## Introduction

Organic aerosols (OA) represent a major fraction of the mass of submicron aerosol in Earth’s atmosphere1,2. OA worldwide is dominated by secondary organic aerosols (SOA), which are formed in the atmosphere from the condensation of low-volatility and semi-volatile organic compounds (L/SVOCs)1,2,3,4. Gas/particle (G/P) partitioning of organic species is generally modeled using equilibrium absorptive partitioning theory5,6. The theory states that at equilibrium, the fraction of SVOCs in the particle phase (Fp) depends on their pure-compound volatilities (c*), compound activity coefficient (γ), and total OA mass concentration (cOA) present. In an aerosol mixture, γ modifies c* to give the effective saturation concentration $$\left( {c_{\rm{eff}}^ \ast } \right)$$ of the compound.

$$F_p = \left( {1 + \frac{{\gamma c^ \ast }}{{c_{OA}}}} \right)^{ - 1} = \left( {1 + \frac{{c_{\rm{eff}}^ \ast }}{{c_{OA}}}} \right)^{ - 1}.$$
(1)

In a more detailed kinetic representation, the mass accommodation coefficient (α) is a critical parameter that describes the fraction of vapor molecules taken up by the particle phase for each vapor collision with a particle. The value of α determines if partitioning is kinetically limited and impacts the G/P equilibration timescale in the atmosphere. α = 1 indicates no mass transfer limitations from vapors to the condensed phase. In atmospheric models, SOA is typically modeled by assuming instantaneous equilibration between gases and particles7,8. In some models that simulate SVOC condensation kinetically, proper consideration of kinetic limitations often lacks9. Previous determinations of α for organic vapors onto particles range from near 1 to as low as 0.00110,11,12,13,14,15,16,17,18,19,20,21. During the complex process of gas molecule incorporation into the bulk of condensed phase, the properties of aerosol particles can affect the magnitude of α. Recent studies show that SOA in the atmosphere can in some cases exist in a highly viscous semisolid (glassy) or solid state, which could retard molecular diffusion within the aerosol matrix, resulting in an apparent α < 122,23,24. In contrast, there has been field and laboratory work showing that at least some ambient and biogenic SOA does not appear to significantly resist the exchange of semivolatile compounds and exhibits mixing times <1 h under typical boundary layer conditions14,25,26,27,28. However, the abovementioned studies have used indirect methods, such as measuring evaporation rates (sometimes at high temperatures) and viscosity, and have been limited to only particle characterization, while the direct measurement of gas- and particle-phase concentrations of specific molecules during the dynamic partitioning process had not been demonstrated until recently. On the other hand, in organic/inorganic and hydrophilic/hydrophobic organic mixtures, particle morphology, such as liquid–liquid phase separation, can also affect the equilibration rates and the thermodynamics of molecules partitioning through phases29,30. Recently, Krechmer et al. determined α for partitioning of oxidized compounds to dioctyl sebacate (DOS) particles in a Teflon chamber by directly measuring and modeling the vapor concentration evolution31. They found an average α of 0.7 for L/SVOCs with saturation concentrations ranging from 10−3 to 102 µg m−3. Given that α could be different for different particle substrates, there is need to quantify α for atmospherically relevant particles with different phases and properties using the experimental techniques that are capable of fast, direct measurement. A better understanding of α also helps constrain the timescales of partitioning from ~1 min (α = 1) to many hours (α = 0.001) at typical atmospheric aerosol loadings. The atmospheric models’ instant G/P equilibration assumption may become inappropriate if this timescale is relatively long compared with other simulated processes.

A number of advances in speciation of compounds relevant to G/P partitioning for SOA have been achieved by new developments in instrumentation for laboratory and field studies27,32,33,34,35,36,37. Among these techniques, gas-phase species-level concentrations can be rapidly monitored in situ using the soft ionization mass spectrometry27,36,38. Measurements of particle-phase speciation and concentrations often suffer from slower time resolution (~1 h) due to the need of aerosol collection on a filter, and/or thermal decomposition when thermal desorption of OA is required27,32,33,34,37. The recently developed technique of extractive electrospray ionization (EESI) provides soft ionization of many organic molecules in real time with minimum sample heating39,40 and has been very recently improved to achieve higher sensitivities, making it now possible to be applied to ambient-level concentrations41. These qualities make EESI, when coupled with an inlet that sufficiently removes the gas phase, well-suited for fast online analysis of OA, as in partitioning kinetic measurements.

This study quantifies the mass accommodation coefficients of L/SVOC species into a variety of preexisting particles of different phases and properties: liquid organics, including oleic acid, squalane, and pentaethylene glycol; solid seeds, including ammonium sulfate (AS) and sucrose; liquid inorganic, including deliquesced AS; and α-pinene/O3 SOA that represents a realistic atmospheric SOA mixture. We use a well-characterized, relatively simple gas-phase chemical system to rapidly produce L/SVOCs in 10 s, which are then taken up by particles and the chamber walls at a slower timescale of ~2 min and ~17 min, respectively. Chemically speciated gas-phase products are monitored by a chemical ionization mass spectrometer (CIMS) coupled with a NO3 source (NO3-CIMS), while an EESI-MS measures the same molecules in the particle phase as they partitioned into the aerosol. By simultaneously fitting gas/particle/wall partitioning with a kinetic box model, we can provide robust constraints on α. We also discuss the implications of our findings to atmospheric partitioning.

## Results

### SOA formation overview

Details of the experiments, including procedures, instruments, measurements, and partitioning processes, are described in “Methods” section and summarized in Supplementary Fig. 1. In short, the partitioning L/SVOCs were produced by a fast (10 s) OH oxidation of alkanols under high NO. The multifunctional products that were monitored by real time mass spectrometry and used to derive α include dihydroxynitrates (DHNs), trihydroxynitrates (THNs), and carbonyl dihydroxynitrates (CDHNs) (Supplementary Table 1)42.

In our seeded experiments (Supplementary Table 2), as well as the DOS seed experiments of Krechmer et al.31, SOA volume formed by the partitioning of these L/SVOCs usually peaked within 2–3 min of the OH pulse. Since the L/SVOC vapor wall loss timescale for this chamber is ~17 min, the initial SOA formation is dominated by G/P partitioning with little wall effects. Typically, peak SOA volume ranged from 2.5 to 11 µm3 cm−3 (smaller than or similar to the seed volumes) depending on the preexisting seed type (Supplementary Fig. 2). Note that the differences in SOA mass across seed types are generally larger than the variability within the same seed (even when combining same-seed experiments with different condensation sink, or CS), owing to thermodynamic differences in partitioning among seeds. The oxidized L/SVOCs then continued re-partitioning among phases. Since the vapor-phase L/SVOCs were lost to chamber walls, which have a large equivalent mass concentration (Cw, Supplementary Fig. 3) but a slower timescale, the net effect of this “wall denuding” is a constantly decreasing aerosol volume with time (even when corrected for particle-wall losses). After 1 h, the fraction of evaporated SOA spanned from ~12% (oleic acid) to over 90% (sucrose) of the initially formed mass concentrations (Supplementary Fig. 2). The SOA amount formed and lost is likely affected by varying activity coefficients of the L/SVOCs in different seeds, which are influenced by the aerosol mixture composition. For almost all seed types, we measured OA composition using an aerosol mass spectrometer (AMS)43,44. The SOA mass spectra of all available experiments show consistent composition (Supplementary Fig. 2 and Table 3). In addition, SOA analysis performed using liquid chromatography and online and offline mass spectrometry methods similar to those used previously indicate that the SOA products are similar to those formed from the reaction of linear alkanes but with an additional hydroxyl group, as expected42,45,46. The major SOA products are DHNs, with a minor contribution from cyclic hydroxy hemiacetals.

This work examines the determined α values, which are predominantly constrained by the time evolution over the first ~20 min, when condensation to particles was the dominant partitioning flux and partitioning to the walls was slow.

### Partitioning kinetics of gas-phase L/SVOCs

We first present results of condensation measured by NO3-CIMS. In a seeded experiment, vapors condense to both particle CS and chamber walls. As condensation proceeds, these two reservoirs start to act as two sources as vapors re-evaporate at volatility-dependent rates, until a steady state is reached. In the experiment with the smallest seed concentration (~1.8 µg m−3 of oleic acid) L/SVOCs reach a steady state in less than 400 s, ~2.5 times faster than the gas-wall equilibrium timescale. Thus in all our experiments, the processes of vapor uptake into particles versus walls can be readily separated due to the difference in their timescales. In addition, we limited the analysis to experiments below an initial surface area of ~2500 µm2/cm3. As aerosol surface area increases, the rate coefficient of gases condensing on particles $$\left( {k_{G \to P}} \right)$$ increases, which results in gaseous concentrations decaying at higher rates. Therefore, at very high surface areas, it is possible that L/SVOCs condensed so fast that the CIMS may not be able to capture the true peak immediately after oxidation, leading to less precise and possibly low-biased condensing rates. An example of the time evolution of C8H17NO6 THNs in the presence of oleic acid seed aerosol with varying seed concentrations is shown in Supplementary Fig. 4. As oleic acid increased from 148 to 622 µm2/cm3, the time that the THNs decayed to equilibrium shortened from ~550 s to ~250 s. This surface area dependence was observed for other seed types and also in previous studies31.

As shown in Supplementary Table 2, experiments with surface areas ~400–650 µm2/cm3, a relatively narrow range, were conducted for almost all seeds. Figure 1 shows gaseous time evolution of C6H13NO6 THNs in the presence of different seed aerosol types that were mostly within this surface area range. We observed similar equilibrium timescales, 300–500 s, for all seeds. This indicates that α values, which characterize the condensation kinetics, are likely of the same order for this wide range of seeds. In the final steady state, the compounds exhibited different gas-phase concentrations. According to partitioning theory (Eq. 1), equilibrium gas concentration is affected by available cOA and the activity coefficient (γ) of the L/SVOC in the seed/SOA mixtures. After accounting for cOA, variation of γ across seeds is apparent in this dataset and explains the differences in steady-state gas concentrations. This variability is consistent with previous results47,48.

### Partitioning kinetics of particle-phase L/SVOCs

An important experimental advance made in this study was to use EESI-MS for the real-time monitoring of some of the same L/SVOCs as they partitioned to the particle phase. Figure 2a shows a SOA mass spectrum obtained at the maximum SOA mass concentration, which contains mainly DHNs and is consistent with the other SOA composition measurements mentioned earlier. THNs were also detected (see “Methods” section for details).

We selected two pentaethylene glycol experiments with similar initial surface areas to compare gas and particle measurements. As shown in Fig. 2b, as gas phase C9H19NO5 and C12H25NO5 DHNs decayed, their particle-phase counterparts accumulated concurrently. Both phases reached equilibrium slightly after 200 s.

### Values of α consistent with the experiments

By fitting the kinetic box model to the gas-phase measurements it was possible to constrain α and effective saturation concentrations $$\left( {c_{\rm{eff}}^ \ast } \right)$$ for each measured L/SVOC in the presence of every seed. Details of the fitting can be found in “Methods” section and examples are shown in Supplementary Fig. 5 along with sensitivity tests performed using different sets of α and $$c_{\rm{eff}}^ \ast$$. As shown, reducing α from 1.0 to 0.1 leads to a much slower decay than observed. Furthermore, since $$c_{\rm{eff}}^ \ast$$determines the equilibrium concentration, higher $$c_{\rm{eff}}^ \ast$$would lead to higher gas concentration than observed. Note that our method successfully separated the effects of α and $$c_{\rm{eff}}^ \ast$$ on partitioning. Regarding diffusivity, our model does not consider diffusion within the particles explicitly. Rather, we consider the two extremes of fast diffusion (and thus the whole particle is available for partitioning, i.e., cOA = cseed + cSOA) and very slow diffusion (and thus only the layer of newly condensed SOA is available for partitioning, i.e., cOA = cSOA). The value of alpha is still the probability of uptake upon collision, and the availability of partitioning mass (and thus the diffusion coefficient of the seed) is then reflected on $$c_{\rm{eff}}^ \ast$$ and the evaporation rate. Liquid organics were all assumed to have fast diffusion while solid AS and sucrose seeds were assumed to have no diffusion of SOA into the seed. The treatment of α-pinene/O3 SOA will be discussed in detail in the next section.

The optimal α and $$c_{\rm{eff}}^ \ast$$ of all studied L/SVOCs (Supplementary Table 1) for all CIMS experiments are shown in Fig. 3a. Example error bars are shown for several L/SVOCs spanning the volatility range. Also plotted for comparison are α values for the same L/SVOC species determined from previous DOS seed experiments31. Since the upper limit of α was not constrained, a few model fittings generated α slightly >1, which is not physically possible. However, the error bars, which reflect uncertainties in parameters, SMPS measurements, and fitting (see “Methods” section), suggest that those values are not statistically >1 or indicative of any bias or artifact in the determination. The overall CIMS-determined average α for each seed range from 0.8 (±0.4) to 1.0 (±0.3), close to the average α = 0.7 for DOS. In the volatility range of 10−2–1 µg m−3, α values clustered tightly around 0.5–1.0. As volatility increases beyond 10 µg m−3, higher variability in α was observed, accompanied by relatively larger error bars. Since these more volatile compounds partition less into the particle phase and the NO3-CIMS technique has lower sensitivity towards them, their measured decays have less contrast and the data have lower CIMS signal-to-noise (S/N) ratios, resulting in larger uncertainties.

We also used the box model to find the optimum α by fitting the EESI-MS observations while constraining $$c_{\rm{eff}}^ \ast$$ using CIMS-determined values (Supplementary Fig. 5) since these are the best available estimates for $$c_{\rm{eff}}^ \ast$$ under our conditions. Since the accuracy of $$c_{\rm{eff}}^ \ast$$ can affect the fitted α, we performed sensitivity tests by multiplying/dividing $$c_{\rm{eff}}^ \ast$$ by 10, which is much larger than the estimated ±35% uncertainty and the differences between $$c_{\rm{eff}}^ \ast$$ and $$c_{\rm{SIMPOL}}^ \ast$$ in most cases (Supplementary Fig. 6). Those changes resulted in α decreasing by up to a factor of 2 for 10 × $$c_{\rm{eff}}^ \ast$$ or increasing by up to ~15% for $$c_{\rm{eff}}^ \ast$$/10 for the most volatile C6–C9 DHNs while α was nearly unchanged for the other less-volatile DHNs and THNs. Still, even with these perturbations the fitted α obtained from EESI-MS measurements ranged from ~0.5 to 1.0. The values of α determined from fitting the model to gas and particle measurements are consistent (Fig. 3b), and both indicate that α is near unity across a wide variety of seeds.

For the more volatile range of $$c_{\rm{eff}}^ \ast$$ > 10 µg m−3, our α values fall within the range measured in previous studies (Fig. 3a, b), and there is no conclusive dependence of α on a single property of the partitioning compounds, such as volatility or polarity.

### Mixing with α-pinene/O3 SOA

α-pinene/O3 SOA, a representative atmospheric SOA mixture in locations subject to biogenic emissions, also shows the ability to rapidly take up the studied L/SVOCs. Since α-pinene/O3 SOA formed under dry conditions has high viscosity23, we determined α and $$c_{\rm{eff}}^ \ast$$ by either including or excluding α-pinene/O3 SOA in the partitioning cOA (Eqs 1 and 5), and thus treating it as either liquid or solid. Treating α-pinene/O3 SOA as a liquid assumes that dry α-pinene/O3 SOA takes up vapors like a liquid organic despite being viscous. This assumption yields reasonable results (Fig. 3a). But when treated as a solid the initial evaporation rates of the more volatile DHNs and C6 THN (with fitted $$c_{\rm{eff}}^ \ast$$ > 1 µg m−3) are too fast, so that neither α = 1 nor even an unrealistic α = 10 can reproduce the observed, fast gas-phase decay (Fig. 4 and Supplementary Fig, 7). Although our model did not explicitly include particle-phase diffusion, the above sensitivity test indicates no kinetic limitation of uptake by dry α-pinene/O3 SOA due to surface accommodation or particle-phase diffusion. Diffusion of L/SVOCs within the near-surface layers of and possibly the entire particle probably occurs on a timescale of ~ 200 s, as this is the timescale of vapor condensation (Fig. 4). Consistent with our observation, Ye et al.25 found that α-pinene/O3 SOA took up L/SVOCs evaporated from toluene/OH SOA without evidence of a mixing limitation, whereas Robinson et al. found that when squalane particles were coated with α-pinene/O3 SOA formed under dry conditions (RH = 5%) most squalane was able to evaporate, indicating that the α-pinene/O3 SOA shell did not inhibit mass transfer49. Saha and Grieshop50 and Saleh et al.14 reported evaporation coefficients for dry (RH < 10%) α-pinene/O3 SOA on the order of 0.1. In contrast, some studies found much slower evaporation and/or smaller α for dry α-pinene/O3 SOA and have attributed the reason to mass transfer limitations in a highly viscous or glassy amorphous state11,24. Without simultaneously constraining the volatility of the SOA components, the slower evaporation rates may instead be limited by the presence of very low-volatility materials rather than high viscosity. Note that in the atmosphere, since OA can undergo further oxidation and/or heterogeneous reactions, ambient α-pinene/O3 SOA may have different viscosities from that generated in laboratory.

### α for toluene SOA

The methods for quantifying α can also be applied to other chemical systems. By conducting 20 s burst of OH oxidation of toluene under high NO, we determined 0.3 ≤ α ≤ 0.6 for SOA-forming L/SVOCs based on AMS measurements of the OA formation (Supplementary Figs. 8 and 9). Gas-phase NO3-CIMS measurements also showed that this system generated some fast-condensing species with α > 0.1 (Supplementary Discussion and Supplementary Fig. 10). This is much larger than the α values estimated between 0.001 and 0.002 for toluene products in previous hours-long photooxidation experiments, where α was determined by fitting SOA mass concentration profiles to the observations13.

## Discussion

In this study, we have determined the mass accommodation coefficients for L/SVOC uptake to a variety of aerosol types in an environmental chamber by directly measuring the disappearance of oxidation products from the gas phase and their appearance in the particle phase, achieving consistent results for a wide range of compound volatilities. The accommodation coefficient, α, is generally between 0.5 and 1.0, across the large range of phases and properties of preexisting seed particles. The selected seeds span a range of viscosities and states that can be present in the real atmosphere: from low viscosity organic liquids, to semisolid or glassy α-pinene/O3 SOA, to solids such as AS and sucrose. The organic liquid seeds should allow compounds to very quickly diffuse throughout the particle phase after surface accommodation. For solid AS, AS/water, and sucrose, the condensed compounds likely form a layer on the surface of the seed cores51. For example, assuming a surface area per molecule of 20–40 Å[2 52,53 and a typical initial seed surface area of 500 µm2/cm3, a monolayer of SOA would have a mass concentration of ~0.5–1 µg/m3, which is about 10–20% of the ~5 µg/m3 of SOA formed in the AS and sucrose experiments. The formation of the first layer is expected to take up to tens of seconds, a timescale that is observed in our experiments. As illustrated by the α sensitivity test for sucrose (Supplementary Fig. 5), condensation with α = 0.1 would be too slow to accurately simulate the measured uptake, even in the earliest stages of growth. This indicates that the α was close to 1 throughout the experiment, including during uptake onto these solid surfaces.

In addition to having different phases, the liquid and amorphous seeds used here also differ by polarity. Squalane is the least polar, AS/water and pentaethylene glycol the most polar, and the other seeds as well as the major DHN products lie in between. Despite the different seed polarities and therefore different interactions with L/SVOCs, these seeds all readily take up the L/SVOCs with similar α and timescales. We do observe differences, however, in the equilibrium gas-phase concentrations (which also appear in the model-determined $$c_{\rm{eff}}^ \ast$$), the initial amounts of SOA formed, and the evaporation rates during the 1 h measurement period (Supplementary Figs. 2a and 6).

In summary, our burst-oxidation experiments with chemically-speciated real-time molecular detection of gases and particles allow us to probe partitioning kinetics more directly than in past studies. We have found near-unity mass accommodation coefficients during G/P partitioning for representative types of aerosol that is at atmospherically relevant mass loadings (several to tens of µg m−3). This potentially indicates insignificant gas-to-particle (and particle-to-gas) mass transfer limitations in the lower atmosphere at near room temperature, which supports the assumption of rapid equilibration between gases and particles currently used in atmospheric models for SOA simulation.

## Methods

### Chamber partitioning experiments

A series of partitioning experiments were conducted in a 20 m3 Teflon environmental chamber. The experimental conditions were maintained at 25 ± 0.3 °C and RH < 1% or RH = 46 ± 1%. We followed the experimental procedures of Krechmer et al.31,42, which measured L/SVOCs partitioning to DOS particles, but with expanded seed types and new particle-phase instrumentation (Supplementary Fig. 1). First, single component seed particles were injected into a clean chamber, followed by the precursors of partitioning L/SVOCs (0.6–1.4 ppmv of 1-alkanols, and 4 ppmv each of NO and methyl nitrite). The α-pinene/O3 SOA as seed was formed by ozonolysis in a dark chamber 1 h before the injection of the partitioning probe compound precursors. After injection, by turning on the chamber UV black lights for precisely 10 s, the fast OH oxidation of the alkanols generated L/SVOCs at part-per-trillion by volume levels including hydroxynitrates (HNs), DHNs, CDHNs, and THNs31,42. The latter three more oxidized types of L/SVOCs were monitored in the gas phase by the NO3-CIMS36,42,54. In addition, we used EESI-MS to measure the appearance of condensed-phase DHNs and THNs. Separate analysis of the evolution of gas- and particle-phase concentrations allowed independent quantification of α for the same species. After the 10 s burst, the system was left unperturbed for 1–1.5 h, during which time the reaction products achieved equilibrium partitioning with the particles and chamber walls. Supplementary Table 1 lists the L/SVOCs that were measured by CIMS and EESI-MS and Supplementary Table 2 summarizes the experiments used for analysis.

### Gas-phase measurements

The gas-phase evolution of oxidation products was monitored by a NO3-CIMS36,54, located inside the chamber enclosure as described in Krechmer et al.31. A flow of 10 standard liters per minute (slpm) chamber air was delivered to the CIMS through a 0.6 m long electropolished stainless steel inlet. The concentric sample flow minimizes wall losses and does not show inlet memory effects for these semivolatile compounds42,54. The total residence time in the sampling inlet and ion source was <4 s. The gaseous products were detected as NO3 cluster ions at a time resolution of 1 s. Background signals were checked by flowing zero air to the inlet and instrument, but were generally negligible.

### Particle-phase measurements

The size distribution and number concentration of seeds and SOA were measured by a scanning mobility particle sizer (SMPS) consisting of an electrostatic classifier (TSI, 3080), differential mobility analyzer (TSI, 3081), and a condensation particle counter (TSI, 3775). The SMPS was placed inside the chamber enclosure and was operated under the same temperature and humidity as in the chamber so as not to alter partitioning states. The residence time of air inside the SMPS at 3 lpm sheath flow rate is 7.5 s, which is short and should have a limited effect on OA evaporation, by comparison to the timescales observed in our experiments. Also the SMPS will be effectively conditioned as its surfaces are coated with SVOC during the start of an experiment, limiting evaporation on the latter part of the experiment. Each scan was performed over 120 s within the diameter range of ~16–583 nm, with 15–25 s to return to the starting voltage, resulting in a time resolution of 135–145 s. Tests of slower scan rates (up to 300 s) showed no differences in the measured distributions versus those at 120 s.

The EESI source was used with the time-of-flight mass spectrometer to monitor particle-phase semivolatile compounds39,55. Air was drawn from the chamber at 3.8 lpm, of which 1 lpm passed through a gas phase denuder that removed gaseous VOCs and entered the EESI source (and 2.8 lpm were exhausted). The primary spray was generated from a solution of water–acetonitrile 1:1 mixture containing 100 ppm (by weight) sodium iodide (NaI). The collisions between particles and highly charged spray droplets dissolve particulate analytes, resulting in the formation of gas-phase ions (typically Na+ adducts). The measurement time resolution was also 1 s. The background of the measured compounds was determined by passing the ambient sample through a high-efficiency particle air filter, demonstrating an effective time response of ~6 s (Supplementary Fig. 11). Data analysis was conducted using DHN measurements for the five available seeded experiments (Supplementary Table 2) and THNs for the sucrose experiment. THNs were only measured at reliable S/N ratios for the sucrose-seeded EESI experiment after more extensive instrument tuning.

### Kinetic modeling

A box model that includes the condensation and evaporation of oxidized products to and from particles and chamber walls was used to calculate the accommodation coefficients and effective saturation concentrations $$\left( {c_{\rm{eff}}^ \ast } \right)$$. The model was modified from Krechmer et al.31,42 and was solved using the KinSim software within Igor Pro56. As shown in Supplementary Fig. 1, the reversible vapor–wall interaction is modeled dynamically using the first-order vapor wall loss rate coefficient $$\left( {k_{G \to W}} \right)$$, the vapor saturation concentration of the partitioning molecule (here c* estimated with SIMPOL57, referred to $$c_{\rm{SIMPOL}}^ \ast$$ hereafter), and the equivalent partitioning mass of the chamber walls (Cw, µg m−3). $$k_{G \to W}$$ and Cw were determined for our chamber by conducting the same oxidation reactions in the absence of particles42. The measured average $$k_{G \to W}$$ is 1.0 × 10−3 ± 20% s−1. Cw was calculated using initial and equilibrium gas-phase signals following the parameterization method in Krechmer et al.42 (Supplementary Fig. 3).

The rate of condensation of vapors onto particles depends on the suspended particle CS. We calculated CS using the following equation and the particle size distribution measured by an SMPS58,59:

$${\rm{CS}} = \mathop {\smallint }\limits_0^\infty r \cdot F_{\rm{FS}}\left( r \right) \cdot N\left( r \right) \cdot dr,$$
(2)

where r is the particle radius, N(r) is the particle number size distribution, and FFS(r) is the Fuchs–Sutugin correction for gas-phase diffusion in the transition regime59:

$$F_{\rm{FS}} = \frac{{K_n + 1}}{{0.377K_n + 1 + \frac{4}{3}\alpha ^{ - 1}K_n^2 + \frac{4}{3}\alpha ^{ - 1}K_n}},$$
(3)

where Kn is the Knudsen number and α is the mass accommodation coefficient. In this case, α represents the accommodation of a specific gas-phase compound into a specific liquid or solid substrate, which is determined by fitting the simulated gas-phase/particle-phase concentration to the CIMS or EESI-MS measurements. Using CS, the actual rate coefficient of gases condensing on particles, $$k_{G \to P}$$, was calculated as58,59:

$$k_{G \to P} = k_{\rm{CS}} = 4\pi \cdot D \cdot {\rm{CS}},$$
(4)

where D, the molecular diffusion coefficients for studied organic nitrates, were estimated using Fuller’s semiempirical method for each species, which range from 5.9 to 7.9 × 10−6 m2 s−1 and average 6.8 × 10−6 m2 s−1 60,61,62. The CS was calculated for each SMPS scan (every 2 min), and then interpolated to the time base of the CIMS data (1 s).

The evaporation rate coefficient $$\left( {k_{P \to G}} \right)$$ of condensed products from the aerosol was determined using partitioning theory:

$$k_{P \to G} = k_{G \to P}\frac{{\overline {MW} \gamma p_{L,i}^0}}{{RT}}\frac{1}{{C_{\rm{OA}}}} = k_{G \to P}\frac{{c_{\rm{eff}}^ \ast }}{{C_{\rm{OA}}}}\frac{{\overline {MW} }}{{MW_i}},$$
(5)
$$c_{\rm{eff}}^ \ast = \frac{{MW_i\gamma p_{L,i}^0}}{{\rm{RT}}},$$
(6)

where cOA is the SMPS-measured aerosol organic mass concentration, a sum of organic seeds and SOA (assuming a density of 1.3 g cm−3 63), R is gas constant, $$\overline {MW}$$ is mole-average molecular weight of the absorbing phase, $$MW_i$$ is molecular weight of compound i, γ is activity coefficient, and $$p_{L,i}^0$$ is the saturation vapor pressure of pure compound i at temperature T. The effective saturation concentration $$c_{\rm{eff}}^ \ast$$ of the compound i in the specific aerosol mixture is determined from the model fitting31.

The particle-wall loss rate coefficient $$k_{P \to W}$$ was also considered in the model. We determined this rate by fitting an exponential function to the measured decay of the seed volume concentration before photooxidation, and then assuming the seed plus condensed SOA decay at the same rate through the experiment. Care was taken to not touch or rub the Teflon bag to avoid inducing static charges during experiments, which would change the particle loss rates64. A typical $$k_{P \to W}$$ value was 5 × 10−5 s−1, which corresponds to ~15% volume concentration loss in 1 h.

By fitting the simulated gas-phase/particle-phase concentration to the CIMS or EESI-MS measurements, we determined α and $$c_{\rm{eff}}^ \ast$$ of each compound for each experiment. The optimization of these two parameters is a nonlinear regression problem based on minimizing the sum of the squares of the residuals (χ2) between the logarithm of the modeled and observed species time series. This optimization was performed using the FuncFit built-in function in Igor Pro 7, which uses the Levenberg–Marquardt method. Since we conducted 2–3 CIMS experiments for a single type of seed (Supplementary Table 2), we fitted all the available experiments together (minimization of the total χ2 of all experiments with a certain type of seed) to reduce uncertainties caused by experimental variability (Supplementary Fig. 5). Note that when simulating gas-phase measurements we fixed $$c_{\rm{SIMPOL}}^ \ast$$ in the vapor–wall partitioning (as Cw was determined that way) while allowing optimization of $$c_{\rm{eff}}^ \ast$$ to optimize the vapor-particle partitioning. For experiments with EESI-MS data, the particle-phase species time series alone cannot be used to constrain both α and $$c_{\rm{eff}}^ \ast$$ since the total or starting concentrations of the partitioning compounds were unknown without CIMS measurements. In these cases, α was the only fitted parameter while $$c_{\rm{eff}}^ \ast$$ of each species was constrained to the value determined from the CIMS experiments for the same seed. The uncertainties of the retrieved parameters were calculated by combining in quadrature those due to parametric uncertainties (2σ) with those of the statistics of nonlinear regression (2σ) (see “Methods” section).

### Quantification of uncertainties for fitted α and c*eff

For the model-determined α and $$c_{\rm{eff}}^ \ast$$, we report their uncertainties by combining uncertainties that vary by partitioning species and by seed type, including the 2σ uncertainties due to the parameters used in modeling and the fitting error of the nonlinear regression (2σ). For the first type of uncertainties, we explored the effects of the following parameters: gas-phase molecular diffusion coefficient D (±30%), SMPS measured number size distribution N(r) (±20%), OA mass concentration cOA (±30%), Cw (±100%), the rate of particle-wall loss (±100%), and the vapor wall loss rate $$k_{G \to W}$$ (±20%). We confirmed that $$k_{G \to W}$$ and the rate of particle-wall loss have a negligible impact on α and $$c_{\rm{eff}}^ \ast$$ (<1%) and thus did not include them in the uncertainty analysis. According to Eqs. (2)–(4), the values of α increase with smaller D, N(r), and Cw. So we estimated upper and lower bounds of a typical range of α with D, N(r), and Cw decreased and increased at the same time by their own uncertainties. Similarly, for $$c_{\rm{eff}}^ \ast$$ we estimated an uncertainty of 35% by combining those of cOA and $$k_{G \to W}$$, while other parameters have negligible impact (<1%). The overall error was then derived by combining in quadrature the uncertainties due to the above parameters and the 2σ error from nonlinear regression between the modeled and the observed time series.