement for the photooxidation of isoprene with OH is observed from the ratio of SOA yield at a temperature of 25 ∘C for 85 % RH vs. 35 % RH as ∼ 1.97 (=4.1/2.1). The SOA yield enhancement for the photooxidation of isoprene at a temperature of 5 ∘C for 85 % RH vs. 35 % RH is ∼ 1.2 (=7.5/6.4). Thus, SOA yield enhancement with respect to high and low RH levels is here predicted to decrease with decreasing temperature. The SOA yield enhancement for the ozone-initiated oxidation of isoprene at a temperature of 5 ∘C for 85 % RH and 35 % RH is ∼ 1.8. Hence, the SOA yield enhancement for the ozone-initiated oxidation of isoprene is estimated to be higher than the SOA yield enhancement for the photooxidation of isoprene at a temperature of 5 ∘C. However, we note that the temperature-dependence of the yield enhancement is also dependent on the choice of surrogate components. Since the SOA mass was only constrained at low RH levels for the photooxidation case, a proper quantification of (chamber-independent) SOA yields at high RH levels are imperative for better constraining and better understanding the role of isoprene SOA as a source of organic particulate matter in global models.

In the following, measurements of SOA mass concentrations in the presence of sulfate- and ammonium-rich aqueous inorganic seed particle populations are compared with model calculations for similar conditions in terms of temperature, pressure, RH, ranges of isoprene reacted, and seed concentrations. Since the measured total sulfate to the ammonium molar ratio of the selected experiments was approximately 1:1, an inorganic particle composition of the stoichiometry of ammonium bisulfate (NH4HSO4) was used for the model calculations. This seed type implies the partial dissociation of HSO4- in an aqueous solution into H+ and SO42- ions and, consequently, moderately to strongly acidic conditions. The AIOMFAC-predicted pH ranges from -1.2 to +1.3 for RH ranging from 10 % to 99 % (pH scale using H+ activity on a molality basis). Since the experiments and corresponding model predictions were carried out for RH > 75 %, typically at ∼ 85 % RH, the seed aerosol is assumed to consist of completely deliquesced aqueous solution particles of liquid-like viscosity (Colberg et al., 2004).

When the model calculations were initially run using the same scaling parameters as for the seed-free case, SOA mass concentrations were found to be overpredicted by the model. Possible reasons for the observed model–measurement disagreement will be discussed in the following. During the seeded CLOUD chamber experiments, studying cloud formation from the formed SOA mixed with the seed particles was also of interest. For that purpose, intermittent adiabatic expansions were carried out (chamber pressure was reduced by 220 hPa), during which water vapour supersaturation and (warm) cloud formation was achieved. Occasionally, the formed clouds led to some precipitation in the chamber, which may have led to a subsequent loss of organic aerosol mass and number concentration (reducing the condensation sink). Our interpretation of the importance of these processes is as follows: in the occasional cases where precipitation occurred, the aerosol condensation sink decreased, which, in turn, may have increased the relative importance of wall losses and may have amplified deviations of SOA mass concentrations from reaching steady-state conditions. In comparison to the MCM model simulations which neglected precipitation, both of these effects have the potential to decrease the species concentrations that actually contributed, via gas–particle partitioning, to the observed suspended organic aerosol mass concentration. The corrected isoprene-reacted concentration responsible for the measured SOA amount would, thus, have to be lower than that predicted by MCM, therefore also lowering the concentrations of the first-generation species modelled by the MCM. On the contrary, the presence of seed particles would be expected to lower the importance of organic vapour wall losses compared to the seed-free cases (CLOUD 10 experiments). However, the application of the equilibrium partitioning model with scaling parameters tuned by CLOUD 10 observations led to overpredicted SOA mass concentrations. Therefore, while changes in the wall loss behaviour between the two series of CLOUD experiments are likely contributing to the resulting discrepancy, our quantitative understanding remains incomplete.

To achieve better model–measurement agreement for SOA mass concentrations formed at varying seed concentrations, a (fitted) scaling parameter of 0.55 was introduced to scale the amounts of semi-volatile and low-volatility species predicted by the partitioning model (the one based on branching parameters from the seed-free cases) via scaling of the branching ratios. This scaling factor effectively accounts for the various differences between the seed-free and seeded experiments, such as differences in the condensation sink, the fraction of vapours lost to the wall, the transient partitioning effects, etc. An optimal value for the scaling parameter was considered to be one where there is good model–measurement agreement for both ammonium bisulfate and sulfuric acid seeded cases simultaneously. It is noted that the branching ratios could be scaled by any factor between 0.5 and 0.6 to achieve agreement with the experimental data, partially due to the ∼ 50 % uncertainty in the AMS measurements, which were used alongside the SMPS-derived particle volume data to calculate the organic mass concentrations, as mentioned in the thesis by Fuchs (2017).

The equilibrium gas–particle partitioning model predictions for SOA mass concentrations resulting in varying ammonium bisulfate mass concentrations are shown in Fig. 6 as black curves, with the different line styles corresponding to different isoprene-reacted concentrations ranging from 120 to 160 µgm-3. Error bars indicate a 50 % uncertainty in the determined experimental SOA mass concentrations. Figure 6a is of interest for model–measurement comparison since it displays both the effects of the variation in isoprene reacted and seed concentration on the SOA mass concentration, while temperature and RH are kept approximately constant. In Fig. 6b, showing SOA mass yield vs. mass concentration, the ammonium bisulfate concentration dependence is not explicitly visible. The end points of the model curves at the lower SOA mass concentrations in Fig. 6b correspond to 0 µgm-3 seed mass concentration, while the highest values correspond to ∼ 13 µgm-3 ammonium bisulfate. The experimental data in Fig. 6a were obtained over a longer time span of approximately 24 h since the start of the experiments, with intermittent cloud formation periods during which no data were taken for the comparison here, but potentially with an effect on the later SOA mass concentration data due to changes in the steady-state dynamics of the chamber (loss of aerosol particles and related condensation sink). This results in potential deviations between the actual experimental conditions and those assumed by the model. Measured SOA mass concentrations range between 1.2 and 2.5 µgm-3 for ammonium bisulfate concentrations varying from near zero up to 12 µgm-3. In Fig. 6a, for an isoprene-reacted concentration of 130 µgm-3, the predicted SOA mass concentration varies from 1.2 to 1.7 µgm-3 over the range of 0 to 13 µgm-3 of the ammonium bisulfate concentrations shown. The modelled SOA mass concentrations are, thus, within the uncertainty of the majority of the experimental data, keeping in mind that there remains an additional potential source of error due to vapour wall loss, which is not included in the error bars of Fig. 6. This is also true for the model calculations at other isoprene-reacted levels and their comparison to pertinent experimental data. SOA yield values determined based on the measurements, without a sophisticated wall loss and chamber dynamics correction accounted for, vary from 0.4 % to 1.9 % for these conditions with isoprene-reacted concentrations in the range from 110 to 165 µgm-3 at ∼ 85 % RH and 283 K. The predicted SOA yield values are in the range of 0.8 % to 1.9 % at similar isoprene-reacted concentrations.

Model calculations for gas-phase and aqueous-solution-phase compositions were performed at fixed amounts of total air parcel compositions, except for a variable RH and, therefore, water content. This primarily affected the aerosol water content but also the organic aerosol amounts via non-linear gas–particle partitioning feedbacks, while the ammonium bisulfate mass concentration remains constant in the particle phase. The computed equilibrium compositions of the gas phase and the predicted liquid particle phases are shown in Fig. 7a–c. In the stacked bar graphs shown, the emphasis is on the mass concentrations of the organic compounds and the inorganic ions, excluding the water content (although some water is present in the phases). Mass fractions of all components in the liquid phases (including water) are shown in Fig. 7d and e. The model predicts LLPS to occur between 0 % and 83 % RH; here, the two particle phases are a hydrophilic bisulfate-rich, organic-poor phase (phase α) and an organic-rich phase β. Both liquid phases contain substantial inorganic ion amounts; therefore, no complete organic- or inorganic-phase separation is predicted by the model. We add that the extension of LLPS to low RH here is also a consequence of ignoring any potential crystalline inorganic phase in these computations. The inorganic-rich particle phase (Fig. 7d) is holding a higher water content compared to the mixed organic–inorganic particle phase (Fig. 7e) at the same RH. Above ∼ 84 % RH, both particle phases merge to form a single liquid phase. The gas phase consists of MCM-predicted first-generation products, while the particle phase mainly consists of surrogate components and the inorganic seed. At 10 ∘C and an isoprene loading of 130 µgm-3, the model predicts an SOA mass concentration of ∼ 0.99 µgm-3, an SOA yield of ∼ 0.76 % at low RH (∼ 1 % to 20 % RH), and, therefore, low PM water content. At ∼ 85 % RH, the aerosol water content is increased, as is evident from Fig. 7d and e, affecting the partitioning of all species and resulting in a predicted equilibrium SOA mass concentration of 1.45 µgm-3 and an SOA mass yield of ∼ 1.12 %. For an ammonium bisulfate seed concentration of 1.3 µgm-3, water-free organic or inorganic mass ratios of ∼ 0.75 at low RH (5 % to 30 % RH) and 1.12 at high RH (∼ 85 %) are predicted.

Observations by Kleindienst et al. (2007), using an ammonium sulfate seed (0.05 µgm-3) at 22 ∘C and an isoprene loading of 1270 µgm-3 in a PTFE chamber, indicated that dark ozonolysis of isoprene produces an estimated SOA yield of 1.0 % at approximately 30 % RH. Using our equilibrium gas–particle partitioning approach to model the SOA formed at varying RH for the case of such an approximately neutral (in terms of pH) ammonium sulfate seed under the same temperature and isoprene loading conditions as used by Kleindienst et al. (2007), we determine SOA mass concentrations of ∼ 7 µgm-3 at 35 % RH and ∼ 13 µgm-3 at 85 % RH (see Fig. S3). The predicted SOA yields are ∼ 0.52 % at 30 % RH, ∼ 0.54 % at 35 % RH, and ∼ 1.03 % at 85 % RH. For comparison, we modelled the SOA formation for the same conditions but with ammonium bisulfate instead of ammonium sulfate as seed aerosol. For the Kleindienst et al. (2007) SOA formation conditions, the equilibrium partitioning model predicts the same SOA yields as for the neutral ammonium sulfate seeded case at low and high RH (see Table 3 and Fig. S4). Thus, the gas–particle partitioning mechanism applied to the same surrogate SOA system, in the absence of potential changes to aqueous-phase SOA chemistry, leads to very similar SOA mass formed at comparable levels of RH for both a neutral ammonium sulfate and an acidic ammonium bisulfate seed. For this case with a comparably low seed mass concentration, this finding was perhaps to be expected. Modelled aqueous solution compositions using the neutral ammonium sulfate seed indicate that the amount of the inorganic ions dissolved in the liquid phase can depend on the solid–liquid equilibrium (SLE) in the case of ammonium sulfate when model calculations are performed accounting for crystallization in such a case (see Fig. S3).

A model–measurement comparison of SOA mass concentration vs. sulfuric acid seed mass concentration is shown in Fig. 8. Experiments with either ammonium bisulfate or sulfuric acid seeds at 10 ∘C were conducted under similar conditions. Therefore, the branching ratios used to calculate the amounts of higher-generation products in our equilibrium model were scaled by the same correction factor of 0.55 as for the ammonium bisulfate seeded case. At a temperature of 10 ∘C, 85 % RH and an isoprene-reacted amount of ∼ 130 µgm-3 measured SOA mass concentrations to range between 0.5 and 2.4 µgm-3 (with uncertainty considered), while the model predicts 1.2–2.2 µgm-3 for sulfuric acid mass concentrations ranging from 0 up to 5 µgm-3 (Fig. 8a; dashed black curve). SOA yield values observed in the chamber vary from 0.3 % to 1.4 % (uncorrected), while the model-predicted values are in the range of 0.8 % to 1.4 % for the same SOA mass concentration range (Fig. 8b). At low sulfuric acid seed concentrations in the experiments, the losses of isoprene oxidation products to the chamber walls may compete substantially with condensation to aerosol particles, which would at least partially explain the observed lower SOA mass concentrations compared to those from our model predictions. At higher seed mass concentrations, such wall loss effects are expected to be smaller. Figure 8 indicates that the model–measurement agreement for SOA mass concentration and yield improves with increasing seed concentration.

Figure 9 shows the predicted equilibrium-phase compositions as a function of water activity for the case with an aqueous sulfuric acid seed of 3.7 µgm-3. For this amount of inorganic seed, the model predicts LLPS between ∼ 22 % and 82 % water activity, characterized by mixed organic–inorganic phases, with both phases containing significant water content. In these calculations, sulfuric acid is assumed to be non-volatile, which is a good assumption at this temperature, except perhaps at the very low RH limit. The AIOMFAC-predicted pH ranges from -3.2 to 0.7 for RH ranging from 10 % to 99 %. This indicates that the aqueous-particle phase is more acidic than with a bisulfate seed for a comparable RH range, as expected. As shown in Fig. 9, within the LLPS range, the liquid-phase β (Fig. 9c) is a minor phase in terms of absolute mass concentration, and it contains organic compounds like the C10 hemiacetal dimer, H+, and HSO4- ions; i.e. both liquid phases are predicted to be organic–inorganic mixtures. For an isoprene loading of 130 µgm-3, SOA yields in the range of ∼ 1.12 % at 60 % RH to 1.76 % at 99 % RH are predicted by the model. SOA mass concentrations are predicted to be in the range from ∼ 2.85 µgm-3 at 1 % RH to a minimum of 1.45 µgm-3 at 60 % RH, followed by a monotonic increase to 2.29 µgm-3 at 99 % RH. The highest SOA mass concentrations for the sulfuric acid seeded case are predicted to be found at low RH levels (1 % to 10 % RH) in the absence of crystalline inorganic phases because one of the major early generation products, methylglyoxal (comprising ∼ 0.8 % of mass concentration of gas-phase isoprene oxidation products), partitions significantly to the particle phase under these conditions. However, the validity of the AIOMFAC-based model predictions at such low water activities and high ionic strengths are rather uncertain. Such results should, therefore, be interpreted with caution; predictions at > 30 % RH are considered to be much more reliable.

For comparison of the seed-amount-based yield enhancement, model predictions were made using sulfuric acid seed concentrations comparable to those for the ammonium bisulfate seed case (see Fig. S7). For such a case with 1.3 µgm-3 of sulfuric acid seed, the model predicts LLPS between ∼ 45 % and 80 % water activity. The predicted pH ranges from -3.2 to 0.7 for RH ranging from 10 % to 99 %. Figure S7b–e show that both liquid phases are predicted to be organic–inorganic mixtures. At an isoprene-reacted concentration of 130 µgm-3, the model predicts SOA yields ranging from ∼ 1.32 % (at 1 % RH) and ∼ 1.10 % (at 35 % RH) to 1.71 % (at 99 % RH), with SOA mass concentrations ranging from ∼ 1.30 µgm-3 (at 60 % RH) to 2.22 µgm-3 (at 99 % RH). The differences in the predicted SOA yields compared to those for 3.7 µgm-3 sulfuric acid seed (the case shown in Fig. 9) are a result of the different inorganic-to-organic mass ratios involved, with the increased amount of seed-contributed water in the case with 3.7 µgm-3 seed and the non-linear feedbacks from the coupled LLPS and gas–particle partitioning.

For a direct comparison of SOA yields of the sulfuric acid seeded case with that of a seed-free case with comparable gas-phase chemistry and early generation product yields, the same pseudo-molar yields (using the same scaling factors) were used for a seed-free equilibrium partitioning calculation (see Table 3 and Fig. S6). At an isoprene-reacted concentration of 130 µgm-3, predicted SOA mass concentrations for this seed-free case are ∼ 0.56 µgm-3 at 1 % RH, ∼ 0.62 µgm-3 at 35 % RH, and ∼ 1.12 µgm-3 at 85 % RH, with corresponding SOA yields of ∼ 0.43 % at 1 % RH, ∼ 0.48 % at 35 % RH, and ∼ 0.86 % at 85 % RH. Thus, here a net enhancement of SOA mass concentrations results in higher SOA yields because of a gas–liquid partitioning feedback of semi-volatile organics caused by added aerosol water. This hygroscopicity effect is especially prominent when comparing seeded and seed-free calculations at intermediate RH conditions. For example, at 60 % RH and [ISOPRCT] of 130 µgm-3, SOA mass yields of ∼ 0.57 % (∼ 0.75 µgm-3) are predicted without seed while ∼ 1.12 % (1.45 µgm-3) are predicted with 3.7 µgm-3 sulfuric acid seed. This implies a substantial (non-ideal) mixing effect on the partitioning of SOA due to inorganic seed amounts and inorganics-contributed PM water content when the chemistry involved in the formation of oxidation products remains the same. For comparison and quantification of the non-ideality, we show, in Fig. S10, the predicted activity coefficients of the organic compounds for both the seeded and seed-free systems. Figure S10 indicates the activity coefficients of the SOA surrogates substantially deviating from unity (expected for ideal mixing behaviour), with values both above and below 1. The activity coefficients are also substantially different when comparing the organic-rich phase (in the case of phase separation; i.e. the system with seed) with the sulfuric-acid-rich phase, as expected, and when compared to the values in the seed-free system. Also, the water activity dependence of the non-ideal mixing in the organic-rich phase in the LLPS case is not simply resembling the mixing in the seed-free aqueous solution; this is because a non-negligible amount of the ions partition also to the organic-rich phase.

Several other studies have focused on the role of seed acidity on isoprene SOA formation. Laboratory chamber studies by Jang et al. (2002) measured higher SOA mass formed as a result of catalysed heterogeneous reactions in the presence of inorganic acids, such as sulfuric acid, for biogenic and anthropogenic carbonyl species. Experimental studies on isoprene ozonolysis in the presence of sulfuric acid seed carried out by Limbeck et al. (2003), Jang et al. (2002) and Czoschke et al. (2003) confirm that acid-catalysed oligomerization reactions result in higher SOA mass compared to that produced in a non-acidic seed particle medium, especially at lower RH. Laboratory studies by Czoschke et al. (2003) were carried out at 24 ∘C under dry (< 10 % RH) conditions to analyse the impact of acidified sulfate aerosols on SOA formation during isoprene ozonolysis in the presence of an OH scavenger. Although the chemical characterization of the aerosol revealed an enhancement of highly oxidized compounds, the reported SOA yields were low, typically in the range of 0.5 % to 0.8 % by volume.

Table 2 lists measured SOA yields from various studies and other properties of these laboratory experiments in comparison to estimated SOA yields predicted with our partitioning model. The predicted SOA mass yield enhancement, defined as the ratio of the yields computed for two different RH levels, are shown in Table 3 for the seed-free cases and seeded cases with ammonium bisulfate or sulfuric acid seeds. Our comparison focuses on the RH effect and differences between the two inorganic seeds on the gas–particle partitioning of semi-volatile organic species and water. That is, we are not accounting for possible changes in gas-phase or particle-phase chemical reaction pathways due to changes in RH, aqueous-phase ionic strength, and/or acidity. For the given scenarios, the model predicts more substantial SOA yield enhancements when comparing yields at 85 % RH to those at 35 % RH, whereas the enhancements from 1 % RH to 35 % RH are modest or, in some cases, even below 1.0, indicating a relative yield decrease. For example, the model predicts an SOA yield enhancement of ∼ 1.52 at 85 % RH relative to 35 % RH for the case with 1.3 µgm-3 ammonium bisulfate seed (SOA / seed mass ratio of 1.1 at 85 % RH), while no enhancement is predicted for the same case when comparing yields at 35 % RH and 1 % RH (yield ratio of 0.97). Using the same pseudo-molar yields (in our surrogate component system) as for the seeded cases to model the SOA formed without an inorganic seed for the purpose of consistent comparisons of predictions made using the same assumptions, we determine an SOA yield enhancement of 1.11 at 35 % RH relative to 1 % RH and a higher SOA yield enhancement of 1.80 at 85 % vs. 35 % RH. The latter enhancement is predominantly because of the added aerosol water amount at higher RH contributed by hygroscopic oxidized organic compounds, indirectly enhancing the partitioning of all semi-volatile organics to the particle phase.

For a sulfuric acid seed concentration of 1.3 µgm-3 (see Fig. S7), comparable to the amount of ammonium bisulfate seed in the shown case, a slightly higher SOA yield enhancement is predicted in comparison with yield enhancements for a case with 3.7 µgm-3 of sulfuric acid seed. The comparison suggests that a sulfuric acid seed, with its effect on the liquid–liquid phase partitioning of water and organics, results in already comparably high values of SOA yield at very low RH levels (1 % RH) and only a small yield enhancement at 85 % RH relative to 35 % RH. The partitioning model further suggests that there are higher amounts of sulfuric acid seed of about 3.7 µgm-3, resulting in an SOA / seed mass ratio of 0.45 at 85 % RH, leading to a slightly lower SOA yield enhancement of 1.06 at 85 % vs. 35 % RH. Comparing the seed-free and the three seeded cases at 10 ∘C listed in Table 3, all computed with the same set of pseudo-molar yields and scaling parameters, shows that the highest SOA yields (but not yield enhancements) are obtained for the cases with sulfuric acid seed, while the seed-free case shows the lowest yields. This is mainly due to favourable partitioning of SVOCs in the system into the particle phase as a result of the substantial hygroscopicity of sulfuric acid, particularly so already at 35 % RH. Irrespective of the seed type, the presence of a substantial aqueous inorganic seed mass concentration is predicted to enhance the SOA yield (see also Figs. 7a and 8a), especially at high RH, and to influence the RH-dependent SOA yield enhancement.

Comparing the modelled cases for 130 µgm-3 of isoprene reacted at a temperature of 25 ∘C with their equivalent cases at 10 ∘C, a temperature effect on the predicted SOA mass yield enhancement is indicated. For the seeded cases at 25 ∘C, the higher enhancement of ∼ 1.39 is found for the ammonium bisulfate seed; however, this enhancement is lower than that of 1.52 for the equivalent case at 10 ∘C.

Comparing the SOA yield enhancements for the ammonium bisulfate seeded case with the sulfuric acid seeded cases, the relatively high yield enhancement with an ammonium bisulfate seed is mainly due to the lower SOA mass yield at 35 % RH relative to 85 % RH and relative to the sulfuric acid seeded cases at 35 % RH. At the same time, the SOA yield values at 85 % RH for the case with 1.3 µgm-3 ammonium bisulfate seed concentration are comparable with the sulfuric acid seeded case at 1.3 µgm-3. A comparison of organic aerosol mass concentrations predicted over a wider range of RH is provided in Fig. S8 for cases with sulfuric acid or ammonium bisulfate seed.