Modeling Secondary Organic Aerosol Formation via Multiphase

Model simulations are evaluated against smog chamber data for SOA yields and ... Secondary organic aerosol (SOA) formation is currently a major source...
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Environ. Sci. Technol. 2006, 40, 4722-4731

Modeling Secondary Organic Aerosol Formation via Multiphase Partitioning with Molecular Data BETTY K. PUN,* CHRISTIAN SEIGNEUR, AND KRISTEN LOHMAN Atmospheric & Environmental Research, Inc., 2682 Bishop Drive, Suite 120, San Ramon, California 94583

A new model for atmospheric secondary organic aerosol (SOA) is presented for biogenic compounds. It is based to the extent possible on experimental molecular SOA data, and it is compatible with any existing gas-phase chemical kinetic mechanism. Six SOA precursors or groups of precursors are used to represent biogenic monoterpenes and sesquiterpenes. SOA formation is modeled using five SOA surrogates to represent classes of compounds with different partitioning properties, e.g., hydrophobicity, aqueous solubility, acid dissociation, and saturation vapor pressure. Model simulations are evaluated against smog chamber data for SOA yields and some adjustments are made to uncertain stoichiometric coefficients and saturation vapor pressure parameters to improve model performance. The model is applied under typical atmospheric conditions to exemplify the effect of relative humidity on SOA formation and the relative contributions of hydrophilic and hydrophobic SOA.

Introduction Secondary organic aerosol (SOA) formation is currently a major source of uncertainty in air quality modeling (1). Most current three-dimensional (3-D) air quality models use an empirical representation of SOA formation that is based on the results of smog chamber experiments (2-5). The SOA yields from several anthropogenic and biogenic precursors are parametrized in those experiments. SOA species are assumed to be in equilibrium between the gas phase and an organic particulate phase. There are only a few models that use a detailed representation of the gas-phase chemistry that leads to SOA formation and account for the distribution of the semi-volatile organic species between the gas phase and two particulate phases, an aqueous phase and an organic phase (3, 4, 6). Such models offer a more comprehensive representation of SOA formation; however, they are designed to be used with a specific gas-phase chemical kinetic mechanism, the Caltech Atmospheric Chemistry Mechanism (CACM) that includes a large number of chemical reactions (about 400) (7) and they are, therefore, computationally demanding. It is desirable to develop an approach to SOA modeling that combines a detailed treatment of hydrophobic and hydrophilic SOA formation with generic gas-phase chemical kinetic mechanisms that do not necessarily follow generations of organic compounds and their interactions. We describe here the development of such a model of SOA formation that combines the current state of knowledge with an efficient computational structure. * Corresponding author. 4722

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A SOA formation model includes several components: • Emissions of VOC precursors. • Formation of semi-volatile oxidation products from those precursors. • Distribution of those semi-volatile species between the gas-phase and the particulate phases. While these components need to represent the current state of the science, efficient management of computational requirements is also desired for models intended for applications over large spatial scales and long time periods. Therefore, one should limit the number of precursors and oxidation products being modeled while maintaining a sufficiently detailed representation for the spectrum of the physicochemical properties of the major SOA species.

Approach A review of available molecular information on SOA formed from VOC precursors provides a basis for selecting a list of precursors and condensable compounds represented in the model. Because we did not identify quantitative information on the molecular constituents of SOA formed from anthropogenic precursors (8-16), model development focuses at this point on biogenic compounds. Physicochemical properties of the SOA species are estimated to facilitate the grouping of all identified SOA species into a more tractable set of surrogate SOA species. Using the surrogate species, the gasphase chemical kinetic mechanism that represents SOA formation and the SOA thermodynamic equilibrium model are developed. Several test simulations are conducted with the model against some available smog chamber experiments. Uncertain chemical reactions and SOA physicochemical properties are modified according to the results of the tests. Several simulations are conducted to illustrate the modeled SOA behavior under a range of precursor concentrations and relative humidity. SOA Precursors. Six biogenic VOC precursors of SOA were selected as surrogates for all SOA precursors. This number presents a reasonable compromise between scientific detail and computational efficiency for 3-D applications (17). Each precursor may represent a group of structurally similar precursors. Formulated based on empirical data (8, 18, 19), the MADRID 1 SOA model included originally twelve individual biogenic precursors that were subsequently combined into six individual or surrogate precursors for computational optimization (4, 17). The same approach is used here with the following six individual or surrogate biogenic precursors: • A group that includes R-pinene and sabinene. • A group that includes β-pinene and ∆3-carene. • Limonene. • Terpinene. • A group that includes other monoterpenes such as ocimene and terpinolene, and monoterpenoids such as linalool, terpinenol, and terpineol. • Sesquiterpenes, e.g., R-humulene and β-caryophyllene. There is new evidence that isoprene leads to some SOA formation (20-22). However, quantitative data on SOA molecular constituents are not yet available to characterize SOA formation from isoprene in a mathematical model and, consequently, SOA formation from hemiterpenes (i.e., isoprene and methylbutenol, MBO) is not represented here.

Molecular Speciation of SOA R-Pinene and Sabinene. Several experimental data sets provide molecular information on the SOA products of 10.1021/es0522736 CCC: $33.50

 2006 American Chemical Society Published on Web 06/30/2006

R-pinene oxidation by ozone (O3) along with the associated stoichiometric coefficients and SOA yields (23, 24). Several experimental data sets also provide molecular information on the SOA products of R-pinene oxidation by hydroxyl radicals (OH) (25-27). Among those data sets, that of Jaoui and Kamens (26) is the most complete as it provides both stoichiometric coefficients and SOA yields. Wangberg et al. (28) reported high gas-phase yields of four identified molecular products for the oxidation of R-pinene by nitrate radicals (NO3); however, no information was provided on the SOA yields or gas/particulate partitioning of those gasphase products. Hallquist et al. (29) pointed out the importance of alkylnitrates in the oxidation of R-pinene by NO3, but provided insufficient information to derive parameters for SOA formation. Jaoui and Kamens (30) studied the products of the oxidation of pinonaldehyde in the presence of sunlight. (Pinonaldehyde is a product of the oxidation of R-pinene by O3, OH, and NO3.) They reported high gas-phase yields of several molecular products but did not provide any gas/particulate partitioning data. No data on molecular SOA formation from the oxidation of sabinene were found. R-Pinene (API) was selected to represent R-pinene and sabinene because the former has larger emissions and available experimental data on SOA products. The experimental data of Yu et al. (23) were used for the O3 oxidation pathway, and those of Jaoui and Kamens (26) were used for the OH oxidation pathway. No molecular data are available for the NO3 oxidation pathway. β-Pinene and ∆3-Carene. Several experimental data sets provide molecular information on the SOA products of β-pinene oxidation by O3 along with the associated stoichiometric coefficients and SOA yields (23, 24, 31). In the experiments performed by Jaoui and Kamens (31), OH was not scavenged; therefore, β-pinene oxidation likely resulted from reactions with both O3 and OH. Several experimental data sets also provide molecular information on the SOA products of β-pinene oxidation by OH (25, 31). Of these two data sets, that of Jaoui and Kamens (31) is more complete as it provides the stoichiometric coefficients and SOA yields. Hallquist et al. (29) pointed out the importance of alkylnitrates in the oxidation of β-pinene by NO3, but provided insufficient information to parametrize SOA yields. No molecular SOA data on the oxidation of ∆3-carene were found. β-Pinene (BPI) was selected to represent β-pinene and ∆3-carene because the former has larger emissions and available experimental data on SOA products. The experimental data of Yu et al. (23) and Jaoui and Kamens (31) were used for the O3 oxidation pathway, and those from Jaoui and Kamens (31) were used for the OH oxidation pathway. No molecular data are available for the NO3 oxidation pathway. Limonene. Glasius et al. (24) reported particulate-phase yields of the oxidation products of limonene by O3. Larsen et al. (25) reported particulate-phase yields of five products of the oxidation of limonene by OH. Hallquist et al. (29) pointed out the importance of nitrates in the oxidation of limonene by NO3, but provided insufficient information to parametrize SOA formation. For limonene (LIM), the experimental data of Glasius et al. (24) were used for the O3 oxidation pathway, and those from Larsen et al. (25) were used for the OH oxidation pathway. The NO3 oxidation pathway was not considered because of a lack of data. Terpinene. No experimental data providing molecular information on the SOA from terpinene oxidation were found. Griffin et al. (7) developed a mechanism for the oxidation of terpinene by O3, OH, and NO3. The SOA products from their mechanism were used here for terpinene (TPE). Other Monoterpenes and Monoterpenoids. A few experimental data sets provide molecular information on the products of the oxidation of ocimene by O3 (32) and OH (32, 33). However, only gas-phase or minor products were

reported. No experimental data were found for the molecular SOA oxidation products of terpinolene, linalool, or terpineol. Griffin et al. (7) developed a mechanism for the oxidation of terpineol by O3, OH, and NO3. Terpineol (TPO) was selected as the surrogate precursor of this group of biogenic compounds and the SOA products from the mechanism of Griffin et al. (7) were used. Sesquiterpenes. Jaoui and Kamens (34) identified molecular SOA products of the oxidation of humulene in a smog chamber experiment with sunlight. Both stoichiometric coefficients and SOA yields were reported for each oxidation product. Data on caryophyllene reacting with O3 were reported by Jaoui et al. (35). Data on cedrene reacting with O3 were reported by Jaoui et al. (36). Humulene (HUM) was selected as the surrogate precursor representing sesquiterpenes to take advantage of the most extensive set of experimental data on SOA formation. The experimental data of Jaoui and Kamens (34) were used. The OH oxidation pathway was assumed to be dominant. Estimation of Physicochemical Properties of SOA Species. The distribution of the condensable organic species, compiled above, between hydrophobic and hydrophilic species is based on the values of their octanol/water partition coefficients (Kow) at 298 K. The physicochemical properties needed to characterize the partitioning of the condensable organic species between the gas phase and the particulate phase include the Henry’s law constant (Kaw) (hydrophilic compounds), the saturation vapor pressure (VPsat) (hydrophobic compounds and, in the absence of an aqueous phase, hydrophilic compounds), the enthalpy of vaporization (∆Hvap), the aqueous dissociation constant(s) for acids, the deliquescence relative humidity (DRH), and the activity coefficients. Two methods were considered to calculate the Kow values (37, 38). The Broto et al. method (37) was used here. The group contribution method of Suzuki et al. (39) was used to calculate Kaw at 298 K. Temperature dependence is not modeled for Kaw. The estimates of VPsat are highly uncertain. Several methods were used. First, VPsat was derived from Kaw (see above) and the solubility (40), both properties being estimated by group contribution methods. For this method, the vapor pressure of a solute is estimated as the product of the aqueous solubility and Kaw. This approximation is typically good for sparingly soluble compounds; the uncertainties can be significant when applied to water-soluble compounds. An alternative method was used that involved using group contribution methods to determine the boiling temperature of individual compounds and relating that property to VPsat (41). In general, the estimated subcooled liquid vapor pressures agree quite well among the different methods. The boiling temperature based method predicts lower VPsat than the first method. The boiling temperature method is used because only the boiling temperature needs to be estimated using group contribution method (42, 43), and there is a stronger conceptual basis for relating boiling temperature to VPsat. The temperature dependence of VPsat is modeled using the Clausius-Clapeyron equation. ∆Hvap are assigned based on experimental values available for a few compounds (44, 45). The first and second acid dissociation constants for twicedissociative acids, and the acid dissociation constant for oncedissociative acids are modeled after malic acid and glyoxalic acid, respectively (46), and are assumed to be constant with temperature. No information is available regarding the DRH of the surrogate compounds. We assume that the twicedissociating compounds with functional groups have a DRH of 79% (same as malic acid), while the other compounds do not exhibit deliquescence behavior (46). UNIFAC was used VOL. 40, NO. 15, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Properties of Hydrophilic (Type A) Surrogate SOA Compoundsa surrogate compound

FIGURE 1. Distribution of the condensable biogenic organic compounds according to their octanol/water coefficient (Kow) and saturation vapor pressure (VPsat). to calculate the activity coefficients of the surrogate SOA compounds as a function of temperature. Grouping of SOA Species. A Kow value of 10 was used as the criterion separating hydrophilic (Kow < 10) and hydrophobic (Kow > 10) compounds. Figure 1 presents the Kow and the VPsat of the individual condensable organic compounds produced from the oxidation of biogenic compounds, i.e., R-pinene, β-pinene, limonene, terpinene, terpineol, and humulene. The sesquiterpene humulene produces the most hydrophobic products. Six groups of SOA compounds were selected. Those groups include three groups of hydrophilic (type A) SOA compounds and three groups of hydrophobic (type B) compounds. The hydrophilic groups were characterized by their acid-dissociation characteristics: nondissociative, single dissociative, or double dissociative. The hydrophobic groups were characterized according to their VPsat: low VPsat, moderate VPsat, or high VPsat. Biogenic Hydrophilic Nondissociative SOA Compounds (BiA0D). These compounds have carbonyl groups (i.e., aldehydes and ketones) and hydroxy groups (i.e., alcohols). They include oxidation products of pinenes (pinonaldehyde, norpinonaldehyde, hydroxypinonaldehyde, and hydroxypinaketone), limonene (limononaldehyde, hydroxylimononaldehyde, and ketolimononaldehyde), terpinene (3,7-dimethyl-6-oxo-3-octenal), and terpineol (2-hydroxy-3-isopropyl-6-oxo-heptanal, 2-hydroxy-3-isopropyl-6-methyl-cyclohexanone, and 2-hydroxy-3-isopropyl-hexandial). Kow values range from 0.5 to 20, and VPsat range between 10-6 and 10-1 Torr. The molecular structure of the surrogate SOA compound includes 10 carbon atoms with an oxo group (CdO) and an aldehyde group (CHO). Biogenic Hydrophilic Single Dissociative SOA Compounds (BiA1D). These compounds have a single carboxy group. They include oxidation products of the pinenes (pinonic acid, norpinonic acid, hydroxypinonic acid, pinalic-4-acid, 4-oxopinonic acid, hydroxynorpinonic acid, and 4-hydroxypinalic3-acid), limonene (hydroxylimononic acid, limononic acid, and ketolimononic acid), terpinene (3-isopropyl-4-hydroxy2-butenoic acid, and 3-isopropyl-6-oxo-3-heptenoic acid), and terpineol (2-hydroxy-3-isopropyl-6-oxoheptanoic acid). Kow values are between about 0.5 and 15, and VPsat are low to moderate (10-10 to 10-5 Torr). The molecular structure of the surrogate SOA compound is that of norpinonic acid with nine carbon atoms, a carboxy group (COOH), and an oxo group (CdO). Biogenic Hydrophilic Double Dissociative SOA Compounds (BiA2D). These compounds have two carboxy groups. They are all oxidation products of the pinenes (pinic acid and norpinic acid) and limonene (limonic acid). Kow values of the diacids are between 1 and 10, and VPsat values are low to moderate (10-8 to 10-5 Torr). The molecular structure of the 4724

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molecular weight Henry’s law constant [(µg/µg water)/(µg/m3 air)]b deliquescence relative humidity VPsat [µg/m3 air]b enthalpy of vaporization [kJ/mol]

BiA2D

BiA1D

BiA0D

pinic acid

nor-pinonic acid

C10 oxo aldehyde

186 170 168 6.25 × 10-3 2.73 × 10-3 4.82 × 10-5 0.79

0

0

1.43 109

1.99 88

2.44 × 103 88

a Bi is biogenic, A is hydrophilic, 2D is twice dissociative, 1D is once dissociative, and 0D is nondissociative. b At 1 atm and 298 K.

surrogate SOA compound is that of pinic acid; it includes nine carbon atoms with two carboxy groups (COOH). Biogenic Hydrophobic SOA Compounds with High VPsat (BiBhP). These compounds have a high Kow (near 100) and a high VPsat (near 0.1 Torr). They include a product of β-pinene (nopinone) and a product of terpineol (butanoic acid). The surrogate compound, nopinone (C9 with one oxo group), was selected because it has been identified in smog chamber experiments. The SOA compounds with high VPsat will typically be present primarily in the gas phase. Biogenic Hydrophobic SOA Compounds with Moderate VPsat (BiBmP). These compounds have a high Kow (between 100 and 1000), and a moderate VPsat (between 10-5 and 10-3 Torr). There are three oxidation products of humulene (humulal aldehyde, humulone aldehyde, and hydroxyhumulone aldehyde), a product of terpinene (methylnitratodihydroxy-isopropylcyclohexane), and a product of terpineol (methylhydroxyisopropylcyclohexane epoxide). The SOA compounds with moderate VPsat will typically partition between the gas phase and the particulate phase. The structure of the SOA compound includes 15 carbon atoms with an oxo group (CdO) and an aldehyde group (CHO). Biogenic Hydrophobic SOA Compounds with Low VPsat (BiBlP). These compounds have a moderate Kow (between 1 and 100) and a low VPsat (between 10-14 and 10-7 Torr). This group includes one oxidation product of humulene (humulaic acid) and two oxidation products of terpineol (isopropylnitrato-methylhydroxycyclohexane and peroxyhydroxyisopropyl-oxo-heptionylnitrate). SOA compounds with low VPsat will typically be present primarily in the particulate phase. The structure of the SOA compound includes 15 carbon atoms with a nitrato group (ONO2), a hydroxy group (OH), and an aldehyde group (CHO). Properties of Surrogate SOA Compounds. The molecular weight of each surrogate compound is determined based on its structure and functional groups. The Kow, Henry’s law constant, and VPsat of the surrogate species are derived from the geometric average property of the group. Other properties are estimated using the structure of each surrogate compound. Selected properties are presented in Table 1 for hydrophilic (type A) compounds and in Table 2 for hydrophobic (type B) compounds.

Gas-phase Chemical Reactions An empirical representation is used for the gas-phase chemistry leading to SOA formation. In this case, the kinetics of the first oxidation step is assumed to be rate-limiting (i.e., the subsequent reactions have faster kinetics). The SOA formation reactions are written in parallel to the existing gas-phase chemical kinetic mechanism in such a manner

TABLE 2. Properties of Hydrophobic (Type B) Surrogate SOA Compoundsa

surrogate compound molecular weight VPsat [mmHg]c enthalpy of vaporization [kJ/mol]

BiBlP

BiBmPb

BiBhP

C15 hydroxy nitrato aldehyde with 2 double bonds

C15 oxo aldehyde with 2 double bonds

nopinone

298 6 × 10-10 175

236 5 × 10-6, 3 × 10-7 175

138 0.048 88

a Bi is biogenic, B is hydrophobic, lP is low VP , mP is moderate sat VPsat, and hP is high VPsat. b Second value corresponds to the value modified after the test simulations. c At 1 atm and 298 K.

that the chemistry represented by the existing mechanism is not perturbed by the added SOA mechanism (3). The emissions of the SOA precursors are derived from the same detailed molecular emission inventory as those used for the existing chemical mechanism to guarantee exact compatibility between VOC emissions in the existing mechanism and the added SOA mechanism (for example, emissions of monoterpenes represented by one surrogate species in the existing mechanism are equivalent to the emissions of the five surrogate precursors of the SOA mechanism). The SOA formation reactions include the oxidant species (i.e., OH, O3, or NO3) as both a reactant and a product so that their concentrations are not affected by the added SOA-forming reactions. The chemical kinetic rate parameters are obtained from available data. The derivation of stoichiometric coefficients is described below. For R-pinene, β-pinene, and humulene, experimental yield data on the gas-phase and particulate-phase oxidation products were available for the OH reaction and, in the case of the pinenes, for the O3 reaction. Those data were used to derive the stoichiometric coefficients of the individual compounds selected for our analysis. Then, stoichiometric coefficients were derived for the corresponding surrogate compounds to obtain the same SOA mass. The selected individual compounds represent only a subset of all the oxidation products because minor products were identified but not represented in the model, and the molecular products characterized in smog chambers may correspond to less than 100% (typically about 30-60%) of the carbon mass of the original precursor. In the case of the pinenes, the missing mass consists mostly of volatile compounds, including formaldehyde and acetone (31). In the case of humulene, smog chamber data suggest that most oxidation products are condensable; therefore, to account for this lack of mass balance in the experimental data, we scaled the stoichiometric coefficients of the humulene products accordingly, thereby assuming that the unidentified products would behave similarly to those that were identified. These reactions are shown in Table 3. As mentioned above, no molecular data were identified for the reactions of the pinenes with NO3. However, β-pinene, carene, and sabinene reacting with NO3 have been shown in smog chambers to result in high yields of SOA (19). In lieu of molecular data, we used the stoichiometric factors from the smog chamber experiments to represent the reactions of biogenic precursors with NO3. The stoichiometric factors of Griffin et al. (19) have values of 1 in mass units. The empirical stoichiometric factors of Griffin et al. (19) were converted using the molecular weights of the SOA surrogate compounds and VOC precursors to obtain molar stoichiometric coefficients. We assumed that the products could be

represented by a hydrophobic compound with a moderate VPsat, because the smog chamber experiments were conducted under low humidity conditions and some gas-particle partitioning was observed. (In comparison, a compound with low VPsat would have too much affinity toward the particulate phase.) Thus, using the molecular weight of BiBmP and monoterpene precursors, a molar stoichiometric coefficient of 0.6 was used. This coefficient is evaluated in the modeling tests. For limonene, the experimental data from the European Joint Research Center included only the particulate fraction. We estimated the total product amount (i.e., gas phase + particulate phase) by analogy with the corresponding compounds produced by the pinenes; i.e., pinonaldehyde for the BiA0D compounds, norpinonic acid for the BiA1D compounds, and pinic acid for the BiA2D compounds. These a priori limonene reactions are as follows:

LIM + OH w OH + 0.20 BiA0D + 0.05 BiA1D + 0.001 BiA2D LIM + O3 w O3 + 0.09 BiA0D + 0.02 BiA1D Because the estimated stoichiometric coefficients are uncertain due to the approximations used to derive the partitioning of limonene products, the stoichiometric coefficients of the limonene reactions are evaluated in the modeling tests. For terpinene and terpineol, the mechanism of Griffin et al. (7) was used because no experimental data were available. Condensable products may be formed as second- or thirdgeneration products of precursors involving condensable intermediates in some cases. In addition, several pathways may be available that lead to different products (typically, for peroxyl radicals, reaction with NO, organic peroxyl radicals, and hydroxyperoxyl radicals). The approximation of multiple steps and branches in a chemical mechanism producing SOA with a single reaction step involves some uncertainties. Therefore, a parameter was used for the uncertain stoichiometric coefficients in the following OH reactions.

TPE + OH w OH + RTPE BiA0D + (1 - RTPE) BiBmP TPO + OH w OH + RTPO BiA0D + 0.25 (1 - RTPO) BiA1D The parameters (RTPE, RTPO) are defined below when conducting the test simulations with available smog chamber data. The O3 reactions (Table 3) do not lead to as many different SOA products depending on the reaction pathway; therefore, adjustable stoichiometric coefficients were not used. The reaction of TPE with NO3 leads to BiA0D with an assumed stoichiometric coefficient of 1; the reaction of TPO with NO3 follows a scheme similar to the OH reaction, and the same reaction products and stoichiometric coefficients were used. Significant uncertainties are associated with these NO3 reactions. Further evaluation awaits new experimental data on SOA yield and molecular product information.

Thermodynamic SOA Model The partitioning model is a modified version of the MADRID 2 thermodynamic equilibrium model (46). As discussed above, the surrogate SOA compounds selected here differ from those used in MADRID 2. New SOA surrogates and their corresponding physicochemical properties (Tables 1 and 2). The model simulates two types of particles as an external mixture: type A is aqueous-phase particles and type B is organic-phase particles. Hydrophilic compounds are asVOL. 40, NO. 15, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 3. Gas-phase Chemical Mechanism for SOA Formation Modified Based on the Test Simulations reaction

reaction rate constant (cm3 molec-1 s-1)a

API + OH w OH + 0.30 BiA0D + 0.17 BiA1D + 0.10 BiA2D API + O3 w O3 + 0.18 BiA0D + 0.16 BiA1D + 0.05 BiA2D API + NO3 w NO3 + 0.8 BiBmP BPI + OH w OH + 0.07 BiA0D + 0.08 BiA1D + 0.06 BiA2D BPI + O3 w O3 + 0.09 BiA0D + 0.13 BiA1D + 0.04 BiA2D BPI + NO3 w NO3 + 0.8 BiBmP LIM + OH w OH + 0.20 BiA0D + 0.25 BiA1D + 0.005 BiA2D LIM + O3 w O3 + 0.09 BiA0D + 0.10 BiA1D TPE + OH w OH + 0.8 BiA0D + 0.2 BiBmP TPE + O3 w O3 + 0.055 BiA0D + 0.15 BiA1D TPE + NO3 w NO3 + 1.0 BiA0D TPO + OH w OH + 0.7 BiA0D + 0.075 BiA1D TPO + O3 w O3 + 0.5 BiA0D + 0.055 BiA1D TPO + NO3 w NO3 + 0.7 BiA0D + 0.075 BiA1D HUM + OH w OH + 0.74 BiBmP + 0.26 BiBlP

1.21 × 10-11 × exp (444/T) 1.01 × 10-15 × exp (-732/T) 1.19 × 10-12 × exp (490/T) 2.38 × 10-11 × exp (357/T) 1.5 × 10-17 2.51 × 10-12 1.71 × 10-10 2 × 10-16 5.3 × 10-8/T 4.2 × 10-14/T 8.7 × 10-9/T 5.1 × 10-8/T 7.5 × 10-14/T 4.3 × 10-9/T 2.93 × 10-10

a Rate constants for TPE and TPO from Griffin et al. (7); rate constants for API and BPI from Atkinson (47); rate constants for LIM and HUM from Lamb et al. (48).

sumed to partition between the gas and the aqueous phases according to Henry’s law. Acidic compounds may dissociate in water, enhancing further partition into the aqueous phase. Type A compounds interact with inorganic species (i.e., sulfate, nitrate, ammonium, sodium, chloride) via the pH and liquid water content of the particles. The ISORROPIA model is used to simulate the thermodynamics of inorganic species (49, 50). If an aqueous phase is not present (e.g., due to low relative humidity), type A compounds are then treated similarly to the type B compounds. Type B particles are formed when condensable compounds, especially nonpolar ones, are absorbed into an organic-phase particle. In the ambient atmosphere, the absorbing medium may be predominantly primary compounds near source areas, but it will contain a mixture of both primary and secondary components downwind. However, in a smog chamber environment, a secondary organic aerosol (SOA) may condense onto itself. Water is not included in type B particles, assumed to be hydrophobic. The formulation of Pankow (51) is used to represent the gas/particulate thermodynamic equilibrium. The activity coefficients of the organic species (both type A and type B) are calculated with UNIFAC. A detailed description of the MADRID 2 thermodynamic model is presented by Pun et al. (46).

Modeling Tests and Final Model Configuration The base model was tested against the smog chamber data of Griffin et al. (19). Smog chamber experiments were conducted at an average temperature of 312K, and the model was applied at the corresponding temperature. The smog chamber data presented in the literature correspond to SOA yield values when the precursor has been depleted. Therefore, we also assume in the simulations that the reaction has gone to completion. The smog chamber results are reported in terms of the particulate SOA yield (i.e., mass of particulate SOA formed divided by the mass of precursor reacted) as a function of the particulate organic mass. In the smog chamber experiments, total organic mass equals the SOA particulate mass since no primary organic aerosol is present. All smog chamber experiments considered here were conducted under dry conditions. Therefore, no type A SOA would dissolve into an aqueous phase, and we assumed that they would instead absorb into an organic particulate phase. Following Griffin et al. (6), the results are presented in terms of the yield of particulate SOA as a function of the mass of particulate SOA formed. The results of the test simulations for R-pinene (API) and β-pinene (BPI) are presented in Figure 2a and b, respectively. The data for API correspond to the smog chamber results for 4726

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R-pinene and sabinene, and those for BPI correspond to the smog chamber results for β-pinene and carene. The comparison between the initial SOA formation mechanism and the data shows that good agreement is obtained for the formation of SOA from the oxidation of R-pinene by O3 but that the model overestimates the formation of SOA from the oxidation of R-pinene and sabinene by OH. However, the model is consistent with the maximum particulate SOA yield reported by Jaoui and Kamens (26) for their experiments with R-pinene in the presence of NOx and sunlight. They reported maximum C yields for particulate SOA of 19-27%. Accounting for the difference in molecular weight and carbon number of the SOA products and VOC precursor, the maximum modeled C yield is about 23%; i.e., the model is consistent with the data from Jaoui and Kamens (26). For the ozonolysis of R-pinene, Yu et al. (23) reported maximum C yields of 12-14%; the maximum modeled C yield is about 18%. The model shows good agreement with the β-pinene and carene data for the oxidation of these compounds by both O3 and OH (except at the high SOA concentrations for the OH pathway where the model underestimates). The model simulation results are consistent with the particulate SOA yields obtained by Jaoui and Kamens (31) for β-pinene; they reported a 13% maximum C yield for the OH pathway and a 20% maximum C yield for the O3 pathway. The model predicts maximum C yields of 12% and 15% for the OH and O3 pathways, respectively. The surrogate product BiBhP that appears in the oxidation of β-pinene with OH and O3 remains in the gas phase due to its high VPsat; therefore, it was eliminated from the mechanism. The results for the NO3 pathway show an underprediction of the model for both R-pinene and β-pinene. This underprediction is likely due to the fact that the formulation of the stoichiometric factors derived by Griffin et al. (19) was capped at 1. Increasing the molar stoichiometric coefficients from 0.6 to 0.8 leads to good agreement between the model and the experimental data. The results of the test simulations for limonene (LIM) are presented in Figure 2c. The comparison between the initial SOA formation mechanism and the data for the OH pathway shows a significant underestimation of the model. As discussed above, the molecular experimental data only provided the particulate SOA yields, and gas + particulate yields were deducted by making some assumptions on the partitioning of the SOA products. Therefore, there are significant uncertainties in these estimates. Moreover, not all particulate SOA products were identified, which leads to an underestimation of the SOA yields. Consequently, the values of the stoichiometric coefficients of some SOA products of limonene

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FIGURE 2. Comparison of simulated SOA yields with smog chamber data of Griffin et al. (19) for (a) r-pinene and sabinene, (b) β-pinene and carene, (c) limonene, (d) terpinene, (e) terpineol and other monoterpenes/monoterpenoids, and (f) humulene and other sesquiterpenes. are increased to account for those underestimations. For the OH pathway, we increased the stoichiometric coefficient of the BiA1D surrogate from 0.05 to 0.25 and that of the BiA2D surrogate from 0.001 to 0.005. Similarly, for the O3 pathway, we increased the stoichiometric coefficient of the BiA1D 4728

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surrogate from 0.02 to 0.10. Good agreement is then obtained between the model and the experimental data. The results of the test simulations for terpinene (TPE) and terpineol (TPO) are presented in Figure 2d and e, respectively. The data for TPE are specific to terpinene,

whereas the data for TPO correspond to the smog chamber results for other monoterpenes and monoterpenoids (i.e., terpinenol, linalool, ocimene, and terpinolene). The comparison between the initial SOA formation mechanism and the data shows that, if a value of the stoichiometric parameter R of 1 is used, the model significantly underestimates the particulate SOA yield (the stoichiometric coefficient of the more condensable compound is defined as (1 - R)). For terpinene, a value of RTPE of 0.8 was selected, and for terpineol, a value of RTPO of 0.7 was used. In addition, the VPsat of the SOA surrogate compound BiBmP was lowered from 5 × 10-6 to 3 × 10-7 Torr (see humulene below). Satisfactory agreement is then obtained between the model and the data available for the OH pathway. The NO3 pathway for SOA formation from TPE leads to a hydrophilic surrogate compound that has a high VPsat and, therefore, does not lead to particulate SOA formation under the dry conditions used in the test simulations. The NO3 pathway for SOA formation from TPO leads to the same surrogate reaction products as the OH pathway; consequently, it is not shown in Figure 2e. The results of the test simulations for humulene (HUM) are presented in Figure 2f. The data for HUM correspond to the smog chamber results for humulene and caryophyllene. The comparison between the initial SOA formation mechanism and the data shows that the model significantly underestimates for SOA concentrations above 20 µg/m3. To improve agreement with the smog chamber data, we reduced the VPsat of the SOA surrogate compound BiBmP from 5 × 10-6 to 3 × 10-7 Torr. This lower value is within the range corresponding to this SOA surrogate compound (see Figure 1) and this adjustment is justified by the uncertainty associated with estimation methods for VPsat. The model then shows good agreement with the experimental data for SOA concentrations above 20 µg/m3, although it overestimates at the low SOA concentrations. Table 3 presents the final chemical kinetic mechanism for biogenic SOA formation. The revised properties of the hydrophobic SOA surrogate compounds are presented in Table 2. No changes were made to the properties of the hydrophilic SOA surrogate compounds (see Table 1).

Model Application This biogenic SOA formation model was applied in a box (0-D) model configuration to illustrate its characteristics in terms of simulating both hydrophilic and hydrophobic SOA. Rural conditions were used. They included initial concentrations of 0.4, 0.5, 0.2, 0.4, 0.4, and 0.4 ppb for API, BPI, LIM, TPE, TPO, and HUM, respectively. The biogenic initial concentrations were deduced from individual terpene species profiles (including isoprene, monoterpenes, and sesquiterpenes) in Georgia and Wisconsin forests (52, 53) that were scaled to typical isoprene concentrations (54). Constant concentrations of O3 (60 ppb) and OH (106 molecules/cm3) were used. Initial inorganic aerosol concentrations typical of the southeastern United States during summertime (3) were used; those were 8, 5, and 7 µg/m3 for sulfate, total (i.e., gaseous + particulate) nitrate, and total ammonium, respectively. Primary particulate organic concentrations were chosen to be 2 µg/m3. The ambient temperature was 298 K. To illustrate the effect of relative humidity on the partitioning of SOA, two simulations of 1 h were conducted: a simulation with a low relative humidity of 10% leading to a dry aerosol and a simulation with a high relative humidity of 90% leading to the presence of aqueous particles. Under dry conditions, no particulate nitrate was formed and sulfate and ammonium concentrations were 8 and 2.8 µg/m3, respectively. Under humid conditions, some nitrate was present in the aqueous particles and sulfate, nitrate, and ammonium concentrations were 8, 1.5, and 3.5 µg/m3, respectively.

FIGURE 3. Simulation of SOA formation with (a) relative humidity of 10% and (b) relative humidity of 90%. Figure 3 presents the results of the two simulations. Under dry conditions, the particulate SOA concentration after 1 h amounts to 2.07 µg/m3; it consists entirely of type B SOA. The presence of aqueous particles under high humidity conditions leads to an enhancement in SOA formation of 8% (2.24 µg/m3). This increase is due to the dissolution of a small amount of type A biogenic SOA (0.17 µg/m3). This result is qualitatively consistent with the results obtained by Pun et al. (3) who obtained about 5-15% type A SOA in their southeastern U.S. simulation with MADRID 2. This model is developed with three-dimensional applications in mind. Equilibrium calculations, such as those illustrated in this section, apply to the bulk particulate phase. In the ambient atmosphere, the SOA product distribution from the gas phase reaction of any precuror likely changes with time, with the formation of several generations of SOA compounds. Neither the composition changes nor the associated changes in thermodynamic properties can be modeled using a single oxidation step of the precursor VOC. (Modeling the evolution of the composition of the SOA products of a precursor would require a detailed gas-phase mechanism of the formation of the organic oxidation products (6, 7, 46)). Nonetheless, at every time step, the equilibrium is recalculated, and mass can be added (condensation) or removed (evaporation) from the particulate phase, depending on temperature, relative humidity, and the amount of absorbing PM present in the system. Instantaneous equilibrium partitioning is a reasonable assumption for mass transfer to and from fine particles (e.g., with aerodynamic diameter less than 2.5 µm). For large particles, equilibrium may not be reached rapidly because mass transfer may be the limiting step; mass transfer between the gas phase and the particulate phase must then be treated explicitly (4, 55). This SOA model provides a useful framework for integrating future experimental molecular data on SOA formation. As new data become available, the model can be upVOL. 40, NO. 15, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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dated with the molecular data and further evaluated against SOA yields from smog chamber experiments. It can be extended to anthropogenic compounds (representative precursors may include aromatic compounds, long-chain alkanes, and alkenes) and hemiterpenes when quantitative data on the molecular composition of SOA products become available. In addition, when the chemical pathways leading to the formation of oligomers in the particulate phase are conclusively determined and their kinetics quantified, the model framework can be extended to represent the formation of higher molecular weight SOA. The incorporation of this SOA model into 3-D air quality models will provide a modeling approach to SOA formation that treats both hydrophilic and hydrophobic SOA with reasonable computational efficiency.

Acknowledgments This work was conducted under the sponsorship of the Institut National de l′Environnement Industriel et des Risques (INERIS), Verneuil en Halatte, France; we thank the INERIS Project Manager, Dr. Bertrand Bessagnet, for his support throughout this work.

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Received for review November 10, 2005. Revised manuscript received May 10, 2006. Accepted May 26, 2006. ES0522736

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