Capturing the Relative‐Humidity‐Sensitive Gas–Particle Partitioning of Organic Aerosols in a 2D Volatility Basis Set

Aerosol water affects the physicochemical properties and mass concentration of organic aerosols (OA), but it is typically omitted by air quality, weather, and climate models. We compare two classes of simplified models to estimate the OA water uptake and gas–particle partitioning of organic compounds. One class uses a single‐hygroscopicity‐parameter (κ) approach while the other is based on the reduced‐complexity Binary Activity Thermodynamics (BAT) model. We show that a BAT‐based two‐dimensional volatility basis set (VBS) model always predicts a higher OA mass concentration at elevated relative humidity (RH), for example, ∼16% at 80% RH, than any variation of the κ‐based method considered—even when BAT‐VBS predicts a lower water uptake. The main reason being that the BAT‐VBS model captures variations in effective saturation mass concentration of organics (C*) with RH, a feature that other VBS methods lack. The BAT‐VBS framework offers an efficient, RH‐sensitive treatment for reduced‐complexity OA modeling.

. Detailed process-level thermodynamic models capable of predicting particle-phase nonideality, such as the Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) thermodynamic model (Zuend et al., 2008(Zuend et al., , 2011)), are currently not implemented in chemical transport models, like GEOS-Chem (Pye et al., 2010), or detailed indoor air quality models, like the Indoor Model of Aerosols, Gases, Emissions, and Surfaces (Cummings & Waring, 2019;Cummings et al., 2021;Shiraiwa et al., 2019;Waring, 2014), because they require molecule-level chemical structure information that is usually not available.Such detailed thermodynamic models can only estimate nonideality (expressed by activity coefficients) when every functional group present in an aerosol system is defined and an interaction parameter exists for every pair of functional groups present (Yin et al., 2022).
The one key species that may significantly alter the thermodynamics of mixing among constituents in an OA phase is water.As the relative humidity (RH) increases, eventually water becomes a significant fraction of the mass of the OA (for at least slightly hygroscopic OA), impacting the gas-particle partitioning of semivolatile organic compounds (SVOCs) (Pankow & Barsanti, 2009) and aqueous-phase chemistry (DeCarlo et al., 2018;Ervens et al., 2011;Lim et al., 2013;Surratt et al., 2007;Volkamer et al., 2007) as well as other properties such as particle viscosity (Shiraiwa et al., 2011).In addition, modeling aerosol water is important for understanding the impact of aerosols on climate (Rastak et al., 2017).Without focusing on any specific set of experimental OA data, the objective of this work is to compare efficient, reduced-complexity methods currently in use for estimating OA-associated water uptake and to provide a detailed overview of its impact on aerosol composition, including nonideal mixing thermodynamics and the gas-particle partitioning of organics.We further show that the level of detail accounted for by two-dimensional volatility basis set (2D-VBS) models can have important consequences for the quality of the prediction of the OA mass concentration of organics as a function of RH.

Single-Parameter Hygroscopicity Model
One of the most common approaches to estimate the ability of OA to absorb (and release) moisture is through κ-based hygroscopicity models (Cummings, 2021;Cummings et al., 2020;Kakavas et al., 2022;J. Li et al., 2020;Pye et al., 2017).Petters and Kreidenweis (2007) introduced a simplified, single-parameter representation of the hygroscopicity of organic and inorganic materials (κ).Representative values of κ for single components or a mixture of organic compounds can be determined by fitting hygroscopic growth factor data from measurements at elevated humidity levels, typically taken in the range from 80% to 90% RH (Cappa & Jimenez, 2010;Duplissy et al., 2011;Raatikainen et al., 2010).Such κ values tend to be smaller than those derived from cloud condensation nuclei (CCN) activation data under supersaturated water vapor conditions (Lambe et al., 2011;Massoli et al., 2010), the reasons for which are understood (Rastak et al., 2017).To estimate effective κ values, and thereby water uptake by OA, we considered two different parameterizations, both of which are functions of the mean elemental oxygen-to-carbon ratio (O:C).The first one being the linear κ-O:C relationship proposed by Lambe et al. (2011) that is based on CCN-derived hygroscopicity measurements of laboratory-generated secondary organic aerosol (SOA): where   OA  is the overall OA hygroscopicity parameter; and O:C is the average O:C of the OA particle-phase organic mass distribution.
The second parameterization is based on published hygroscopicity data by Duplissy et al. (2011) determined from hygroscopic (diameter) growth factor measurements at a solution water activity of 85% (GF(a w = 0.85)) for smog chamber data and 95% (GF(a w = 0.95)) for field data.It utilizes a fitted sigmoidal relationship between   OA  and O:C that we have established as follows: More information about this approach can be found in Text S1 in Supporting Information S1.
Hereafter, we will use the short-hand notations "κ-linear" and "κ-sigmoidal" to refer to the associated 2D-VBS equilibrium partitioning model variants using such single-hygroscopicity-parameter method for the prediction of OA water uptake. 10.1029/2023GL106095 3 of 11

Binary Activity Thermodynamics Model
An alternative, more detailed approach for predicting the aerosol water content involves the application of a thermodynamic equilibrium model.The Binary Activity Thermodynamics (BAT) model developed by Gorkowski et al. (2019) is a reduced-complexity activity coefficient model which enables accounting for the nonideal mixing behavior in aqueous organic solutions as a function of water content (or, indirectly, RH).BAT is characterized and evaluated against a more robust thermodynamic model in detail elsewhere (Gorkowski et al., 2019), and also outlined in Text S2 in Supporting Information S1.BAT can be coupled with an equilibrium gas-particle partitioning framework, for example, a VBS.One of the attractive features of determining OA equilibrium partitioning with the BAT-VBS method is its thermodynamically sound and efficient framework for computing the water uptake and related feedback on the OA mass concentration of organics, which as discussed in Section 3.1.1,is shown to be important.
Thermodynamic models offer the necessary outputs to establish the impact of nonideal mixing in aerosol phases on gas-particle partitioning.In the case of OA consisting of one liquid phase, the gas-particle partitioning coefficient, also known as the effective saturation mass concentration, of each organic component j is given by (Gorkowski et al., 2019;Zuend & Seinfeld, 2012): where   *  is the effective saturation mass concentration, can be recognized as the mass-concentration-weighted harmonic mean molar mass of the OA phase.C OA represents the summation over all components involved (Zuend et al., 2010): where   OA  and   OA  are the cumulative organic mass concentration and the mass concentration of water in the OA phase.
As shown in Gorkowski et al. (2019)  In this work, BAT was coupled with the 2D-VBS described in Texts S4 and S5 in Supporting Information S1 to predict the OA mass concentration of organics and water.Note that hereafter, for brevity, we use the notation "BAT" or "BAT predictions" to refer to predictions using the BAT-based 2D-VBS equilibrium partitioning model.

Organic Aerosol Systems
Three OA compositions representing different archetypal OA factors were used as test systems to compare the two classes of water-sensitive partitioning schemes in this work: a hydrocarbon-like OA (HOA) system, an oxygenated OA (OOA) system, and a 1:1 mixture (by mass) of the HOA and OOA systems, referred here as HOA+OOA.
The distribution of the total (gas-phase plus particle-phase) organic mass concentration among the bins of the 2D space (Texts S4 and S5 in Supporting Information S1) for each OA factor were obtained from published volatility distributions (Cappa & Jimenez, 2010) and O:C measurements (Canagaratna et al., 2015) that were normalized to yield 5 μg m −3 of dry OA mass concentration (at RH = 0%).The distribution of mass, illustrated with a heatmap in Figure 1, can be represented in terms of the fraction, with respect to the system's total, that corresponds to each bin of the 2D space.The histograms above and to the right of each 2D space show the column and row (fraction) totals, respectively.The exact mass concentration value per 2D bin can be found in Tables S3-S8 in Supporting Information S1.

10.1029/2023GL106095
4 of 11 HOA is a proxy for fresh anthropogenic emissions; most of its total (gas-phase plus particle-phase) organic mass concentration can be found in the higher volatility bins (higher   *  ) of the 2D-VBS (Figure 1a).OOA is a proxy for aged SOA outdoors and/or other types of highly oxidized OA; most of its total organic mass concentration is distributed within the high-polarity bins (high O:C) of the 2D-VBS (Figure 1c).The 1:1 mixture, HOA+OOA, has intermediate volatility and polarity characteristics (Figure 1b).See Text S5 in Supporting Information S1 for more details about the 2D-VBS distributions of the three OA systems.

Organic Aerosol Mass Concentration
The outcomes of the BAT and κ-based models for the systems described in Section 2.3 are presented in terms of predicted OA mass concentrations of organics (Figure 2a) and OA water uptake (Figure 2b) as functions of RH (0% ≤ RH ≤ 95%).An equivalent κ is calculated by BAT and compared to the κ values inputted to the linear  for dry conditions at a temperature (T ) of 298.15 K.The polarity axis is represented by the elemental oxygen-to-carbon ratio (O:C j ).The heat map shows in shades of red the contribution (%) of each individual 2D bin to the total organic mass concentration of the system.The histograms above and to the right of each 2D space show the column and row totals, respectively.The HOA, HOA+OOA, and OOA systems have a total organic mass concentration of 20.2, 14.1, and 8.0 μg m −3 , respectively.By design, the three systems have a common equilibrium organic OA mass concentration of 5 μg m −3 for dry conditions at T = 298.15K. and sigmoidal κ models (Figure 2c).Differences in κ-based model performance are also cast relative to BAT in Figure S3 in Supporting Information S1.The following three subsections detail various model predictions and the differences between them.

BAT-VBS Predictions
The OA mass enhancement due to an increase in RH can be thought of as a coupled, iterative partitioning process: (a) absorption of water by a hygroscopic particle amplifies the overall mass in the absorbing (liquid) phase, which (b) decreases the OA mole fractions of all present organic compounds, impacts their activity coefficients and, via modified Raoult's law (Eq.( S8)), also equilibrium     values, which (c) drives additional partitioning of SVOCs to the OA, (d) resulting in a further increase of C OA , leading to adjustments of the component mole fractions and subsequently (via step 1) of the water content.This sequence of steps repeats until a new equilibrium state is found.
With an increasing RH, BAT predicts similar organic OA mass concentrations for both HOA and OOA, with the OOA mass exceeding the HOA mass when RH > ∼20% (Figure 2a).This similarity in predicted RH impact might seem counter-intuitive, since these systems have opposite polarity characteristics (Figures 1a and 1c).HOA particles contain more volatile compounds but are less polar (i.e., less hydrophilic).So, a substantial fraction of the total organic mass concentration of the HOA system should reside in the gas phase, and the increase in OA mass concentration due to the absorption of some water should be rather limited.OOA particles exhibit less semivolatile behavior and are more polar (i.e., more hydrophilic).Thus, all else being equal, one would expect the potential for a substantial OA mass concentration enhancement with RH in the OOA case, but not for the HOA system.If equilibrium conditions are perturbed by introducing aerosol water, the increased sorbing mass facilitates the condensation of SVOC gases which further increases the OA sorbing mass and enhances water uptake.This self-amplification effect continues until a new equilibrium is established.In reality, HOA and OOA have distinct main amplification mechanisms increasing the sorbing mass that BAT captures, as further discussed below.
In the case of HOA, the predicted increase in organic OA mass concentration with RH is mainly controlled by the enhanced gas-to-particle partitioning of semivolatile organic material (   *  of 10 0 -10 2 μg m −3 ), here triggered by a modest water uptake from the lowest volatility organic mass (   *  of 10 −7 -10 −1 μg m −3 ) that is condensed.The presence of OA-associated water increases C OA which promotes the condensation of organics.A self-amplification effect of semivolatile organics then takes place, where the partitioning of semivolatile organic material to the particle phase is stimulated and continues attracting modest amounts of water, thereby increasing the equilibrium aerosol mass fraction (AMF) of each organic component (Eq.(S10)).Due to the greater amount of total semivolatile organic mass in HOA, complete gas-phase depletion does not occur, and some semivolatile and intermediate-volatility organics (   *  of 10 0 -10 3 μg m −3 ) remain in the gas phase even at high RH levels.BAT predictions of water uptake follow expectations based on the mean O:C.The most water uptake occurs for OOA, followed by HOA+OOA, and then HOA.In other words, since the modeled OOA exists entirely within higher O:C bins (O:C j of 0.5-0.9)(Figure 1c), its water affinity is greater than that of the other two considered systems, resulting in higher predicted water uptake (Figure 2b).For OOA, the main source of variation in OA mass concentration with increasing RH comes from the addition of water that forms a bigger aqueous absorption medium, increasing C OA .This effect results in an enhanced transfer of polar SVOCs to the particle phase as the equilibrium AMF of each organic component increases (Eq.( S10)).Because the semivolatile (mass) fraction for OOA is lower than that of HOA, the self-amplification effect of SVOCs is not as substantial.
The HOA+OOA system, having volatility and polarity properties between those of the HOA and OOA systems (Figure 1b), benefits from both sources of OA amplification, and thus yields a higher organic OA mass concentration than either HOA or OOA, individually.
The variation of κ with particle composition as a function of RH predicted by BAT (Figure 2c) is consistent with hygroscopicity tandem differential mobility analyzer and CCN counter measurements (Pajunoja et al., 2015;Rastak et al., 2017).
To contrast with and better understand the findings presented in Figure 2, we also generated three related artificial OA systems, each of which having identical volatility profiles and dry mass concentrations, with differences only in the polarity dimension (Tables S9-S11 in Supporting Information S1).For those systems, as expected, BAT predicts the more polar system to have both a higher water content and a greater organic OA mass concentration 10.1029/2023GL106095 6 of 11 at any RH > 0% (Figure S4 in Supporting Information S1).Water uptake amplifies the mass of the absorption medium, which triggers a cascade effect that promotes the condensation of semivolatile organic species to the OA.Since the three artificial systems have the same total organic mass concentration in their semivolatile bins, the difference in partitioning behavior is only governed by a difference in particle-phase water content.However, in real OA systems, more polar systems are frequently associated with a smaller mass concentration of semivolatile compounds (Cappa & Jimenez, 2010).

Predictions by κ-Based 2D-VBS Models
The OA-associated water predicted by the κ-based models strongly depends on the representative hygroscopicity parameter assigned to the OA system, which in this work, was calculated as a function of the average particle-phase O:C.However, there are alternative κ-based models that estimate hygroscopicity based on the OA solubility distribution parameterized by O:C (Nakao, 2017) instead of using the average particle-phase O:C.This method assumes that water uptake is directly proportional to κ, according to Eq. (S2).Like the BAT-based predictions, since OOA has the highest O:C, its effective κ value is the highest (Figure 2c) and so is its predicted OA-associated water mass concentration at any RH value, followed by the water uptake of HOA+OOA, and lastly HOA (Figure 2b).
In general, the organic OA mass concentration predicted by the κ-linear model (Figure 2a) seems to follow the opposite trend of the OA-associated water uptake (Figure 2b), suggesting that the overall feedback effect due to water uptake is less significant than in the case of the BAT predictions.In other words, the κ-predicted enhancement of OA through the presence of water in the particle does not seem to affect the partitioning behavior of organic species to the same extent as suggested by BAT.The main reason for the differing partitioning behavior between the two classes of models is discussed in Section 3.2.Here, the organic OA mass concentration is thus mainly controlled by the amount of total organic material, especially the amounts distributed among the semivolatile bins.As such, in the case of the κ-linear model, HOA results in the highest organic OA mass concentration, followed by HOA+OOA and OOA (Figure 2a).At RH > 0%, the κ-sigmoidal model predicts an organic OA mass concentration that stays close to that at dry conditions for HOA.The small amount of water content of HOA particles predicted with that model (Figure 2b) implies a partitioning tendency of organic species that does not change with RH.
A system of lower mean O:C (O:C < 0.5) is shown to be particularly sensitive to the choice of dependency of the hygroscopicity parameter on the O:C.For example, both the organic OA mass concentration (Figure 2a) and OA-associated water mass concentration (Figure 2b) seem to vary considerably for HOA depending on the O:C-based relation used to estimate   OA  .The κ-linear function predicts a distinctly higher hygroscopicity than the sigmoidal function for an O:C below 0.45 (see Figure S2 in Supporting Information S1 for a comparison); for example, for an O:C of 0.2, the two models predict   OA  = 6.6 × 10 −2 (linear) and   OA  = 7.7 × 10 −4 (sigmoidal).As a result, the water uptake associated with HOA (mass-weighted mean O:C of ∼0.13) is close to 0.0 μg m −3 when the κ-sigmoidal model is applied, whereas the OA-associated water is comparable to that of OOA with the κ-linear model.The sensitivity on the type of   OA  fit is less pronounced for OOA and HOA+OOA (Figures 2a  and 2b), since the linear and sigmoidal κ models predict similar values when the mean O:C is about 0.5.In particular, HOA + OOA has a considerable amount of total organic mass concentration above and below the O:C j of 0.5 (Table S4 in Supporting Information S1), leading to a mean O:C close to that value.Therefore, the organic OA and OA-associated water mass concentrations show little discrepancy when using either the linear or sigmoidal κ functions.The OOA system contains all of its organic mass at the O:C j levels of 0.5 and above (Table S5 in Supporting Information S1), corresponding to the O:C range in which the hygroscopicity models diverge again (Figure S2 in Supporting Information S1).In this case, the OOA water uptake predicted by the κ-sigmoidal function is slightly larger than in the case of the κ-linear function (Figure 2b).
Given that hygroscopicity depends only on the mean O:C of the OA system (Equations 1 and 2), which does not vary significantly with RH,   OA  appears to be unaffected by RH as well (Figure 2c).Since OOA has the highest O:C, it is assigned the highest hygroscopicity, followed by HOA+OOA and HOA.

Comparison Among Water Uptake Models
Since BAT predicts water uptake based on the molecular interactions between organics and water, it does not rely on κ parameters to model aerosol water content.BAT-derived κ values are calculated according to Eq. (S1) to allow for a comparison with the values from the two κ-based models; see Figure 2c.With the exception of 10.1029/2023GL106095 7 of 11 HOA, for which the κ-sigmoidal function predicts the lowest   OA  and subsequent water uptake among all models, OOA and HOA+OOA are predicted to have a higher water affinity when using the κ-based models (Figure 2b).An interesting result emerges from the comparisons shown in Figure 2. On one hand, the κ-based models typically predict a higher water uptake with RH than BAT (in particular for HOA+OOA and OOA).For the HOA+OOA system, the κ-based models overestimate OA water mass by ∼48% at 50% RH and ∼117% at 80% RH.On the other hand, BAT predicts a greater organic OA mass concentration enhancement with RH than the κ-based methods.For the HOA+OOA system, κ-based models underestimate organic OA mass concentration by ∼10% at 50% RH and ∼16% at 80% RH.This might seem counter-intuitive since a greater water content should translate into a larger aqueous absorbing medium, which further promotes the condensation of organic species.We analyze and discuss the reasons for the greater organic OA mass enhancement with RH predicted by BAT in the following section.
A key reason is that the BAT-VBS model accounts for a RH-dependent feedback on gas-particle partitioning of semivolatile organics, an effect that is neglected by the simpler single-parameter hygroscopicity approach.

Effective Volatility of Organics as a Function of RH
Two factors were identified as driving the divergent predictions from BAT compared to the κ-based models: (a) nonideal mixing (i.e., activity coefficients change as a function of water content), which affects both     (Eq.( S8)) and   *  (Equation 3), and (b) the change in OA composition, which affects the mean OA molar mass.Both factors are only considered by BAT.
The top panel of Fig. S6 in Supporting Information S1 illustrates the variation of the BAT-predicted mole-fraction-based binary activity coefficient (γ j ) with RH for each selected organic surrogate compound (or bin) in isolation (for binary aqueous mixtures), with each compound having a fixed O:C j .The bottom panels show the corresponding binary mixture mole fraction of water (x w ).A more polar organic component (e.g., O:C j = 0.9) has a higher implied water affinity.When RH < 90%, γ j decreases as RH increases above dry conditions, meaning that thermodynamic mixing between the organic species and its associated water becomes more favorable.Above ∼90% RH, γ j values begin to rise with increasing RH.At that point, the particle phase is mainly composed of water, so molecular interactions between different species become less favorable both for water and the organics.This behavior is even more pronounced and occurs at a slightly lower humidity for moderately polar organic components (O:C j ≈ 0.5).Components of lower polarity (O:C j ≈ 0.1) tend to uptake far less water (lower x w ), so their γ j values remain close to unity, but would increase substantially if these organics were forced to mix at a higher water mole fraction, which would result in liquid-liquid phase separation (Gorkowski et al., 2019;Shiraiwa et al., 2013;Zuend et al., 2010).
As water uptake increases with RH, the mass-concentration-weighted harmonic mean molar mass of the OA system (see Equation 3) decreases because water has a substantially lower molar mass than particle-bound organics (Figure S7 in Supporting Information S1).The relationship between the curves shown in Figure S7 in Supporting Information S1 is correlated with the polarity of the OA system.OOA attracts more water and contains more organic compounds of lower molar masses than the other two OA systems, so its weighted harmonic mean molar mass is the lowest.HOA has the highest weighted harmonic mean molar mass because it contains more organic compounds of higher molar masses and attracts less water than the other two OA systems.
The findings presented in Figure 2 confirm that at elevated RH levels, BAT predicts a lower water uptake, yet a greater enhancement in OA organic mass concentration than any variant of the κ-based approach, in particular for the OOA and HOA+OOA systems.This at-first counter-intuitive behavior occurs because BAT implicitly accounts for the RH-dependency of   *  , according to Equation 3. In contrast, the common κ-based approach assumes fixed   *  bins as part of the 2D-VBS axis, independent of RH. Figure 3 summarizes the combined effects of binary activity coefficients of organics that deviate from unity and the decrease in mass-concentration-weighted harmonic mean molar mass on   *  as a function of RH.The two terms that contribute to the variation of   *  with RH are visualized in Figures S8 and S9 in Supporting Information S1.Changes in the mass-concentration-weighted harmonic mean molar mass drive changes in   *  more substantially than deviations from ideal mixing (γ j ≠ 1), yet both factors play a role.For example, at RH = 80%, γ j of SVOCs (   *  = 10 0 μg m −3 at T = 298.15K) decreases by up to ∼53.4% (for O:C j = 0.9) whereas the weighted harmonic mean molar mass of the system is reduced by ∼68.5% with respect to the corresponding values at dry conditions (Figure S8 in Supporting Information S1).For different OA systems, it is possible that nonideal mixing is the main factor driving changes in   *  (Chang & Pankow, 2010).When γ j < 1.0, both terms will contribute to the decrease in   *  as RH increases.Consequently, BAT predicts a higher organic OA mass concentration at any elevated RH level compared to a κ-based method, which uses constant dry-state-based   *  defined by the fixed resolution of the 2D-VBS (only accounting for temperature dependence of   *  ).The shift in   *  is more important for organics of higher O:C j and lower   *  at dry conditions (RH = 0%), since these species promote the absorption of more water as RH increases (Figure 3).As a consequence, OOA, which is the most polar system, has more organic OA mass concentration than HOA when RH > ∼20% (Figure 2a).The resulting impact on the organic OA mass concentration is dominated by the partitioning of polar SVOCs.In contrast, a decrease in   *  with increasing RH does not directly affect the partitioning behavior of LVOCs, since their reservoir amounts in the gas phase are negligible (i.e., all LVOCs are already particle-bound).For SVOCs with appreciable mass residing in both the gas and particle phases, a decrease in effective volatility can substantially impact organic OA mass concentrations.
In the case of SVOCs (   *  ≈ 10 0 -10 2 μg m −3 at T = 298.15K), the relative change in activity coefficients becomes comparable to the relative change in mean molar mass when organic species have a higher O:C j (Figure S9 in Supporting Information S1).As such, the need for an activity coefficient model like BAT is critical for predicting the allocation of mass of SVOCs between the gas and particle phases.BAT provides an efficient yet thermodynamically sound way of estimating the RH-induced shift in effective volatility, which as demonstrated, causes a substantial increase in organic OA mass concentration.We argue that this effect can and should be accounted for in VBS-type OA partitioning schemes, in addition to the usual temperature-driven variations in   *  .The RH-dependency of the OA effective volatility distribution is also represented in more robust thermodynamic models such as AIOMFAC (Amaladhasan et al., 2022) and supported by measurements of particle-phase composition (Surdu et al., 2023).As particle water content increases, the mass concentration of SVOCs and intermediate-volatility organic compounds in the OA increases since their effective volatility is reduced.Even though extremely low-volatility organic compounds and LVOCs experience the same effect, their OA mass concentration seems to be unaffected by RH given that their volatility is low, and they remain in the particle phase even at dry conditions, consistent with theoretical work by Pankow (2010).

Conclusion
In this study, two classes of methods to account for OA water uptake have been compared, which highlights differences in related feedback effects on OA mass concentration.A κ-based method is attractive due to its relatively simple water uptake treatment, and it improves over a "dry" 1D or 2D-VBS scheme.However, a more rigorous thermodynamic model like BAT demonstrates why we expect additional feedback effects from water uptake on the organic component partitioning, aside from enhancing C OA .A thermodynamic activity coefficient model, coupled with an equilibrium gas-particle partitioning model, can capture the variation of effective volatility of organic species with RH, a feature that the κ-based method is completely lacking.We showed that, at any RH > 0%,   *  is expected to be lower than at dry conditions, driving more semivolatile organic mass into the particle phase.As a result, BAT predicted a higher organic OA mass concentration than any variation of the κ-based method for the OA systems studied.
Due to BAT's computational efficiency (see quantitative analysis in Text S10 in Supporting Information S1), adequate physicochemical representation and accuracy (Gorkowski et al., 2019), and due to its flexibility in terms of the relatively simple input requirements, the integration of a 2D BAT-VBS framework within commonly used equilibrium gas-particle partitioning schemes could be of interest to the indoor and outdoor aerosol modeling communities.In particular, BAT is of use in applications in which RH exceeds 40% and may vary substantially.Satellite observations from the Atmospheric Infrared Sounder suggest that monthly mean RH levels tend to be greater than 40% near the surface (Gettelman et al., 2006).Regarding indoor environments, maintaining RH between 40% and 60% is optimal for human health (Ahlawat et al., 2020).Furthermore, BAT can be used in

Figure 2 .
Figure 2. Predictions of (a) organic organic aerosols (OA) mass concentration  (  OA  ) , (b) OA-associated water mass concentration  (  OA  ) and (c) effective OA hygroscopicity  (  OA  ) as a function of relative humidity.By design, the three systems have an organic OA mass concentration of 5 μg m −3 at dry conditions.The HOA, HOA+OOA, and OOA systems have total organic mass concentrations of 20.2, 14.1, and 8.0 μg m −3 , respectively.Predictions by the Binary Activity Thermodynamics model, the hygroscopicity model based on a linear   OA  -O:C relationship, and the hygroscopicity model based on a sigmoidal   OA  -O:C relationship are shown in solid,

Figure 1 .
Figure 1.Distributions of total (gas-phase plus particle-phase) organic mass concentration of binned 2D volatility versus polarity spaces for the (a) HOA, (b) HOA+OOA, and (c) OOA systems.These distributions were derived from the organic aerosols (OA) factors defined in Cappa and Jimenez (2010).The volatility is represented by the base-10 logarithm of the effective saturation mass concentration  (  *  )for dry conditions at a temperature (T ) of 298.15 K.The polarity axis is represented by the elemental oxygen-to-carbon ratio (O:C j ).The heat map shows in shades of red the contribution (%) of each individual 2D bin to the total organic mass concentration of the system.The histograms above and to the right of each 2D space show the column and row totals, respectively.The HOA, HOA+OOA, and OOA systems have a total organic mass concentration of 20.2, 14.1, and 8.0 μg m −3 , respectively.By design, the three systems have a common equilibrium organic OA mass concentration of 5 μg m −3 for dry conditions at T = 298.15K.

Figure 3 .
Figure 3.Comparison between a water-sensitive effective saturation mass concentration  (  *  (RH) ) , as predicted by the Binary Activity Thermodynamics model, and a constant "dry" effective saturation mass concentration  (  *  (dry) ) , used by the discussed κ-based methods, as function of RH.Each shaded region depicts the relative deviation based on 10 organic components of the same O:C j but distinct dry volatilities  (  *  (dry) ) .The blue envelope includes organics of O:C j = 0.8 and the green envelope encompasses organics of O:C j = 0.2.For each envelope, the volatility increases from the lower boundary of   *  (dry) = 10 −7 μg m −3 to the upper boundary of   *  (dry) = 10 3 μg m −3 .
•,sat the pure-component saturation mass concentration, γ j the mole-fraction-based activity coefficient, and M j the molar mass of organic component j.C OA is the total OA mass concentration, while