Detailed Analysis of Estimated pH, Activity Coefficients, and Ion

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Detailed Analysis of Estimated pH, Activity Coefficients, and Ion Concentrations between the Three Aerosol Thermodynamic Models Xing Peng,†,|| Petros Vasilakos,‡,|| Athanasios Nenes,§,# Guoliang Shi,*,† Yu Qian,|| Xurong Shi,† Zhimei Xiao,⊥ Kui Chen,⊥ Yinchang Feng,*,† and Armistead G. Russell*,||

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State Environmental Protection Key Laboratory of Urban Ambient Air Particulate Matter Pollution Prevention and Control & Center for Urban Transport Emission Research, College of Environmental Science and Engineering, Nankai University, Tianjin 300350, P. R. China ‡ School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia, 30332, United States § Laboratory of Atmospheric Processes and Their Impacts, School of Architecture, Civil & Environmental Engineering, Ecole Polytechnique Federale de Lausanne, CH-1015, Lausanne, Switzerland # Institute of Chemical Engineering Sciences, Foundation for Research and Technology Hellas, GR-26504, Patras, Greece || School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ⊥ Tianjin Eco-Environmental Monitoring Center, Tianjin 300191, P. R. China S Supporting Information *

ABSTRACT: In this work, we utilize a rich set of simulated and ground-based observational data in Tianjin, China to examine and compare the differences in aerosol acidity and composition predicted by three popular thermodynamic equilibrium models: ISORROPIA II, the Extended Aerosol Inorganics Model vision IV (E-AIM IV), and the Aerosol Inorganic−Organic Mixtures Functional groups Activity Coefficients model (AIOMFAC). The species used to estimate aerosol acidity for both simulated and ambient data were NH4+, Na+, SO42−, NO3−, and Cl−. For simulated data, there is good agreement between ISORROPIA II and E-AIM IV predicted acidity in the forward and metastable mode, resulting from the hydrogen ion activity coefficient (γ(H+)) and the molality (m(H+)) showing opposite trends. While almost all other inorganic species concentrations are found to be similar among the three models, such is not the case for the bisulfate ion (HSO4−), which is linked to m(H+). We find that differences in predicted bisulfate between the three models primarily result from differences in the treatment of the HSO−4 ↔ H+ + SO2− 4 reaction for highly acidic conditions. This difference in bisulfate is responsible for much of the difference in estimated pH for the ambient data (average pH of 3.5 for ISORROPIA II and 3.0 for E-AIM IV).

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INTRODUCTION Aerosol acidity plays a critical role in chemical and physical processes by affecting the oxidation of inorganic and organic species,1,2 driving the gas-aerosol partitioning of semivolatile components,3,4 and affecting the solubility and oxidation state of metals.5−7 Accurately predicting pH in atmospheric models is important, as pH inaccuracies may lead to unrealistic behavior in the atmospheric models.8 However, it is currently not possible to measure aerosol pH,9 and most estimates are indirect, using thermodynamic models constrained by ambient aerosol and gas-phase partitioning data.2,4,8,10−14 Given the above, there is renewed interest in evaluating aerosol thermodynamic models. Thermodynamic models assume volatile species in the gas and aerosol phases achieve thermodynamic equilibrium in order to calculate the aerosol compositions and phase state. They consider the equilibrium reactions among multiphase aerosol and use either the Gibbs free energy minimization (e.g., Extended Aerosol Inorganics Model (E-AIM)) or © XXXX American Chemical Society

chemical potential method (e.g., ISORROPIA) to calculate the concentrations of species in the gas, liquid, and solid phases. Both the Gibbs free energy minimization and chemical potential methods are equivalent, but the former more readily includes additional reactions, while the latter allows for faster solution procedures. Simultaneously, mass conservation, charge balance, water activity, and water content are involved in the calculation of concentrations of compositions.14−17 ISORROPIA and E-AIM are two popular models that are applied to estimate the composition of particulate matter, including aerosol acidity.14−20 Such models calculate aerosol pH, liquid water content, and species concentrations in the solid, aqueous, and gas phases. Since this process can be computationally intensive, especially when it takes place within Received: Revised: Accepted: Published: A

January 9, 2019 June 22, 2019 June 25, 2019 June 25, 2019 DOI: 10.1021/acs.est.9b00181 Environ. Sci. Technol. XXXX, XXX, XXX−XXX

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also evaluated using ambient data to further examine the implications of model differences by comparing the observed to the model-determined partitioning.

an air quality model, ISORROPIA was designed to improve the computational speed, in part by optimizing the calculation of activity coefficients during the solution processwhich can include a combination of precalculated lookup tables and/or optimal calling of the activity coefficient routines during the bisection solution process.17,18 Given that it uses mean activity coefficients to address solution nonidealities, ISORROPIA requires some assumptions for the activity coefficient of single ions when computing pH and other single-ion derived properties, e.g., for some species for which nonideality information is not available (e.g., for NH3(aq)) the code assumes a unity coefficient.16 Given its computational efficiency and accuracy, ISORROPIA has been incorporated in many air quality and general circulation models.16,18 Like ISORROPIA, E-AIM can also predict liquid water content, solid and liquid phase states, and gas partitioning. It uses a single-ion activity coefficient model that relies on the Pitzer, Simonson, and Clegg equations (PSC).15 The Aerosol Inorganic−Organic Mixtures Functional groups Activity Coefficients model (AIOMFAC) is formulated to calculate the activity coefficients of inorganic and organic species and to account for the interactions of these species over a wide concentration range. The activity coefficients are further used in thermodynamic equilibrium computations.21−23 Both ISORROPIA and E-AIM can calculate gas-aerosol partitioning; both AIOMFAC and E-AIM have the capacity to consider organic species; ISORROPIA and AIOMFAC can treat a range of crustal species (e.g., Ca2+, Mg2+, K+), which is important for coarse mode aerosol and in regions with considerable dust influence. Prior studies that used ISORROPIA and E-AIM have shown differences in the calculation of aerosol acidity between the two models when used under similar conditions.12,14,18,24,25 While ISORROPIA uses an H+ activity coefficient equal to unity when used to calculate pH and E-AIM does not, the differences in calculated pH are only weakly associated with the difference in activity.26 The discrepancy in H+ molality (m(H+)) also is another reason for the difference in pH between the two models, but the reason for this difference in molality is not clear.12,14,26 Here we develop an extensive application using both detailed observational and constructed data to identify details of the differences in aerosol thermodynamic model results and link those results to the modeling approaches and data, noting that the model specific approaches and thermodynamic data used are documented elsewhere.14−18,21−23,27−34 In particular, E-AIM and ISORROPIA use the Zdanovskii-Stokes-Robinson (ZSR) approach to calculate the water content.17,32 The three models calculate the activity coefficient using different methods based on ionic strength.21,35 AIOMFAC uses a method that merges a Pitzerlike approach with a slightly modified version of the original UNIFAC model.36 Both E-AIM and AIOMFAC use the singleion method of Pitzer.15,35 ISORROPIA either uses the mean activity coefficient method based on the Kusik and Meissner method (KM) to calculate binary activity coefficients and Bromley’s rule to calculate the activity coefficients in the presence of additional species in the solution, or precalculated tables.14,17 To examine the specific causes for differences in aerosol acidity and composition between E-AIM IV (version IV), ISORROPIA II (version 2.3), and AIOMFAC models, the three models were evaluated for a set of simulated cases, representing different levels of inorganic species commonly observed in real ambient conditions. The three models were

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DATA AND METHODS Simulation Experiment. Data used here are based on ambient data from Tianjin, China (described below), simplified to focus more comprehensively on the ammonium-sulfate-nitrate system in a structured fashion. Five cases used a varying RH with fixed temperatures and total species concentrations (gas and aerosol) (Table S1 of the Supporting Information, SI). Cases 1−3 differed in their initial (NH4)2SO4 and NH4NO3 concentrations, having high (Case 1), moderate (Case 2), and low (Case 3) levels of inorganic species. The efflorescence relative humidity (ERH) of (NH4)2SO4 is 35 ± 2%, and the ERH of NH4NO3 is not observed.37,38 When particles consist purely of (NH4)2SO4 and NH4NO3, the ERH is related to the molar ratio of (NH4)2SO4:NH4NO3, and the ERH decreases monotonically with decreasing molar ratio.38 For Cases 1−3, we modeled the aerosol activity variation over an RH range from 35% to 99% (by the 5% step) at a constant temperature of 298.15K. Case 4 examined how the addition of NaCl affected acidity and the partitioning of inorganics. Case 5 was a sensitivity test and examined the pure NH4NO3−H2O system to assess how sulfate impacted the calculation of the gas phase partitioning, aerosol nitrate formation, and aerosol activity. RH ranged from 60% to 99% for Case 4 and 70% to 99% for Case 5. We assume an aqueous phase exists at low RH ( 60% because particles transit from semisolid to liquid state when the RH increases above 60%.19 This led to 93 samples being used. Thermodynamic Equilibrium Models. ISORROPIA II, E-AIM IV, and AIOMFAC were employed to simulate the chemical species concentrations, activity coefficients, and aerosol acidity. More details about the three models and pH calculations are provided in the SI. In this work, ISORROPIA version 2.3 (http://isorropia.epfl.ch) uses the total species (NH4+ + NH3, SO42−, Na+, Cl− + HCl, and NO3− + HNO3) concentrations as input in the gas and condensed phases, temperature, and RH. ISORROPIA v2.3 is referred to ISORROPIA hereafter to make the discussion clearer. E-AIM IV (called E-AIM in the following discussion section) simulates the H+−NH4+−Na+−SO42−−NO3−−Cl−−H2O system, and can also address cases with some organic species (http://www.aim.env.uea.ac.uk/aim/model4/model4a.php). As with ISORROPIA, the forward and metastable mode was used. The total species concentrations were used in E-AIM. The AIOMFAC model (http://www.aiomfac.caltech.edu) calculates the equilibrium RH, activity coefficients (based on molality), and species mass/molar fractions in aqueous solutions.21 The different models have different inputs and outputs, which leads to difficulties in comparing results. Furthermore, AIOMFAC does not account for gas-aerosol partitioning, further complicating comparison.21 For these reasons, we used a method that allows for a more accurate comparison between models when applied to ambient systems where such

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RESULTS AND DISCUSSION Comparison of Model Results between E-AIM and ISORROPIA. ISORROPIA and E-AIM yield similar results, with relatively small differences in predicted pH, and molar fractions of each species (H+, NH4+, Na+, SO42−, NO3−, Cl−, and H2O) (Figure S2). Cases 1−4 followed the same trend with pH increasing with RH, as the higher RH corresponded to higher LWC concentration and lower overall concentrations for all species. Average values of pH are the highest in Case 1 (2.1 pH units for ISORROPIA and 1.9 for E-AIM), followed by Case 2 (1.2 pH units for ISORROPIA and 1.3 for E-AIM), and then Case 3 (0.3 pH units for ISORROPIA and 0.4 for EAIM) for both models, since more air pollution (high concentrations of species) led to a greater calculated LWC concentration that diluted H+.4 C

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Figure 2. (a, b) Relationship between the difference in ISORROPIA−AIOMFAC pH (ΔpH) and the paired Δlog10(γ(H+)) and Δlog10(m(H+)) for Cases 1−4 (data from Table S1). (c−h) Relationship between the difference in ISORROPIA−AIOMFAC m(H+) (Δm(H+)) and the paired difference , Δm(HSO−4 ), Δm(NH+4 ), Δm(NO−3 ), Δm(Na+), and Δm(Cl−)) for Cases 1−4. The unit of m(H+) is mol kg−1 water. in other species molality (Δm(SO2− 4 )

(Figure 1(c, e, f)). Δm(H+) and Δm(NO−3 )show different trends for Cases 1 and 3; Δm(NO−3 ) is larger in Case 1, but only Case 3 resulted in larger in Δm(H+). The levels of the Δm(H+) and Δm(NO−3 ) for different cases mainly depend on the levels of the two species’ molalities. Compared with the m(H+) in Case 3 (0.32 ± 0.17 for E-AIM and 0.84 ± 0.73 mol kg−1 water for ISORROPIA), lower m(H+) are found in Case 1 (0.024 ± 0.011 for E-AIM and 0.011 ± 0.008 mol kg −1 water for ISORROPIA) because higher species concentrations lead to a greater calculated LWC diluting H+. In contrast to m(H+), m(NO−3 ) in Case 1 (6.8 ± 1.9 for E-AIM and 5.8 ± 1.8 mol kg−1 water for ISORROPIA) are higher than in Case 3 (0.0032 ± 0.0037 E-AIM and 0.0034 ± 0.0030 mol kg−1 water for ISORROPIA) mainly linked to differences in gas - aerosol partitioning of NO3−. The average ε(HNO3) (ε(HNO3) = HNO3/ (HNO3 + NO−3 )) in Case 1 are 0.37 for E-AIM and 0.27 for ISORROPIA, which is lower than 0.99 for Case 3 for both two models. There are small differences in simulated NH3 and HNO3 between ISORROPIA and E-AIM, most notably for Case 1 (Figure S3) and the resulting Δε. The calculated Δε(NH3) showed a positive correlation with Δm(HSO−4 ) and Δm(NH+4 ), except in Case 1, and a negative relationship with Δm(H+) (Figure S4), suggesting the partitioning of semivolatile species links the discrepancy in m(H+) and sulfate partitioning. ISORROPIA and E-AIM calculate similar LWCs (Figure S3) because both are based on the ZSR equation (see SI) and use a similar water activity database.17,32 Given that both models have similar ion levels, LWCs are similar as well. A detailed discussion of Case 2 and 4 can be found in the SI to analyze the influence of NaCl on pH (Figure S5). In general, additional NaCl has less influence on pH in this work, possibly because Case 4 used high ammonium sulfate concentrations that can overpower NaCl. Comparison of Model Results between AIOMFAC and ISORROPIA/E-AIM. ISORROPIA and E-AIM were also

The pH differences are typically small, which may seem counterintuitive given the large changes in species concentrations. Specifically, pH values estimated by ISORROPIA are very similar to the E-AIM results with an average difference of 0.05 ± 0.2 pH units (ranging from −0.7 to 0.3 pH units, Figure 1). This is driven by the increased LWC (which is roughly proportional to the aerosol concentrations in the test conditions), with a small perturbation due to gas-aerosol partitioning of nitric acid and ammonia since a greater fraction of both species can go into the gas phase under the cleaner cases.39 There are greater differences in the estimates of m(H+) and γ(H+). Compared to results estimated by E-AIM, higher m(H+) and lower γ(H+) were calculated by ISORROPIA under low RH, and lower m(H+) and higher γ(H+) were calculated under high RH, leading to the similar results for pH (Figure 1). The discrepancy in γ(H+) is due to its being set to unity for ISORROPIA when used to diagnose pH. Except for H+ and HSO4−, the rest of the species molar fractions estimated by ISORROPIA are similar to the corresponding results calculated by E-AIM. As there are low concentrations of HSO4− and nonvolatile Na+, the agreement of SO42− and Na+ calculations with observations is unsurprising, and the results are provided here merely for completeness. There is a slight difference in the calculated sulfate ion concentration when compared to total observed sulfate under the presence of calcium, due to the formation of calcium sulfate which could not be fully represented in the models.16 The profiles of m(H+) and the molar fraction of bisulfate closely track each other (Figure S2), suggesting that the discrepancy in m(H+) between the two models is associated with differences in HSO4−. Relationships between the difference in molality of H+ (Δm(H+)) and HSO4− (Δm(HSO−4 )) are similar for Cases 1−4 which present a nearly linear relationship (Figure 1(d)), further supporting the finding that Δm(H+) is associated with Δm(HSO4−). Relationships between Δm(H+) and the paired , Δm(NO−3 )) are dissimilar for Cases 1−4 Δm(NH+4 ) (or Δm(SO2− 4 ) D

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Figure 3. (a−c) Relationship between difference in pH (ΔpH) and the paired Δlog10(γ(H+)) and Δlog10(m(H+)), for Case 5 (data from Table S1). (d) Relationship between difference in ISORROPIA−E-AIM m(H+) (Δm(H+)) and the paired difference in gas concentration (ΔHNO3 and ΔNH3). The unit of m(H+) is mol kg−1 water.

associated with Δm(HSO−4 ), and H+ in the two models are in fact entirely dissociated from HSO4− (Figures S7 and S8, for details see SI). We also applied the three models for the NH4HSO4− NH4NO3 system at 298.15 K, and evaluated three cases representing sulfate rich conditions as a proof-of-concept experiment (Figure S9). ISORROPIA and E-AIM exhibit significant differences in the calculated molalities of SO42−, HSO4−, and H+ for sulfate rich conditions, while Δm(H+) and Δm(HSO−4 ) present a nearly linear relationship. Δm(H+) between ISORROPIA/E-AIM and AIOMFAC has a positive linear relationship with Δm(SO2− and a negative linear relationship 4 ) with Δm(HSO−4 ), while the AIOMFAC estimated molalities of other species are very similar to the ISORROPIA/E-AIM calculations. Overall, model results deviate more at lower RH might since the three models calculate activity coefficients using different methods that are based on ionic strength, and each of the methods’ results differ more when ionic strengths are high due to low RH.16,35 This finding is similar to Fountoukis et al.,16 who reported larger discrepancies between ISORROPIA and SCAPE2 when RH is low, primarily from differences in the calculations of water content and solid state composition. Role of HSO4− on H+ Molality. To further assess the finding that the discrepancy in m(H+) calculations between the AIOMFAC, ISORROPIA, and E-AIM models is linked to the difference in HSO4−, (NH4)2SO4 was removed in Case 5.

evaluated against the predictions of AIOMFAC for Cases 1−4 using the approach specified in the methods section to examine the differences in the thermodynamic analyses (Figures 2 and S6). pH calculated by ISORROPIA is typically lower than the pH calculated by AIOMFAC with an average difference of 1.2 ± 0.5 pH units (ranging from −1.88 to −0.27 pH units). ΔpH between ISORROPIA and AIOMFAC is linked to Δγ(H+) and Δm(H+) and mainly related to Δγ(H+). The γ(H+) calculated by AIOMFAC ranges from 0.08 to 0.45 with an average value of 0.14 ± 0.07. Compared to ISORROPIA results, the values of log10(γ(H+)) calculated by AIOMFAC are lower by 0.34−1.1 with an average value of 0.9 ± 0.2, when calculating pH by neglecting the γ(H+) (set to be equal to unity for both models), the predicted differences in pH between ISORROPIA and AIOMFAC are significantly smaller with ΔpH ranging from −1.0 to 0.23 with an average value of 0.3 ± 0.4 for Cases 1−4. Δγ(H+) between ISORROPIA and AIOMFAC increased with the decreasing RH. ISORROPIA and AIOMFAC exhibit significant differences in the calculated molalities of SO42−, HSO4−, and H+ for Cases 1−4 (Figure 2). Δm(H+) has a positive linear relationship with (correlation coefficient r = 1) and a negative linear Δm(SO2− 4 ) relationship with Δm(HSO−4 ) (r = −1), while the AIOMFAC estimated molalities of other species are very similar to the ISORROPIA calculations, indicating that the discrepancy in m(H+) between the two models is associated with the difference in HSO4−. The Δm(H+) between E-AIM and AIOMFAC is E

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Figure 4. SO42−/HSO4− fractions (molality/molality) of total sulfate dependence on pH for Cases 1−4 (data from Table S1). The first and second rows show the results of E-AIM and ISORROPIA, respectively. The third and fourth rows show the AIOMFAC results using species mass fractions estimated by the E-AIM and ISORROPIA, respectively. The fifth and sixth rows show the recalculation of the results based on H+ molality estimated by ISORROPIA and activity coefficients estimated by E-AIM and AIOMFAC, respectively. pH used in the first row was calculated by EAIM. pH used in the second, fifth, and sixth rows was calculated by ISORROPIA. pH used in the third and fourth rows was calculated by AIOMFAC.

Role of HSO4−/SO42− Partitioning on pH. The main difference in the model results involved the SO42−/HSO4− levels for simulated data (Figures 1, 2, and S8). The relationship between pH and HSO4− and SO42− fractions (molality/molality) of total sulfate (see SI) was also investigated. For the E-AIM results (first row in Figure 4), the F[HSO−4 ] and

Comparison of pH, m(H+), γ(H+), and the molar fractions of species calculated by ISORROPIA/E-AIM and calculated by AIOMFAC for Case 5 show that the pH and γ(H+) estimated by AIOMFAC had notable differences with ISORROPIA/E-AIM calculations (Figure S10) when compared to cases where sulfate and bisulfate were present in the system. Both pH and log10(γ(H+)) calculated by AIOMFAC are slightly higher than those found using ISORROPIA and E-AIM with an average difference of 0.1 ± 0.1 pH units for both. The ΔpH between AIOMFAC and ISORROPIA/E-AIM models is consistent with Δlog10(γ(H+)) and Δlog10(m(H+)) close to zero (Figure 3(a−c)). Without SO42−/HSO4− in the system, the mH+ calculated by the AIOMFAC is very similar to the results calculated by E-AIM and ISORROPIA, strongly suggesting that differences in estimated HSO4− for those models are the reason for differences in m(H+) and vice versa, since differences in HSO4− can also affect m(H+). Prior studies have also suggested that bisulfate is important in estimating aerosol acidity, activity coefficients, and concentrations accurately.43,44 ΔpH, Δlog10(γ(H+)), and Δlog10(m(H+)) between ISORROPIA and E-AIM ranged from −0.6 to 0.004, −0.2 to 0.2, and 0.1 to 0.4, respectively (Figure S11). Although the influence of HSO4− is excluded, the m(H+) calculated by the two models in this case are still different, indicating that there could be other reasons for the remaining discrepancy in m(H+). The small difference in calculated NH3 and HNO3 between the two models (Figure S11, as also shown by Allen et al.10) can drive small differences in m(H+), although there is no obvious relationship between Δm(H+) and ΔHNO3 or ΔNH3 (Figure 3(d)). The (NH4)2SO4−NH4NO3 system in Cases 1−3 differs more because of its treatment of bisulfate.

in Case 1 change little with pH. For Cases 2 and 3, the F[SO2− 4 ] F[HSO−4 ] decreased with increasing pH and remained constant when pH was greater than 1.5 pH units. The reason for the different levels at which the fractions change is the availability of ammonia to participate in gas-aerosol partitioning. The average F[HSO−4 ] in Case 4 is 0.09, slightly lower than 0.12 in Case 2, indicating NaCl has a negligible influence on sulfate partitioning in this work. For ISORROPIA (second row in Figure 4), F[HSO−4 ] changes very little with pH (less than 0.01) for Cases 1, 2, and 4. The F[HSO−4 ] slightly increases with pH increases, ranging from 0.02 to 0.1 with an average of 0.06 for Case 3. The difference in the F[HSO−4 ] between E-AIM and ISORROPIA is more pronounced at low pH (e.g., < 1.5) than at high pH. The third row in Figure 4 shows the AIOMFAC results using input data of species mass fractions estimated by E-AIM. The F[HSO−4 ] dependence on pH is the same as E-AIM. F[HSO4−] estimated by AIOMFAC based on ISORROPIA outputs is less than 0.01 for Cases 1, 2, and 4 and around 0.1 for Case 3, as shown in the fourth row in Figure 4. Overall, E-AIM displays a trend where F[HSO−4 ] increases with decreasing F

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Figure 5. Comparisons of measured and calculated species concentrations from E-AIM and ISORROPIA calculations, for Tianjin data.

Atmospheric Implications. Ambient data were also used to further examine the implications of model differences. ISORROPIA and E-AIM were employed to analyze the ambient data collected in Tianjin, China, using daily average concentrations of species for the cases where RH was greater than 60% (see section 2.2). The cation to anion molar ratio is 1.3 ± 0.5. Few studies report HCO3−, though in India, it ranged from for 4% to 13.3% of the PM2.5.46,47 If HCO3− is included to the anions and this range is used, then the cation to anion molar ratio ranges from 1.1 ± 0.4 (4% used) to 0.9 ± 0.3 (13.3% used), indicating that HCO3− might be one reason for the deficit in anions. Calculated pH, γ(H+), m(H+), and molar fractions of species were compared between ISORROPIA and E-AIM (Figure S12). Mg2+, K+, and Ca2+ were accounted for as equivalent Na+. We also applied ISORROPIA on the original Tianjin data with the three crustal species directly input to the model. Similar results were obtained from the two input data sets, indicating that the input method had little influence on pH. The treatment of crustal species has some influence on LWC and SO42− equilibria. Discrepancies in LWC are due to CaSO4 being out of the solution and the water uptake of Na+ being different than Mg2+ and K+. The insoluble CaSO4 can also perturb the SO42− equilibria. We assess the performance of ISORROPIA and E-AIM by comparing measured and calculated species concentrations (Figure 5). For both ISORROPIA and E-AIM, Figure 5 shows that the calculated NH3 deviation from the corresponding measured values under high SO42− concentrations and low temperatures. This suggests that the discrepancies between calculated and measured NH3 concentration under low temperatures are due to the gas and aerosol phases not achieving equilibrium because the equilibration time scale is longer than the sampling

pH (calculated with E-AIM), while ISORROPIA results are almost insensitive to pH (calculated with ISORROPIA). The reason behind the discrepancies in F[HSO−4 ] between ISORROPIA and E-AIM might have to do with the differences in the activity coefficients of H+, HSO4−, and SO42− and how they are estimated by the three models since the three models use different methods to estimate the activity coefficients. Zaveri et al.35 found that the multicomponent γ(H2SO4) and γ(HHSO4) (the mean ionic activity coefficient of the 2H+−SO42− and H+−HSO4− ion pair) calculated by the KM method differs with the ones estimated using the PSC model, resulting in a corresponding difference in H+ molality. We recalculated F[HSO−4 ] using the H+ molality estimated by ISORROPIA and the activity coefficients for H+, HSO4−, and SO42− estimated by E-AIM, according to eq (S11). Compared to F[HSO−4 ] and estimated by ISORROPIA, the recalculated F[HSO−4 ] and F[SO2− 4 ] 2− F[SO4 ], using these updated inputs, are closer to the results obtained with E-AIM, highlighting that F[HSO−4 ] and F[SO2− are 4 ] sensitive to the H+, HSO4−, and SO42− activity coefficients. It is worth noting that this work focused explicitly on inorganics rather than organics. However, recent studies using E-AIM and AIOMFAC show that organic acids have a small impact on aerosol acidity for conditions similar to the ones seen in our study, although organics may still impact LWC and phase state, but not to the extent that pH is affected.8,14,45 More discussion about the impact of organic species on aerosol acidity (e.g., organonitrates and organosulfates, phase separation, organic acid) is presented in the SI. G

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Figure 6. (a, c, e) Relationship between difference in pH (ΔpH) and the paired Δlog10(γ(H+)) and Δlog10(m(H+)), for Tianjin data. (b, d, f) Relationship between difference in m(H+) (Δm(H+)) and the paired Δm(HSO−4 ), for Tianjin. (a) and (b): E-AIM−AIOMFAC; (c) and (d): ISORROPIA−AIOMFAC; (e and f): ISORROPIA−E-AIM. The unit of m(H+) is mol kg−1 water.

time.4,48 For HNO3, discrepancies in model calculations are highest under low temperatures, and they do not show clear trends with SO42− concentrations, implying that these discrepancies might be caused from a multitude of factors. Time scales of gas-aerosol equilibrium for the volatile species depends on the temperature, its partial pressure in the gas phase, the concentration of aerosol and its size distribution, the species diffusivity, and the species accommodation coefficient.49 Guo et al. reported the gas-particle partitioning of NH3−NH4+ accurately calculated by thermodynamic calculations over the complete T (18−33 °C) and RH (36 to 96%) ranges.4 For pH, a slope of 1.0, intercept of 0.4, and high coefficient of determination (R2 > 0.9) indicates very good agreement between the two approaches (Figure S12). The average pH values were 3.5 for ISORROPIA and 3.0 for E-AIM. Measurement of ambient aerosol pH in field studies such as this are not currently practical. One indirect method is to measure the pH of aqueous filter extracts; however, this method changes the ion distribution during filter extraction, leading to high uncertainty.9 A method coupling Raman microspectroscopy with extended Debye−Hückel activity was used to directly measure the individual aerosol pH.9,50 This method has challenges for application to ambient aerosol because ambient aerosol can yield complex spectra that can be

difficult to identify.9 The differences in average predicted pH between ISORROPIA and E-AIM are similar to Liu et al.,25 who found the mean absolute difference between the two models to be 0.3 pH units. As shown in Figure 6(e), Δlog10(γ(H+)) is closer to zero than Δlog10(m(H+)), suggesting that the differences in pH between ISORROPIA and E-AIM for the Tianjin data are mainly due to differences in the molality estimates and not due to the activity coefficient. Specifically, the average value of log10(γ(H+)) calculated by EAIM is 0.04, as compared to zero in ISORROPIA ((γ(H+) = 1), while the average value of log10(m(H+)) calculated by E-AIM is −3.1, which is higher than the −3.5 estimated by ISORROPIA. Both ISORROPIA and E-AIM calculations led to similar results for the concentrations of gaseous pollutants (NH3, HCl, and HNO3), as well as the molar fractions of most aqueous species (NH4+, Na+, Cl−, NO3−, and SO42−) (Figures S12 and S13). A noticeable deviation from the 1:1 line is found for HSO4−, as might be expected from the prior analyses. The Δm(H+) between E-AIM and ISORROPIA showed a strong correlation with the paired Δm(HSO−4 ) (R2 = 0.4, Figure 6(f)). There is no obvious relationship between Δm(H+) and ΔHCl, ΔHNO3, or ΔNH3 (Figure S14). pH and m(H+) calculated by E-AIM and ISORROPIA agree well with those calculated using AIOMFAC (Figure S15). ΔpH between E-AIM/ISORROPIA and AIOMFAC is correlated with Δlog 10 (γ (H + ) ) and H

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Environmental Science & Technology Δlog10(m(H+)) for the Tianjin data (Figure 6(a, c)). The differences in H+ molality between E-AIM/ISORROPIA and AIOMFAC are associated with the corresponding differences in bisulfate (Figure 6(b, d)). For similar atmospheric conditions, pH, m(H+), and molar fractions of species calculated by E-AIM and ISORROPIA are similar to those calculated using AIOMFAC, though the γ(H+) values calculated by the three models showed some differences. All three models predict that F[HSO−4 ] decreases with increasing pH in a similar fashion (Figure S16, see SI). The discrepancy in the bisulfate ion between ISORROPIA and E-AIM does not significantly impact LWC. Indeed, given that sulfate is nonvolatile and that the pH predicted by E-AIM, AIOMFAC, and ISORROPIA are similar, the impact of this difference is limited. Overall, the three models lead to similar values of pH, m(H+), and molar fractions for most species. However, the pH and concentrations of species calculated by the models depend closely on the ion concentrations, temperatures, and RH. Zhang et al. reported significant discrepancies in PM compositions and concentrations among five thermodynamic models if the nitrate/chloride concentrations are high and the RH is low.51 Likewise, we find increased error at low RH. If the partitioning between SO42− and HSO4− is important to a study, then an additional step to account for model differences is advised, where for pH’s below about 1.5, the estimated HSO4−/SO42− split can be obtained by re-estimating m(H+) and activity coefficients using eq (S11).

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granting agencies do not endorse the purchase of any commercial products or services mentioned in the publication. We would also like to thank Nash Skipper and Gigi Pavur for their helpful grammatical edits to the manuscript.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.est.9b00181. Additional figures and tables, the details of the three models and the Zdanovskii−Stokes−Robinson method as well as further discussion on the impact of NaCl and organics on aerosol acidity, and additional discussion on model evaluation of ISORROPIA and E-AIM, HSO4−/ SO42− partitioning (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. ORCID

Xing Peng: 0000-0003-2279-4115 Athanasios Nenes: 0000-0003-3873-9970 Guoliang Shi: 0000-0001-5872-0236 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the National Key Research and Development Program of China (2016YFC0208500), the National Natural Science Foundation of China (No. 41775149, 91544226), the Tianjin Science and Technology Foundation (No. 16YFZCSF00260), the Tianjin Natural Science Foundation (No. 17JCYBJC23000), Fundamental Research Funds for the Central Universities and the Blue Sky Foundation, and Grants from the US National Science Foundation (1243535) and the US EPA (R 83588001). The I

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