Additive Water Uptake of the Mixtures of Urban Atmospheric HULIS and Ammonium Sulfate

The hygroscopicity of atmospheric aerosols affect the global climate and human health. However, the hygroscopic behavior of mixtures of inorganic salts and organics in atmospheric aerosols have not been well characterized for ambient complex organic mixtures. Here, the hygroscopic growth of humic‐like substances (HULIS), which represent the complexity of organic aerosol compounds, from urban aerosols and their mixtures with ammonium sulfate were investigated with measurements from a hygroscopicity tandem differential mobility analyzer and model analyses. The Zdanovskii–Stokes–Robinson (ZSR) relationship, which assumes that the water uptake of each component is additive, was examined for the mixtures. The dependence of the hygroscopicity parameters (κ) of the mixtures on the volume fraction of HULIS is generally represented by the ZSR relationship with the deviations of κ on average of 16% (4%–27% in different mixing ratios), and 0.03 (0.02–0.04) on absolute basis. An assumption of asphericity for the dry particles reduced the deviations (14%). Approximations for the surface tension depression by surfactants and surface‐bulk partitioning were predicted to account for the deviations to a small extent. Furthermore, a thermodynamic model for simplified compound systems showed that the non‐ideality of the solutions potentially explained the deviations from the ZSR relationship. The results of this study support the use of the ZSR relationship for organic‒inorganic mixtures as a practical approximation in atmospheric models, provide a guide for the uncertainty associated with this approximation, and suggest directions for future studies.


Introduction
The hygroscopicity of atmospheric aerosols, that is, the ability to absorb water vapor, can impact Earth's radiative balance by directly altering the particle optical properties and indirectly influencing cloud formation (McFiggans et al., 2006;Titos et al., 2016).In addition, hygroscopicity affects the formation and alteration of aerosols through aqueous-phase processes in aerosols.Also, the hygroscopicity could affect the adverse effects of aerosols on human health by influencing the deposition of particles in the respiratory system (Peng et al., 2020;Swietlicki et al., 2008;Titos et al., 2016).Inorganics and a myriad of organics are internally mixed in atmospheric aerosols, and both are thought to contribute to the hygroscopicity of aerosols to various degrees (Kuang et al., 2020;Nguyen et al., 2016;Petters & Kreidenweis, 2007).
An important but unresolved question regarding the contributions of organic components to aerosol hygroscopicity is whether there is a synergistic effect for organic and inorganic components as a result of their interactions in the mixtures.This question is fundamental for estimates of aerosol liquid water and cloud condensation nuclei (CCN) in modeling and field-based studies of the hygroscopicity of organic aerosols (OA).
The hygroscopicity of organic-inorganic mixed particles are generally predicted with the Zdanovskii, Stokes, and Robinson (ZSR) relationship, which calculates the total water content in a particle as the sum of the water taken up by each component with no interactions between the components (Petters & Kreidenweis, 2007;Stokes & Robinson, 1966;Zdanovskii, 1948).Several studies have examined the validity of this assumption for one or several organic acids mixed with inorganic salts (Table 1), suggesting that the hygroscopicity of the mixed particles was described appropriately with the ZSR relationship (Q.Liu et al., 2016;Wu et al., 2011;Zardini et al., 2008).Mixtures of ammonium sulfate and polyethylene glycol (PEG), an organic oligomer, were also found to follow the ZSR relationship (Bouzidi et al., 2020).In addition, hygroscopicity studies on mixtures of inorganic salts and fulvic acids (FA, including Nordic Aquatic FA (NAFA) and Suwannee River FA (SRFA)) and humic acid (HA), which are isolated from soil or water and have been used as model substances of water-soluble organic matter (WSOM), suggested that the ZSR relationship generally predicted hygroscopic growth (Svenningsson et al., 2006;Zamora & Jacobson, 2013).
However, inconsistencies between measurements and the ZSR relationship have also been reported for organicinorganic mixtures (Table 1).In theory, the ZSR relationship does not hold, for example, if the non-ideality of the solution and/or the dissolution of solutes is influenced by interactions between the organic and inorganic molecules.Chan and Chan (2003) found that hygroscopic growth of internally mixed aerosols comprising ammonium sulfate and NAFA or SRFA were higher than those estimated with the ZSR relationship.In addition, Kristensen et al. (2014) suggested that the ZSR relationship generally overestimated the CCN activities of NAFA-NaCl mixtures.Vaishya et al. (2013) analyzed marine aerosols online with an aerosol mass spectrometer (AMS) and a hygroscopicity tandem differential mobility analyzer (HTDMA) and found large deviations from the ZSR relationship.Their results suggested that organics or inorganics controlled the hygroscopicity of the particles when the organics or inorganics dominated.In the cases of the studies with NAFA or SRFA, given that their molecular weights and polarities have been suggested to be different from those of atmospheric humic-like substances (HULIS) (Graber & Rudich, 2006;Spranger et al., 2020), their representativeness as atmospheric organic mixtures is not clear.On the other hand, in the work by Vaishya et al. (2013), the difficulty in analyzing the ZSR relationship arose from the fact that the inorganic and organic compositions should not have been the same in the analyzed period.Moreover, the compositions and hygroscopicity of the atmospheric aerosols should not have been analyzed with identical aerosol fractions because of the different sizing methods used.In this sense, to test the additivity of water uptake by atmospheric organic-inorganic mixtures, an alternate approach should be taken to overcome the drawbacks of previous studies based on the representativeness of organic compositions and the identities of samples for multiple analyses.
Humic-like substances (HULIS) are atmospheric organic compounds extracted from the WSOM of atmospheric aerosol samples and are new model components of atmospheric OA with characteristics suitable for analyzing the additivity of water uptake.HULIS are ubiquitous in the atmosphere with relatively high average molecular weights (suggested to be 200-300 Da (Chen et al., 2016;Kiss et al., 2003)), and their hygroscopicity have been investigated for different environments (Dinar et al., 2007;Kristensen et al., 2012;Zheng et al., 2013).HULIS have complex compositions with moderate degrees of oxygenation among the OA fractions (Zhou et al., 2021) and constitute a large proportion of the water soluble organic matter in atmospheric OA (Chen et al., 2016;Zheng et al., 2013).Additionally, they contain multiple functional groups, unlike some of the simplified model systems used in previous studies (Q.Liu et al., 2016;Y. Wang et al., 2016;Zamora & Jacobson, 2013).Only limited amounts of inorganic species were found in HULIS aqueous solutions prepared by solid-phase extraction (Kristensen et al., 2012;Zheng et al., 2013), which makes it easy to prepare organic-inorganic mixtures in the laboratory as needed.These characteristics make HULIS a representative of complex atmospheric organic compounds and a suitable material for investigating the hygroscopicity for mixtures of inorganic and atmospheric OA in the laboratory.Although the fractional contribution of HULIS to the hygroscopicity of aerosols has been investigated (Zhou et al., 2022), there has not been an experimental study with a mixture of atmospheric HULIS and other chemical components.In addition, atmospheric HULIS extracts and mixtures with inorganic components can be subjected to offline analyses to compare the compositions and hygroscopicity for identical samples.
In this study, we analyzed the hygroscopic growth of internally mixed particles composed of atmospheric HULIS and inorganic salts under subsaturated water vapor conditions and tested the applicability of the ZSR relationship.Under subsaturated water vapor conditions, because of the high concentrations of solutes, the non-ideality of the solution, which represents different interactions among various solutes and solvents, may strongly affect the hygroscopic behavior of organic and inorganic mixtures (Roston, 2021).For these measurements, HULIS extracted from urban aerosol samples were mixed with ammonium sulfate (AS), which is abundant in many environments (J.Wang et al., 2008) with different proportions.The deviations from the ZSR relationship resulting from measurement uncertainties or biases (dry particle shapes, residual inorganics in HULIS solution), the presence of surfactants, and the non-ideality of the organic-inorganic solutions are discussed.

Sample Collection and Preparation of the Mixtures
Three total suspended particle (TSP) samples were collected on precombusted quartz fiber filters with a highvolume sampler on the roof of the Environmental Common Building, Nagoya University, Nagoya, Japan, from April to May 2018.Each filter was continuously sampled for 5 days (∼168 hr).Three punched pieces (diameter: 34 mm) from each filter sample were used for extraction of the HULIS solution, which followed the one-step method described in Varga et al. (2001).First, approximately 30 g of Milli-Q water in total was used to extract the WSOM via ultrasonication three times.The WSOM solution was filtered with a 0.2 μm PTFE filter.The pH of the WSOM was adjusted to around 2 (2.2 for all three samples) with an HCl solution to make HULIS compounds protonated and therefore retained by column, and then loaded on an Oasis HLB cartridge.The effluent was considered to contain highly hydrophilic matter and almost all inorganic salts (Gysel et al., 2004;Varga et al., 2001).The HULIS solution were then eluted from the HLB cartridge with 18 mL of methanol after drying the cartridge with N 2 .More details for the extraction procedures can be found elsewhere (Zhou et al., 2021).The O/C and H/C elemental ratios were obtained from offline aerosol mass spectrometer (AMS) analyses based on Canagaratna et al. (2015).The organic matter of the HULIS was quantified by adding an internal standard (phthalic acid) for the AMS analyses (Mihara & Mochida, 2011).Details of the AMS analyses were reported in a previous study (Zhou et al., 2021).
The HULIS solution was mixed with ammonium sulfate (AS) to produce nine different mass ratios of HULIS to AS.The density of the HULIS was estimated with the O/C and H/C ratios based on Kuwata et al. (2012).The volume-based OM proportions for each mixture were calculated and are presented in Table S1 of the Supporting Information S1.
In this study, the HULIS solutions were mostly free of inorganic salts because solid-phase extraction with an HLB column separates HULIS from inorganic salts.Although the presence of inorganic salts in the HULIS solutions cannot be ruled out, the amounts of inorganic salts in the HULIS solutions were found to be small in previous studies (less than 5% in volume in Kristensen et al. (2012) and Zhou et al. (2022)).The influence of the possible presence of inorganic salts will be discussed later.

Hygroscopic Growth Measurements
The hygroscopic growths of the HULIS, AS, and their mixtures were measured with an HTDMA.A schematic diagram for the instrumental setup is provided in Figure S1 of the Supporting Information S1.The solutions were nebulized into particles in pure cylinder air with a homemade atomizer.Downstream of the atomizer, the aerosols were first humidified to ∼90% relative humidity (RH) using a prehumidifier with a Nafion tube, followed by drying in two diffusion scrubbers with silica gel and molecular sieves.The use of a prehumidifier may improve the sphericity of dry particles, according to the measurement for AS (Zhou et al., 2022).Then, the dried polydisperse particles (RH < 6%) were transferred to the first differential mobility analyzer (DMA1) in HTMDA to classify the particles with mobility diameters of 100 nm.The HTDMA was operated in humidification and dehumidification modes.In the humidification mode, the first Nafion humidifier (humidifier 1, Figure S1 in Supporting Information S1) was bypassed, and monodisperse particles selected by DMA1 were humidified to 85% RH in the second humidifier (humidifier 2) and transferred to DMA2 coupled with a condensation particle counter (CPC) to analyze the hygroscopic growth of the particles.The residence time from the end of humidifier 2 to upstream of the DMA2 was estimated to be ∼11 s.In dehumidification mode, the monodisperse particles were first humidified to nearly 100% RH in humidifier 1 and then dehumidified to the target RH (85% and 70%) before being introduced into DMA2.Each sample was analyzed three times.All analyses were performed within the temperature range 23.0-24.5°C.The DMAs in the HTDMA were assessed with standard PSL particles.Pure AS was used to check the performance of the HTDMA routinely at 85% RH in both humidification and dehumidification modes.Particles with mobility diameters of 150 and 190 nm were also selected for DMA1 to assess the effects of doubly and triply charged particles.These multiply charged particles were calculated to comprise 5%-20% (on average of 9%) of the singly charged particles after considering the transfer function (Mochida et al., 2010;TSI Incorporated, 2006;Wiedensohler, 1988), and this was considered negligible in terms of its impact on the growth factor measurements (Text S4 in Supporting Information S1; Duplissy et al., 2009;Kawana et al., 2014).
The hygroscopic growth factor (g f ) is defined as the ratio of the mobility diameters of the humidified particles (d p ) to those measured under dry conditions (d p,dry ).The Twomey algorithm with consideration of transfer functions of the two DMAs was used to retrieve the distributions of the hygroscopic growth factors after humidification (Mochida et al., 2010).
Based on the κ-Köhler theory (Petters & Kreidenweis, 2007), the hygroscopicity parameter κ was calculated as: where a w is the water activity in the solution, V s is the volume of the solute, and V w is the volume of water.For an aqueous solution droplet, a w was calculated from: where S is the saturation ratio of water vapor, σ is the surface tension of the solution, M w is the molecular weight of water, ρ w is the density of water, R is the universal gas constant, and T is the temperature.The surface tension of pure water was assumed except for analysis of the surface tension (Kelvin) effect in Section 3.3.1.

The ZSR Relationship in the κ-Köhler Theory
The hygroscopicity represents a property of a component and is regarded as bulk hygroscopicity in this study.
From the ZSR relationship, the liquid water content of the particles was represented by the sum of the water volumes for the respective particle components.Thus, the bulk hygroscopicity should be additive for estimations of the ZSR relationship, as expressed in Equation 3.
where κ mix is the κ of the mixture, κ org and f org are the κ value and volume fraction of the organics, respectively, and κ inorg and f inorg are the κ value and volume fraction of the inorganics, respectively.
However, the hygroscopicity derived from the measurement of the hygroscopic growth of a particle is affected by the Kelvin effect (Equation 2).For a given relative humidity and temperature, a w is affected by the surface tension of the droplet and the particle diameter (d p ).The uncertainties affecting the ZSR relationship by a w are discussed in the next section.

Hygroscopicity of the Mixtures of HULIS and Ammonium Sulfate
The hygroscopicity parameters (κ) for the mixtures of HULIS and AS under different RH conditions and their averages are shown in Figure 1.The κ values of the mixtures decreased nearly linearly with increasing organic proportions.In the humidification mode at 85% RH, the κ of the HULIS was 0.047 ± 0.003, and the hygroscopicity of the AS was 0.57 ± 0.01.The κ of the HULIS was comparable to those from other urban areas (0.06 in Beijing (Zhou et al., 2022); 0.07 in Copenhagen (Kristensen et al., 2012)), and the κ for the AS was consistent with that calculated from E-AIM (0.54).The tendencies of the κ for the mixtures against the organic volume fractions were similar, although the regressions varied among the samples.Dashed lines represent the estimated κ based on the ZSR relationship.For sample 1, most of the κ values for the mixtures were represented well by the ZSR relationship.However, some points deviated from the ZSR relationship for sample 2, and all mixtures represented increased deviations for sample 3. The results from the humidification mode at 85% RH suggested that the κ values of the mixtures were generally fitted with the ZSR relationship, and the degrees of deviation varied among the samples.
The deliquescence point of AS is approximately 80% RH (Cruz & Pandis, 2000;Tang et al., 1977), which was lower than the RH from the measurements in the humidification mode.However, AS mixed with organics could alter the deliquescence point of the mixture (Wu et al., 2011).In addition, the hydration or dehydration that particles experienced could also affect the hygroscopic behavior of the particles (N.Wang et al., 2019).For these reasons, hygroscopic growth of the mixtures in the dehumidification mode at 85% and 70% RH was also analyzed.The κ values for the HULIS-AS mixtures in these conditions were similar to the values in the humidification mode that showed a nearly linear relationship, where samples 1 and 2 showed good linear regressions and sample 3 showed larger deviations.Because similar hygroscopic behaviors were observed under different RH conditions, the κ values for the three different RH conditions were averaged and are presented in Figure 1.These results showed that deviations from the ZSR relationship varied among the samples, suggesting that organic compounds that broke the ZSR relationship were present in atmospheric HULIS to different degrees.Possible reasons for these deviations are discussed in the following sections.Note that the κ for HULIS of 0.020 ± 0.006 at 70% RH in the dehumidification mode was much lower than that at 85% RH and those in other studies (Kristensen et al., 2014;Zhou et al., 2022), while the κ of HULIS and AS at 85% RH in the dehumidification mode were similar to those in humidification mode at the same RH.This is possibly because the particle shapes upstream of DMA1 were not fully spherical; aspherical particles and/or cracks and cavities could overestimate the mobility diameters from DMA compared with the volume-equivalent diameters (Varutbangkul et al., 2006).With the application of a correction factor for dry HULIS particles (Text S1 in Supporting Information S1), the κ for HULIS at 70% and 85% RH were similar (Figure S4 in Supporting Information S1).In addition, if the κ for HULIS were RH dependent (P.Liu et al., 2018), it could also be a reason.Despite the difference in the κ for HULIS, it did not affect the linear relationship for each sample.
With different RH conditions, samples 1 and 2 were fitted well with the ZSR relationship, while sample 3 deviated to some extent.To evaluate the extent of the deviations, we quantified them.To assess the differences of the κ values for the mixtures from the sum of the κ values for the individual components, that is, an estimation based on the ZSR relationship, a parameter ξ' was used to quantify the difference.
where κ mix is the κ for the mixture, κ org is the κ of HULIS, f org is the volume fraction of HULIS, κ inorg is the κ for the AS, and f inorg is the volume fraction of AS.This evaluation was similar to that suggested by Chan and Chan (2003), but their analysis was based on masses with an electrodynamic balance (EDB), while the analysis here is on a volume basis.In addition, we calculated the absolute difference between the measured κ and the κ estimated from the ZSR relationship as κ mix -(κ org f org + κ inorg f inorg ) to compare the magnitudes of the differences.
The ξ′ values for each sample under different RH conditions are shown in Figure S3 of the Supporting Information S1, and the average ξ′ and the average absolute differences for the different RH conditions for each sample and the average for all samples are shown in Figure 2. The ξ′ values for all mixtures under different RH conditions ranged from 1.04 to 1.27, and the average ξ′ for all samples was 1.16, meaning that the ZSR relationship generally explained the hygroscopicity of the mixtures with a 16% difference.The absolute differences for all mixtures were in the range of 0.02-0.04 with a mean value of 0.03, suggesting a small magnitude of the differences in κ.The average ξ′ values for samples 1, 2, and 3 were 1.07, 1.09, and 1.31, respectively.The near unity ξ′ values for samples 1 and 2 suggested that the ZSR relationship described the hygroscopicity of the mixtures for these two samples well.For sample 3, increases in ξ′ with increases in the organic fraction were observed for all ranges of the organic fractions except for the most organic-abundant mixture.Unlike ξ′, the absolute differences between the measured κ and κ estimated from the ZSR relationship showed a different pattern, in which the dependence on the organic fraction was less evident (Figure 2; Table S2 in Supporting Information S1).Because small uncertainties in the measured κ org significantly increased ξ′ for the organic-abundant mixtures but not for inorganicabundant mixtures, the high ξ′ values for organic-abundant mixtures may be strongly influenced by measurement uncertainties, including the dry particle shapes and inorganics in the extracted HULIS solution.Sensitivity analyses were performed to show how these measurement uncertainties affected the results.

Uncertainties Associated With Measurements (Dry Particle Shapes)
The nebulized dry particles may not be fully spherical before they were transferred to DMA1 of the HTMDA, which would lead to overestimates of the mobility diameters for DMA from the volume-equivalent diameters.A previous study (Gysel et al., 2004) showed that the measured growth factor of HULIS particles slightly decreased when the RH was increased from dry to 20%-30%.This was attributed to asphericity or cracks and cavities in the dry particles.This uncertainty would lead to bias, particularly for the components with small growth factors.Here, a sensitivity analysis (Text S1 in Supporting Information S1) was performed by assuming a factor to represent the differences between the mobility-and volume-equivalent-diameters of the dry particles (Figure S4 in Supporting Information S1).The correlations of κ and the organic proportions were similar to those obtained from the measurements with decreased ξ′.The average ξ′ for samples 1, 2, and 3 decreased to 1.06, 1.09, and 1.27, respectively.The highest ξ′ value (1.62) decreased significantly (1.46), suggesting that the high ξ′ values were partly due to the uncertainty of the dry particle shapes.Because a fixed asphericity for the dry particles may not be representative of different organic-inorganic mixtures because the shapes of the dry particles for the inorganics or organics may be different, factors that represented the differences between the mobility-and volume-equivalentdiameters of the dry particles were also applied for different mixtures.A decreasing tendency in ξ′ was also observed, except in three individual points for samples 1 and 2, which showed minor increases (Table S4 in Supporting Information S1).Although the degrees of asphericity for the dry particles were uncertain in this analysis (they may have been overestimated by using the data from Gysel et al. (2004) considering the use of a prehumidifier upstream of the HTDMA), the sensitivity analysis showed that consideration of the aspherical shapes reduced ξ′ and that the deviation from unity decreased.This sensitivity analysis suggested that considering the asphericity of the dry HULIS particles would slightly reduce ξ′.The deviation of κ for the mixtures from that estimated from the ZSR relationship should be within an acceptable moderate range (14%-16%).This result supported general fitting with the ZSR relationship for the atmospheric HULIS and AS mixtures.
The HULIS solution may have contained small amounts of inorganics, which could lead to uncertainties in κ org and the organic proportions.However, this is not an essential point for applying the ZSR relationship to the hygroscopicity of the HULIS-AS system if HULIS is operationally defined as a mixture containing organics and possible residual inorganics.Furthermore, if the solution of residual inorganics and organics in HULIS is assumed to follow the ZSR relationship, the presence of residual inorganics would not affect the ξ′ values (Text S2 in Supporting Information S1).

Uncertainties From the Physical/Chemical Properties of Droplets
The hygroscopicity derived from the hygroscopic growth factors is affected by the Kelvin effect and thus affected by the surface tension for a given RH and dry diameter.Furthermore, the bulk hygroscopicity could be affected by the pH of the solution, which is associated with the dissociation of acids and the non-ideality of the solution.In this section, we evaluate and discuss the effects of surfactants, pH, and non-ideality on the ZSR relationship of the HULIS-AS system.

Surfactants
If surfactants are present in an aqueous droplet, they may partition to the surface of the droplet and affect hygroscopic growth (Bzdek et al., 2020;Fors et al., 2010;Lowe et al., 2019;McNeill et al., 2014).This is because surfactants affect the Kelvin effect by lowering the surface tension of an aqueous solution (Petters & Kreidenweis, 2013;Prisle, 2021) and the solute effect by lowering the bulk concentration of the solute (Ovadnevaite et al., 2017;Zhang et al., 2021).Because HULIS were suggested to contain abundant surfactants (Kiss et al., 2005;Salma et al., 2006;Taraniuk et al., 2007), simplified models are used here to estimate how the surface tension depression of the droplets and the bulk-surface partitioning would affect the HTDMA measurements.The details of the calculations are provided in Text S2 of the Supporting Information S1.
Application of a decreased surface tension resulted in lower κ values for all mixtures (Figure 3).As an extreme condition, surface tension was fixed to zero (σ zero ), which resulted in κ values with smaller deviations from the ZSR relationship than those for assumptions of the surface tension of pure water (σ water ) for most mixtures.
However, a surface tension of zero is not realistic for considering the critical micelle concentration (Hede et al., 2011).The estimated surface tension based on the Szyszkowski-Langmuir equation (σ SLeq ) should provide a better approximation of the real situation.In general, the κ values from σ SLeq are represented better by the ZSR relationship (the average ξ′ value of all samples is 1.12, which is slightly better than the measured value of 1.16).
For sample 1, the improvements were not obvious.The κ values from σ SLeq showed better agreement with the ZSR relationship than those from σ water for most mixtures of sample 2 (average ξ′ value of 1.05) and all mixtures of sample 3 (average ξ′ value reduced to 1.27).
Bulk-surface partitioning of the surfactants also reduced the bulk concentration of the solute and affected the bulk hygroscopicity.A simplified estimation was provided by assuming a monolayer of surfactants on the droplet surface (Text S2.2 in Supporting Information S1).The changes in the bulk concentrations of organics represented an increase in κ, which increased with increasing inorganic proportions.However, these increases were small (Figure 3).This slight change in κ was also expected from the small κ values for the HULIS.Compared with the decreased κ from surface tension depression, the absolute increase in κ from the solute effect was comparable to or slightly lower than the absolute decrease in κ from σ SLeq and lower than that from σ zero .Surface tension depressions stronger than those from solute effects were also suggested in another study (Ovadnevaite et al., 2017).As a result, the presence of surfactants in the HULIS lowered the calculated κ, resulting in better fits with the ZSR relationship for most mixtures, although the degree of improvement was small.In general, surfactants have a minor effect on the ZSR relationship.

Acidity
The hygroscopicity of the HULIS-AS system could be affected by variations in the pH, which affect dissociation of the carboxylic acids in HULIS.The pH of each solution was measured with three samples, and the results are presented in Table S5 of the Supporting Information S1.The pHs of the solutions were in the range 3.99-5.76,and the H + should mainly originated from adjustment of the pH to 2 during preparation.By assuming that the concentration of H + relative to those of the other solutes did not change from the solution to the generated particles and that the particle components were fully dissolved, the pHs of the HULIS and HULIS-AS particles in the HTDMA were estimated to be 0.02-2.18.This pH range was lower than the typical pK a values of atmosphericrelated carboxylic acids (Ault, 2020;Vysotsky et al., 2020), suggesting that dissociation of the carboxylic acids in the particles was inhibited.The estimated pH values for the particle-phase solutions were not very different for pure HULIS and the 50% HULIS and AS mixture, suggesting that dissociation should not change substantially in the HULIS-abundant fractions.In AS-abundant mixtures, although the pH values were relatively high, the increases could be mostly explained by dilution of the HULIS, and the hygroscopicity of the mixture was governed by AS because the κ for AS is much higher than that for HULIS.The effect of carboxylic acid dissociation in the AS-abundant mixtures must be less significant in terms of the absolute and percentage changes in the κ values for the mixtures.

Non-Ideality of the Solutions in Aerosol Particles
Whereas the ZSR relationship is suited for consideration of ideal solutions, it is inconsistent with the behaviors of non-ideal solutions.In HTDMA analysis under subsaturated conditions, the non-ideal behavior of the solution may not be ignored (Roston, 2021) and may introduce bias in the hygroscopicity analysis.In this section, the non-ideality of the solutions of some organic-AS mixtures were calculated using Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model, and the possible influence of nonideality on hygroscopic growth of the HULIS-AS mixtures are analyzed.The water activity a w of a solution is given by where γ w is the activity coefficient of water and x w is the mole fraction of water in the solution.Combining Equations 2 and 5, κ can be written as follows: In an ideal solution, γ w is unity, and therefore, κ is equal to V w /V s .In a non-ideal solution, the measured κ deviates from the ideal solution by a factor of (1 a w )/(γ w a w ).
The κ values for mixtures based on the ZSR relationship and consideration of different γ w values are presented in Figure 4.For the selected phenols and aromatic acids, that is, methoxy phenol, hydroxybenzoic acid, phthalic acid, and benzenetricarboxylic acid, resulted in higher κ values than those estimated from the ZSR relationship due to the nonideal solutions.These enhancements represented higher values than the measured κ from sample 1 and some mixtures from sample 2, while the enhancements of κ from different γ w exhibited a similar tendency to the measured κ from sample 3. The measured κ was influenced by both surfactants and non-ideality; the surfactants represented reduced κ from the ZSR relationship (Figure 3), which could be offset by the nonideality.This may explain the measured κ values for samples 1 and 2. The similar tendency for the measured κ and the nonideality effect suggested that the deviations of sample 3 from the ZSR relationship could be explained by the nonideality of the solution.A higher proportion of C x H y groups and a lower O:C (elemental ratio of oxygen to carbon) Journal of Geophysical Research: Atmospheres 10.1029/2023JD040553 ZHOU ET AL.
were found for sample 3 than for the other two samples (Table S7 in Supporting Information S1) based on an HR-ToF-AMS analysis, indicating a higher proportion of aliphatic compounds in sample 3.For a long-chain fatty acid (hexadecanoic acid), high γ w values were obtained for organic-abundant mixtures, which resulted in significant increases in κ, as shown in Figure 4. Aliphatic compounds such as hexadecanoic acid could result in a higher γ w value for the solution and higher value for κ if they were in the aqueous phase.
The κ values for the hexadecanoic acid-AS system in Figure 4 exhibits an "S" shape.Interestingly, the shape is similar to that reported for marine aerosols by Vaishya et al. (2013), which showed higher κ values in inorganicabundant mixtures and lower κ values in organic-abundant mixtures relative to the ZSR relationship.Our analysis implies that their finding could be explained by the non-ideal properties of the studied marine aerosols.A test of hexadecanoic acid mixed with NaCl, the major inorganic compound in marine aerosols (Ovadnevaite et al., 2012), also showed a similar pattern (Figure S5 in Supporting Information S1).Submicrometer sea-spray aerosols from the ocean, which should have contributed largely to the aerosols studied by Vaishya et al. (2013), are known to contain abundant organic aerosols (O'Dowd et al., 2004;Quinn et al., 2015), and fatty acids are thought to be present in marine aerosols (Mochida et al., 2002(Mochida et al., , 2003;;Quinn et al., 2015).Although the extent of dissolution of these aliphatic compounds into the aqueous phases of atmospheric aerosols is not clear, the strong non-ideal interactions of the aliphatic compounds and inorganics in the aqueous phase are possible contributors to the large deviations from the ZSR relationship for marine aerosols.

Conclusion and Atmospheric Implications
We studied the hygroscopic growth of mixtures of atmospheric HULIS from an urban area and ammonium sulfate in different proportions under humidification and dehumidification conditions.The hygroscopicity parameters (κ) of the mixtures generally followed the ZSR relationship with some deviations.The parameter ξ′, which represents deviations from the ZSR relationship, was determined to be 1.16 on average for all samples and was 1.04-1.27for the mixtures with different mixing ratios.The measurement uncertainties for the dry particle shapes slightly reduced the deviations to 14%, which supported the use of the ZSR relationship for estimating the hygroscopicity of organic and inorganic mixtures in atmospheric models.In addition to the measurement uncertainties, the physical/chemical properties of the droplets also affected the deviations.Previous studies, to the authors' knowledge, did not investigate the effects of surfactants and non-ideality on the ZSR relationships for atmospheric organic mixtures.The presence of surfactants that partitioned between the bulk and surface of the droplet resulted in slight decreases in the deviations from the ZSR relationship.The non-ideal properties of the solutions would increase the κ values for the mixtures, which may explain the relatively large deviations of sample 3 from the ZSR relationship.The effect of non-ideality on the hygroscopicity might be strong if the aqueous phase behaves as a hypothetical fatty acid solution.
This study provides evidence that water uptake by mixtures of urban atmospheric OA and inorganic salts generally follows the ZSR relationship.This result supports the ZSR-based estimates of aerosol liquid water (ALW) with the consideration of OA contributions in the atmospheric models.It could be effective in modeling estimation with the combination of the average κ values for organics and inorganics, as recently suggested by Pöhlker et al. (2023).The ZSR relationship is widely used in estimating the hygroscopicity of aerosols or their components.However, some studies found disagreements between the measurement and the ZSR relationship.These deviations may have been derived from measurement uncertainties and the use of components that differed from those of atmospheric aerosols (e.g., mixtures of single compounds, SRFA).Some measurement uncertainties, including dry particle shapes, were evaluated in this study, which also confirmed the applicability of the ZSR relationship with acceptable deviations.Furthermore, this study evaluated the effects of the physical properties of the droplets, including the surfactants and non-ideal properties.The estimated non-ideality of the hypothetical fatty acid solution would be related to the large deviations from the ZSR relationship observed for marine aerosols by Vaishya et al. (2013).This raises a caution about the use of the ZSR relationship for fatty acidabundant aerosols (e.g., marine aerosols).Although this study in general supports the application of the ZSR relationship to explain the hygroscopicity of organics-AS mixtures, the degree of the deviation from the ZSR relationship may depend on the presence of non-HULIS OA components, and on OA types associated with sources, formation pathways, and aging.Further, the variety of the composition of inorganics in atmospheric aerosol may also affect the degree of the deviation from the ZSR relationship.Further studies are encouraged to assess the ZSR relationship for a variety of organic-inorganic mixtures related to atmospheric aerosols.
A limitation of the present study is that the microscopic behavior of the particle phase was not observed.It is possible that liquid-liquid phase separation (LLPS) occurred in the organic and inorganic mixtures (Huang et al., 2021), leading to the formation of organic and inorganic phases under the RH conditions in this study.The potential occurrence of LLPS could affect the non-ideal interactions between the organic and inorganic components, which invalidates our assumption of homogeneous mixtures.LLPS could also affect the water uptake kinetics for mixed organic and inorganic particles (Li et al., 2021).While this study did not identify any significant influence on the hygroscopic growth factor due to the possibility of a thicker organic coating, it is worth noting that the residence times in our HTDMA analyses (∼11 s) might also play a role.Further studies are needed to investigate the phases of the organics and inorganics to better explain the hygroscopic behavior of the mixtures.
Also, the present approach using HULIS from aerosol components collected on filters still has limitations in terms of the representativeness for total atmospheric OA.HULIS are water-soluble OA components with relatively high molecular weight and hydrophobic compounds (Varga et al., 2001;Zheng et al., 2013).The role of organics other than HULIS, for example, high polarity components (Gysel et al., 2004), is a subject for further investigation.Additionally, the degradation of highly reactive or unstable compounds during sampling and storage has not been ruled out, although a recent study showed good agreement between the online and offline analyses for aerosol composition and hygroscopicity (Deng et al., 2022).To obtain a full picture of the hygroscopicity of organicinorganic mixed particles, further studies based with the presented and other approaches are encouraged.

Figure 1 .
Figure 1.Relationships between the hygroscopicity parameter κ and the organic volume fraction of the HULIS, AS, and HULIS-AS particles; (a-c) κ for the respective organic fractions at 85% RH in the humidification mode (rectangle) and 85% (rhombus) and 70% RH (triangle) in the dehumidification mode and the averages (solid circle) across these conditions for samples 1-3, and (d) the κ averages for all samples.The dashed lines represent the estimates based on the ZSR relationship for the averaged values in the respective panels.The error bars in Panel (d) represent the standard deviations from three samples.

Figure 2 .
Figure 2. Relationships of the ξ′ values and the absolute differences in κ (measured κ and κ estimated from ZSR) with organic fractions; (a-c) averages across three humidification conditions (85% RH in the humidification mode and 85% and 70% RH in the dehumidification mode) for samples 1-3 and (d) the averages for all samples.The solid-squares and cross markers represent the ξ′ values and the absolute differences in κ, respectively.

Figure 3 .
Figure 3. Relationships between the hygroscopicity κ and organic fractions with consideration of (a) surface tension depression and (b) bulk-surface partitioning.The averages across three humidification conditions (85% RH in the humidification mode and 85% and 70% RH in the dehumidification mode) are presented.

Figure 4 .
Figure 4. Measured hygroscopicity κ from the HULIS-AS system from three samples and their hygroscopicity estimated by considering the non-ideality of some organic-AS systems.

Table 1
Summary of Substances Used, Instruments, and Results in Previous Studies and This Study a a AS, ammonium sulfate; AN, ammonium nitrate; PEG, polyethylene glycol; SRFA, Suwannee river fulvic acid; NAFA, Nordic aquatic fulvic acid; CCNC, cloud condensation nucleus counter; EDB, electrodynamic balance; SS, supersaturation; a w , water activity.b Based on views in respective reports.