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SOA Formation from Partitioning and...

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Environ. Sci. Technol. 2006, 40, 3013-3022

SOA Formation from Partitioning and Heterogeneous Reactions: Model Study in the Presence of Inorganic Species MYOSEON JANG,* NADINE M. CZOSCHKE, AMANDA L. NORTHCROSS, GANG CAO, AND DAVID SHAOF Department of Environmental Sciences and Engineering, CB# 7431, Rosenau Hall, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, 27599

A predictive model for secondary organic aerosol (SOA) formation by both partitioning and heterogeneous reactions was developed for SOA created from ozonolysis of R-pinene in the presence of preexisting inorganic seed aerosols. SOA was created in a 2 m3 polytetrafluoroethylene film indoor chamber under darkness. Extensive sets of SOA experiments were conducted varying humidity, inorganic seed compositions comprising of ammonium sulfate and sulfuric acid, and amounts of inorganic seed mass. SOA mass was decoupled into partitioning (OMP) and heterogeneous aerosol production (OMH). The reaction rate constant for OMH production was subdivided into three categories (fast, medium, and slow) to consider different reactivity of organic products for the particle phase heterogeneous reactions. The influence of particle acidity on reaction rates was treated in a previous semiempirical model (1). Model OMH was developed with medium and strong acidic seed aerosols, and then extrapolated to OMH in weak acidic conditions, which are more relevant to atmospheric aerosols. To demonstrate the effects of preexisting glyoxal derivatives (e.g., glyoxal hydrate and dimer) on OMH, SOA was created with a seed mixture comprising of aqueous glyoxal and inorganic species. Our results show that heterogeneous SOA formation was also influenced by preexisting reactive glyoxal derivatives.

Introduction Gas-phase reactions of volatile organic compounds (VOCs) linked to photochemical cycles associated with atmospheric oxidants such as OH, O3, and, NOx, have been of great interest in predicting both O3 concentration and secondary organic aerosol (SOA) formation. SOA has long been studied by many research groups because of potential influences on climate forcing (2), visibility degradation (3) and adverse health effects (4, 5). Therefore, great efforts have been invested in both predicting and characterizing SOA (6-9). Our previous studies (10-16) indicated that atmospheric carbonyls can be further transformed via heterogeneous acidcatalyzed reactions between the gas and the particle phase in the presence of inorganic acids such as sulfuric acid (H2SO4), ammonium hydrogen sulfate (NH4HSO4), and nitric acid (HNO3). The net outcome is an increase in SOA mass * Corresponding author phone: (919)966-9010; fax: (910)966-7911; e-mail: [email protected]. 10.1021/es0511220 CCC: $33.50 Published on Web 04/04/2006

 2006 American Chemical Society

and formation of oligomeric species (10). Recently, studies in many research groups (17-20) have evinced oligomeric structures in diverse SOA created from atmospheric oxidation of both biogenics and aromatics. Oligomers are observed in SOA in the presence of both acidic and nonacidic seed aerosol, although a much greater oligomeric fraction is seen in acidic aerosol. Such studies indicate that heterogeneous reactions are important processes in SOA formation. Our studies have also shown that the acid catalytic effect on aerosol growth is influenced by humidity, composition of seed inorganic aerosols, and molecular structure of carbonyl species (1, 21). In particular, the recent study by Czoschke and Jang (21) has demonstrated the effect of particle acidity on the SOA yields from the ozonolysis of R-pinene. In 2005, Jang et al. (1) attempted to develop semiempirical model approaches to predict the organic aerosol growth by heterogeneous acid-catalyzed reactions of various organic carbonyls by implementing inorganic (22, 23) and organic thermodynamic approaches. The derived model parameters to predict aerosol growth were semiempirically fit to the experimental data from aerosol yields in a flow reactor. This semiempirical approach revealed that both the chemical structure of carbonyls and characteristic environmental parameters, such as humidity and inorganic seed composition, are significant in the prediction of organic aerosol growth. In this study, a predictive model for SOA formation by both partitioning and heterogeneous reactions has been established for an extensive experimental data set including both the SOA data in this study and the SOA data recently presented by Czoschke and Jang (21). The objectives of this study were to (1) develop a model to predict SOA formation by heterogeneous acid-catalyzed reactions in strong acidic conditions implementing both inorganic and organic thermodynamic model parameters, (2) extrapolate the model to SOA formation in weak acidic conditions which are more relevant to atmospheric aerosols, and (3) understand the effects of preexisting reactive organic material (e.g., glyoxal oligomer) on heterogeneous SOA formation.

Experimental Section The detailed experimental procedure used in this study has been reported previously (1, 21). All experiments were conducted in a 2 m3 indoor polytetrafluoroethylene film chamber under darkness. The chamber was flushed with clean air from two clean air generators (Aadco model 737, Rockville, MD; Whatman model 75-52, Haverhill, MA) prior to each experiment. A seed aerosol was injected into the chamber using an atomizer (TSI, model 3076, Shoreview, MN) and passed through a diffusion drier (TSI, model 3062). Inorganic seed aerosols were made from an aqueous solution (0.01 M) of ammonium sulfate [(NH4)2SO4, AS], ammonium hydrogen sulfate (NH4HSO4, AHS), and sulfuric acid (H2SO4). The data set used for the predictive model are shown in Table 1 including both new data obtained for this study and a previous data set (21). In particular, seed inorganic mass had the range of 64-340 µg/m3 in the new data set to study the effects of inorganic seed mass on SOA yields for a given inorganic seed composition (50% of sulfuric acid and 50% of AHS, mol/mol). Seed aerosols were also created from combinations of inorganic/organic solutions (0.05 M glyoxal aqueous solution). After injecting seed aerosols, ozone was injected into the chamber by passing clean air through a photolytic ozone generator (Jelight model 600, Irvine, CA). The ozone was monitored using a photometric ozone detector (Thermo VOL. 40, NO. 9, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY







Figure 6

3 8 1 0.40-0.76

Figure 6

4 1

validation (Figure S3) Figure 6

48 1

Figure 3A, Figure 3B, Figure 4 & Figure 5 Czoschke & Jang (21), Figure 1 and Figure 3B Czoschke & Jang (21) 10 1

comments on dataa # of exp. inorganic fraction of Mseed

Environmental Instruments, Model 49). An excess of ozone was injected in order to achieve an R-pinene limited experiment. R-Pinene (Aldrich, 98%) as 20% solution in carbon tetrachloride (Aldrich, 99.9%) was introduced into the chamber by passing the clean air stream trough a T-shaped glass tube and gently heated using a heat gun. The R-pinene concentration in the chamber was measured using a GC-FID (Carlo Erba Strumentazione) with a 30 m 0.025 ID Restek RTX-5 column at 130 °C. Particle size population were measured using a scanning mobility particle sizer (TSI, SMPS model 3080 Shoreview, Minnesota) associated with a condensation nuclei counter (TSI, model 3025A). The particle number concentration was corrected for particle loss to the wall using a semiempirical exponential decay function for each particle diameter over time (24). Aerosol volume concentrations and aerosol mass were also estimated from the corrected number distribution. All compounds were purchased from Aldrich (Milwaukee, WI). Temperature and relative humidity (RH) were measured with an electronic thermo-hygrometer (Hanna Instruments, Italy). The temperatures for experiments in the new data set were 22-25 °C.



0.33 163 10 0.3 glyoxal VII

Figure 2A and Figure 2B are made of experimental set I, II, and III.

10-47 0.3-0.4 (NH4)2SO4/glyoxal VI

NH4HSO4/H2SO4 NH4HSO4/H2SO4/glyoxal IV V




30-39 10-47 0.18-0.25 0.3-0.4


0.65 0.75

20-63 0.6-0.7

63-235 75-262

10-83 0.3-0.4


1.0, 0.33, 0.5, 0.65, 0.85 0.5, 0.65, 1.0






Aerosol Yields. The fractional aerosol yield (Y) is often defined as the fraction of a hydrocarbon that is converted to SOA and calculated by (7)

850 (average 150 ppb) 729-936 (average 150 ppb) 1,588-1,931 (average 300 ppb) 258 (45 ppb) 840-860 (average 150 ppb) 840-860 (average 150 ppb) 850 (NH4)2SO4 NH4HSO4/H2SO4 (NH4)2SO4 NH4HSO4/H2SO4 NH4HSO4/H2SO4 I

initial O3 (ppm) r-pinene (µg/m3) seed exp. set

TABLE 1. Summary of Indoor Polytetrafluoroethylene Film Chamber Experiments

RH (%)

Mseed (µg/m3)



Results and Discussion




where OM is the organic mass concentration (µg/m3) and ∆ROG is the mass of hydrocarbon that reacted (µg/m3). The hydrocarbon used in this study is R-pinene. The experimental OM in the presence of inorganic seed aerosols is measured from Mmix - MSeed, where Mmix and Mseed are the mass of an aerosol mixture (SOA + inorganic seed aerosol) and the seed aerosol, respectively. SOA mass created from condensable oxidation products has typically been estimated using a gas-particle partitioning theory (25). The gas-particle absorptive partitioning coefficient (Kp,i) of species i in a given media can be experimentally determined by Fi/(TSP Ai), where Fi and Ai are the particle and gas-phase concentrations (µg/m3) of compound i, and TSP is the total suspended particulate matter (µg/m3). The partitioning coefficient (Kom,i) for a given organic matter (om) is obtained by Kp,i/fom, where fom is the mass fraction of the absorptive liquidlike material. Thus, Kom,i is given by (25)

Kom,i )

7.501RT (m3/µg) 10 MWomγom,ipL,i0 9


where R is the gas constant (8.314 JK-1mol-1), T is the ambient temperature (K), and MWom is the average molecular weight 0 (g/mol) of the given organic matter (om). pL,i is the vapor pressure (mmHg) of a pure compound (i) and can be calculated by previously known methods such as group contribution (26-29) and Antoine regression (30). γom,i is the activity coefficient of a compound (i) in a given liquidlike medium and is estimated using a group contribution (31). The general chemical description of formation of secondary organic species is kOx

ROG + Ox 98 R1SOx,1 + R2SOx,2 + ...


where Ox is an oxidant (e.g., ozone or an OH radical) and Ri is a stoichiometric coefficient relating the consumption of ROG in a given reaction to the total concentration (Ai + Fi) of product i (Si). Previously (6, 7), a two-product model

associated with partitioning theory was developed implementing R1, R2, Kom,1, and Kom,2. In our study, SOA mass has been decoupled into partitioning (OMP) and heterogeneous reaction (OMH) modes. This decoupling process allows us to elegantly develop a predictive model to estimate the heterogeneous SOA production.

OM ) OMP + OMH (µg/m3)


Overall, the mass changes of monomers by both hydration and dehydration in heterogeneous reactions are trivial. OMP can be expressed as (6, 7)


RiKom,i Mo 1 + Kom,iMo


Mo is the sum of particle organic mass contributed from partitioning, heterogeneous reactions and preexisting absorbing matter. At a given temperature, the effects of an inorganic species on partitioning are critically changed above and below the deliquescence and the efflorescence RH. Cocker et al. (32) showed how SOA yields are influenced by inorganic salts, and created different empirical fit parameters for “wet” and “dry” inorganic salts. In our study, the partitioning was chosen for the “wet” condition because most acidic seed aerosol comprising of sulfuric acid and AHS is classified as “wet”. Only the AHS system below 15% RH is “dry”. Particle Acidity. Particle acidity is associated with %RH and inorganic compositions (Table 1) (1, 10-16). Specifically, the acidity greater than AHS was mainly focused to model acid-catalytic effects on aerosol growth. The inorganic compositions were controlled by varying the mole fraction of each inorganic species by mixing H2SO4 and AHS solutions (1, 21). A mathematical descriptor of inorganic composition is defined here using FS,

H2SO4 FS ) H2SO4 + NH3


FS corresponds to the mole fraction of a proton associated with amounts at sulfuric acid in the total inorganic species (21): e.g., FS ) 1.0 at 100% sulfuric acid, FS ) 0.5 for AHS, and FS ) 0.333 for AS. The protonation equilibrium constant (KBH+) of a simple base (B) is commonly given by

KBH+ )

Cin,BCin,H+γin,Bγin,H+ Cin,BH+ γin,BH+


where Cin,B, Cin,BH+, and Cin,H+ are the concentration of base (B), protonated base (BH+), and proton (H+) in a given inorganic medium (in), and γin,B, γin,BH+, and γin,H+ are the activity coefficients of each species. The negative logarithm of KBH+ is pKBH+. Another value used to treat the rate constant for the acid-catalyzed reaction is “excess acidity” (X), which is described by log(γin,Bγin,H+/γin,BH+) (33). X can be treated as a function of the %RH (14) from the relationship of the H2SO4-water composition vs X (33) and the relationship of the H2SO4-water composition vs %RH (1, 10, 14, 34, 35). Kinetics of Heterogeneous Acid-Catalyzed Reaction of Carbonyls. Our previous semiempirical kinetic model (1) for heterogeneous aerosol yields allows us to model the heterogeneous SOA formation (decoupled OMH). The rate of polymerization (RH) initiated by a Lewis acid has been derived based on a second-order rate, which depends on the

concentration of monomer (aldehyde). At a given T, %RH, and particle acidity, RH is expressed by (1, 36)

RH ) dCH,i/dt ) -kapp,iCH,i2


where CH,i is the concentration (mol/L) of a carbonyl, i, in the inorganic media, t is the reaction time (s), and kapp,i is the apparent rate constant for the observed second-order reaction rate. In previous studies (1, 37), kapp,i was described through a rate determining step, which assumes polymerization progresses by polyacetal formation and imitates the rate of dimerization.

kapp,i ) k0 Cin,H+ ain,w (Khyd/KBH+) γin,B (γin,B γin,H+/γin*) (9) where k0 is the heterogeneous reaction rate constant in infinite dilution of an acid catalyst, Cin,H+ is the concentration of a proton and γin* is the activity coefficient of the transition state (37). The hydration equilibrium constant (Khyd) of a carbonyl is described by Khyd ) ahydrate/(ain,Bain,w) where ahydrate, ain,B and ain,w are the activities of a hydrate, a carbonyl, and water. If γin,B γin,H+/γin* is a linear function of X (33) and the variation of γin,B with acidity is small, eq 9 is rewritten as

log kapp,i′ ) log (Khyd) + pKBH+ + coefficient1X + log (ain,w Cin,H+) + constant (10) kapp,i′ is the observed apparent rate constant normalized by Mseed. Cin,H+ and ain,w are calculated from an inorganic thermodynamic model (22, 23). Semiempirical Model for Rate Constants of Heteroge0 neous Aerosol Production. When t is small, kapp,itCH,i can be negligible (much less than 1) (1). Then the analytical solution of CH,i in a second-order reaction is described by

C0H,i - CH,i ) kapp,itC0H,i2


0 CH,i is the initial concentration (mol/L) of i in the inorganic phase of aerosol. OMH normalized by Mseed is proportional to the consumption of i.

C0H,i - CH,i A0H,i - AH,i 1000Kom,i γom,iVOM ) ) Mseed Mseed MWi γw,iVw OMH 1000Kom,i γom,iVOM ) Mseed MWi γw,iVw 1000Kom,i γom,iVOM kapp,i′t A0H,i MWi γw,iVw





0 AH,i and AH,i are the gas-phase concentrations (µg/m3) of compound i, which participates in heterogeneous reactions. We assume that the density of OM is one. The partitioning of i on a water medium (Kw,i) is estimated from Kom,iγom,iVom/ γw,iVw. Thus, kapp,i′ can be experimentally determined from eq 12.

kapp,i′ ) Y2,i )

MWi(OMH) 3

10 tMseedKom,iA


2 H,i

γw,iVw γom,iVOM


The Y2,i, called “second-order relative organic aerosol increase”, is the same as kapp,i′ at a given temperature and reaction time. MWi is the average molecular weight (g/mol) of organic i. Vom and Vw are the molar volume of om and water. γom,i and γw,i are the activity coefficients of compund VOL. 40, NO. 9, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY



TABLE 2. The Input Parameters to Estimate the Rate Constants for Heterogeneous Reactions of Each Category level of ri,H-j

lumping reactivity I

H-s H-m H-f

2 4 5

pKBH+ -4 -3 -2






k0′ inorganic only -1 (s mol-1L)

0.66 0.66 0.66

0.143 0.143 0.143

1.57 1.57 1.57

1 1 1

-6.37 -6.37 -6.37

0.24 41.4

i in om and water. Then, the logarithm of Y2,i is semiempirically expressed by (1)

log Y2,i ) x1X + z1log (ain,w CH+) + r1pKBH+ + s1log (Khyd) +c1 (14)

OM is entirely formed from OMP and OMH, OMH is described by



∑M 1 + K o



Coefficients x1 and z1 depend on the particle environment in a given class of compounds and reactions, while coefficients r1 and s1 correspond to the chemical properties of carbonyls. In general, aldehydes result in higher aerosol growth (1) than ketones due to the higher reactivity of aldehydes and the favorable equilibrium constants for hydration and enolization (38). In our previous study, an indicator variable (I), of a finite number of values, is introduced into the semiempirical model to adjust the variability of reaction types from different molecular structures (1).

Using the analytical solution of C0H,i-CH,i in a second-order reaction (eq 11), OMH is described by


∑(A i


ROG + O3 98 R1,PS1,P + R2,PS2,P + ... + R1,H-fS1,H-f + R2,H-fS2,H-f + ... + R1,H-mS1,H-m + R2,H-mS2,H-m... + R1,H-sS1,H-s + R2,H-sS2,H-s + ... (16) The “P” denotes partitioning and “H-f”, “H-m”, and “H-s” for fast, medium, and slow in the particle-phase heterogeneous reaction. Substrate Si,H-j is a product resulting from heterogeneous reaction of substrate Si,P. The rate constant for heterogeneous reactions is symbolized as ki,H-j. The stoichiometric coefficient (Ri) is based on mass fraction, where Ri for the total consumption of ROG at a given oxidation reaction is the sum of individual contributions. Assuming

Ri ) Ri,P +









- AH,i) )


( ∑(

∑ (C i

Log Y2,i ) x2X + z2log (ain,w CH+) + r2 pKBH+ + s2I + c2 (15) The z2 is one and I values used here are shown in Table 2 along with the kinetic input parameters related to estimation of the rate constant. When I is used to lump the reactivity of different molecular structures, it provides statistically significant improvement to the model prediction (1). Thus, our previous flow reactor study suggests that semiempirical approaches can vastly improve our ability to predict the organic aerosol growth of a variety of different carbonyls in the presence of an inorganic acid. Y2,i is not only a function of the particle environment, principally %RH and inorganic seed compositions, but also a function of organic molecular structure and chemistry. As such, this work is an advanced step in developing a model for predictive SOA formation from complex oxidation products. Predictive Model for Heterogeneous SOA Formation. To determine the contribution of particle-phase heterogeneous reactions on SOA formation, diverse reaction mechanisms should be included in the model. We categorize OMH into the three heterogeneous reactions based on the reaction rate in the particle phase. A fundamental assumption in this approach is that no cross reactions occur in the particle phase. For example, the ozone reaction of ROG (R-pinene) and the formation of product substrates (Si) can be described by

(µg/m3) (18)


0 H,i


MWiγw,iVw - CH,i) ) 103Kom,iγom,iVom




1 + k′H-jMseedtC0H,i 103Kom,iγom,iVom



The k′H-j normalized by Mseed is the rate constant lumped by reactivity of organics. C0H,i can be substituted with 103Kom,iA0H,i/ MWi[γom,iVOM/(γw,iVw)]. Equation 19 is the general analytical solution of a second-order reaction, while eq 12 is the specific case at a small t in the flow reactor. If A0H,i ) Ri,H-j∆ROG, OMi,H-j can be rewritten as


∑∑ i






103Ri,H-j∆ROGKom,i γom,iVOM MWi

1 + k′H-jtMseed



103Ri,H-j∆ROGKom,i γom,iVOM MWi







(µg/m3) (20)

Fundamentally the same values of Kom,i (eqs 5 and 18), which is used for the neutral environments can be implemented for the particle phase reaction. The parameters relevant to partitioning are divided into three categories (subscript i ) 1, 2, and 3). Decoupling of OMP and OMH from Experimental OM. The fitting parameters, Ri (eq 17) and Kom,i used for the partitioning mode (i ) 1, 2, and 3) are shown in Table 3. The mathematical fitting parameters Ri and Kom,i were obtained by readjusting Cocker’s data set for wet ammonium sulfate (32) with an OH radical scavenger (Figure S1 in the Supporting Information). No scavenger was included in our experimental set to avoid creating products reactive for heterogeneous acid-catalyzed reactions in addition to those produced from the oxidation of R-pinene. Iinuma et al. (39) has reported

TABLE 3. Stoichiometric Coefficients and Partitioning Coefficients Used for the Predictive Model of heterogeneous aerosol formation (n.a.: not applicable)


Kom,i (wet)

Kom,i (dry)


1 1 1 1 2 2 2 2 3 3 3 3

0.05 0.05 0.05 0.05 0.0004 0.0004 0.0004 0.0004 1.2 × 10-5 1.2 × 10-5 1.2 × 10-5 1.2 × 10-5

0.144 0.144 0.144 0.144 0.0012 0.0012 0.0012 0.0012 5.4 × 10-5 5.4 × 10-5 5.4 × 10-5 5.4 × 10-5

0.167 0.167 0.167 0.167 0.385 0.385 0.385 0.385 0.366 0.366 0.366 0.366




level of ri,H-j

0.732 0.732 0.732

0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.7 0.7

partitioning only H-f H-m H-s partitioning only H-f H-m H-s partitioning only H-f H-m H-s

ri,P/ri (fi,p) ri,H-j/ri (fi,H-j) 0.6b n.a. 0.6 0.6 0.1c n.a. n.a. n.a. 0.1c n.a. n.a. n.a.

n.a. n.a. n.a. n.a. n.a. 0 0.3f 0.7f n.a. n.a. n.a. n.a.



n.a. 0 0 0.047e n.a. 0 0.073g 0.17g n.a. 0.223h 0.205i 0

0.701d n.a. n.a. n.a. 0.027d n.a. n.a. n.a. 0.026d n.a. n.a. n.a.

factor for partitioning in water


100 200 100 300

a f b f ozone is the ozone reaction fraction of the total R-pinene consumption. 1,p was obtained from the ratio of pinic acid to oxygenated pinonic acids in the experimental composition by Yu et al. (8). c An arbitrary number for diacid fraction of secondary organic products at i ) 2 and 3. d Rozone × f e Rozone × f f ozone × fi,P. ozone × (1-fi,P). f2,H-j was determined using both the experimental data and the chemical composition estimated i i from a chemical solver. g Riozone × fozone × (1-fi,P) × f2,H-j. h R3,H-f was obtained by fitting experimentally determined OMH for acidic seed systems (Fs g 0.65). i (1-fi,P) × (Riozone × fozone + RiOH × fOH) - R3,H-f.

that SOA yields in the presence of an acid catalyst are higher without an OH scavenger than those with an OH scavenger, and also vary with diverse OH scavengers. Our estimation using a kinetic solver with a chemical mechanism (9) shows the OH radical reaction fraction (fOH) of total R-pinene consumption is about 0.3. Table 3 also shows Ri values for ) and the OH radical reaction (ROH both ozonolysis (Rozone i i ) with R-pinene. In general, the products with a scavenger include less aldehyde (e.g., pinonaldehyde) than those without a scavenger. Thus, the data set with a scavenger in the absence of acid catalyst can be considered as a base for the gas-particle partitioning because their organic products are less reactive and SOA yields by heterogeneous reactions can be also minimized. OMP is calculated from ∆ROG and partitioning SOA yields, which are obtained from observed OM, Ri, and Kom,i. It is known that heterogeneous reactions produce high molecular weight structures in SOA. Partitioning of organics decreases with the presence of oligomers due to changes in MWom and γom,i(equation 2). The average molecular weight of the oligomeric OMH was selected as 2MWom (a dimer, 2 × 180). This assumption allows us to adjust the Kom,i and sequentially estimate a 2nd generation of OMP and OMH (Figure S1 in the Supporting Information). Lumping of Reactivity for Particle-Phase Heterogeneous Reactions. Table 3 shows classifications of Ri,H-j for heterogeneous reactions (eq 16). The least volatile SOA products categorized as Kom,1 are relatively inert carboxylic diacids (e.g., pinic acid norpinic acid), and multifunctional carboxylic monoacids (e.g., hydroxy-pinonic acid) which have a weak reactivity for heterogeneous reactions. Thus, the category i ) 1 only includes OM1,H-s in Table 3. The SOA products for i ) 2 are oxo-carboxylic acids (e.g., pinonic acid, norpinonic acid, and pinalic acid) and multifunctional carbonyls (e.g., hydroxy-pinonaldehyde). This category includes the products with medium and slow reactivity (OM2,H-m and OM2,H-s) for heterogeneous reactions. The most volatile products (i ) 3) consist mostly of oxoaldehydes which have at least two carbonyls (e.g., pinonaldehyde, nonpinonaldehyde, and oxo-pinonaldehydes). These products have medium and fast reactivity for heterogeneous reactions. The Ri,H-j at i ) 1 and 2 were estimated using both the experimental data (8) and the chemical composition by a chemical solver (9, 40), and the Ri,H-j at i ) 3 is obtained by fitting experimental data for OMH by minimizing the square of the residuals for acidic aerosol systems (Fsg 0.65).

Ratio of ∆ROG to Mseed. We propose that heterogeneous reactions slow as the reactions progress and eventually stop. For the possible explanation for this change of reactivity, we suggest that (1) the solubility of polymeric matter is poor resulting in the phase transition (41), (2) insoluble high molecular weight structures accumulate near the boundary between the organic and the inorganic phases, (3) organics lose mobility resulting in poor cage effects, and (4) formation of organic sulfates may consume available sulfuric acid. This study accounts for the delay of heterogeneous reactions by controlling the maximum time scale and the degree of reactions. Based on observation of aerosol growth in flow reactor and polytetrafluoroethylene bag studies with a high concentration of model carbonyl (10), and the SOA growth of this study, the apparent SOA formation by heterogeneous reactions is completed within one scan of sampling in a SMPS (3 min). This time scale to complete the reactions is fixed at 1 min in the model. Another mathematical parameter, “degree of reaction” (fH), corresponding to the reactivity according to the ratio of ∆ROG/Mseed is introduced to the model. fH permits us to adjust the phase transition of organic layers as heterogeneous reactions progresses. In particular, fH is influenced by amounts of inorganic seed in a given ∆ROG concentration and given experimental conditions. OMH in eq 20 can be corrected by fH which is semiempirically calculated from the relationship between ∆ROG/Mseed and OMH in given experimental conditions (see Figure S2 in the Supporting Information). fH is 1 at

fH )

1 1 + a(∆ROG/Mseed)


very small ∆ROG/Mseed, and fH is 0 at values of very high ∆ROG/Mseed. Heterogeneous Reactions in Ammonium Sulfate Seed. Heterogeneous reactions in the particle phase can also occur with nonacidic seed aerosol, although the reaction rate is much greater in an acidic environment. Heterogeneous reactions at infinite dilution of an acid catalyst are represented by k0 in eq 9. The contribution of k0 to heterogeneous reactions is insignificant in the presence of acid catalyst, but important at dilute concentrations such as SOA with AS and also in the absence of a seed aerosol. To adjust the mediumVOL. 40, NO. 9, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY



FIGURE 1. (A) OMH fraction of the total OM in week acidic conditions [(NH4)2SO4, NH4HSO4, and composition at Fs ) 0.65]. Model OMH is calculated by eq 22. (B) The OM0 fraction of model OMH. OM0 corresponds with k0′, which adjusts the heterogeneous rate constant at infinite dilution (neutral). independent k0 in eq 9, k0′ is added to eq 20, and the inclusion of fH gives OMH )

∑∑ i


fH(kH-jtMseed + k0-j′t)



103Ri,H-j∆ROGKom,i γom,iVOM


1 + (kH-jtMseed + k0-j′t)





103Ri,H-j∆ROGKom,i γom,iVOM MWi





10 Kom,iγom,iVOM 3



The value for k0′ is obtained by fitting experimental SOA data in weak acidic conditions with AS and AHS. Figure 1A illustrates how the SOA formation is influenced by the heterogeneous reactions in weak acidic conditions, such as those most likely to occur in atmospheric ambient aerosols. OM0 in Figure 1B is the organic mass associated only with k0′. Figure 1B shows that the contribution of OM0 changes for each seed system at both low and medium %RH. The ratio of OM0/OMH increases, as %RH increases or Fs is reduced. Derivation of the Predictive Model for OMH in Medium and Strong Acidic Conditions. The essential strategy of the predictive model for OMH is (1) advance of the predictive model with medium and strong acidic inorganic seed aerosols, and (2) extrapolation or validation of the model approach to SOA formation in weakly acidic conditions (Fs e 0.5), which are more relevant to realistic atmospheric aerosols. The outcome of this predictive model is estimation of the optimal range of rate constants and Ri,H-j. The model fit to the experimental data is conducted for acidic seed 3018


FIGURE 2. (A) Model OM (2, model OMH + decoupled OMP), decoupled OMP (]) and model OMH (slash X) (eq 22) vs experimental OM for acidic systems, Fs g 0.65. Experimental conditions vary with %RH, Mseed, Fs, and ∆ROG as shown in Table 1. The solid line is the one to one line of experimental OM. (B) Model OM (filled symbols, model OMH + decoupled OMP), decoupled OMP (]), and model OMH (X) (eq 22) vs experimental OM for neutral (ammonium sulfate) and weak acidic systems (Fs ) 0.5 and 0.65). The solid line is the one to one line of experimental OM.


conditions ranging from pure sulfuric acid (Fs ) 1) to partially neutralized conditions (Fs ) 0.65). The advantage of model development at Fs > 0.5, is that the decoupled OMH from experimental data is less affected by errors in the decoupling process than those in weak acidic seed conditions. The model outcome from strong acidic conditions can then be extrapolated to SOA formation at weak acidic and neutral aerosols, which are more sensitive to the decoupling methods used to determine OMP and OMH. Ri,H-j is obtained using the experimental data, the chemical composition estimated from a chemical solver, as well as mathematically fitting eq 22 to experimentally determined OMH for each level of heterogeneous reactions. Table 3 shows Ri,H-j along with a partitioning class. The MWi of each lumped species is selected as 180 g/mol for all categories. The decoupled OMP and model OMH using eq 22 are illustrated in Figure 2A along with model OM estimated by the sum of OMP and model OMH. The performance of a predictive model approach has been evaluated using one to one line of observed OM in Figure 2A (R2 ) 0.866). Heterogeneous SOA Formation in Weak Acidic Conditions and the Model Validation at Low Concentrations of r-Pinene. Figure 2B shows the experimental OM with weak acidic inorganic seeds, which are more environmentally relevant to atmospheric aerosols. The experimental results are also compared to the model prediction. As shown in Figure 1A and Figure 2B, the contribution of OMH to the total SOA is 30-50% for weak acidic conditions in our experimental conditions. The validation of model OMH was also performed using the experimental data which were not included for the

FIGURE 4. Predicted OMH plotted vs the experimental OMH (experimental data set I in Table 1) at Fs ) 0.75, along with the contributions of individual lumped species (see ri,H-j in Table 3) on model OMH. “P” and “H” in the legend denote the partitioning and heterogeneous reactions. %RH and Mseed for each experiment are shown in the x-axis. Model OM (P + H) (filled diamond) is calculated from model OMH + decoupled OMP (eq 22). OM-H denotes model OMH (eq 22) for individual species which are categorized by Kom,i and ri,H-j.

FIGURE 3. Model prediction for OMH using eq 22 and experimentally estimated OMH. (A) The predicted OMH demonstrated at different Mseed levels at %RH ) 20 and compared to the experimental OMH estimated at %RH ) 17-22. (B) The predicted OMH demonstrated at different Fs at %RH ) 20 and compared to the experimental OMH estimated at %RH ) 20-25. (C) The model prediction versus %RH at Fs ) 0.75. OMH model development. To evaluate the relevance to atmospheric conditions, the low concentration of R-pinene (45 ppb in Table 1) was reacted with ozone in the presence of week acidic inorganic sees aerosol (Fs ) 0.65). The experimental OMH is greatly close by the model OMH as shown in Figure S3 of the Supporting Information. Model Simulation by Individual Parameters. The influence of major environmental parameters (%RH, Mseed, Fs, and ∆ROG/Mseed) on OMH is shown in Figure 3. Both Mseed (Figure 3A) and the acid fraction of the total seed mass (Figure 3B) are significant for heterogeneous SOA formation. The contribution of OMH can vary with ∆ROG/Mseed and molecular structure of SOA products. When fH (eq 21) of the reaction system is higher, OMH becomes more significant (Figure 3A). Figure 3C illustrates %RH effects on OMH, which is modeled at different levels of fH changing Mseed and ∆ROG. The

individual contributions of Ri,H-j on OMH are demonstrated in Figure 4 using data set I (Fs ) 0.75). To see the OMH production as ozonolysis of R-pinene progresses, model OMH was estimated from the ∆ROG time profile and compared to SOA data in experimental set I (Table 1). Figure 5A illustrates the experimentally observed SOA formation created from two different seed compositions (Fs ) 0.75 for acidic seed and Fs ) 0.33 AS) along with ∆OM between the two different experiments. Model OMH was estimated using eq 22 and ∆ROG predicted using a kinetic solver (40) from the reaction of R-pinene with an OH radical and ozone. In Figure 5A, ∆OM is reasonably predicted by the model OMH. The time profile of SOA yields is also calculated from the SOA data and ∆ROG and shown in Figure 5B. SOA yields with AS seed aerosol increase as ROG (R-pinene) is consumed, while SOA yields drop with acidic seed aerosol. Partitioning is dominant for SOA formation with dry AS seed and increases with the organic mass in the particle phase. Efficiency of the heterogeneous SOA formation drops as fH decreases due to the formation of high molecular weight structures, which can change both solubility and mobility of organic species in SOA. Influence of Preexisting Glyoxal. Understanding the effects of preexisting organic matter on heterogeneous reactions of newly formed SOA species is also important in atmospheric environments. In particular, it has been known that SOA created from the photooxidation of aromatics is greatly polymerized due to highly reactive multifunctional carbonyls (19). In our study, the R-pinene ozone SOA was also produced with preexisting mixture seed aerosol made of glyoxal polymer and inorganic seed solution as shown in Table 1, Figure 6A, and Figure 6B. The experimentally measured OM is illustrated in Figure 6A. The inorganic mass fraction (finor) of seed aerosols is estimated from the initial aqueous seed solution. The result presented in Figure 6A suggests that (1) glyoxal and its derivatives as a surrogate for preexisting reactive matter increases SOA yields when an acid catalyst is present, and (2) the apparent SOA yield increases with polymeric glyoxal is not effective with AS seed aerosol. Under the assumption that OMH is influenced only by the inorganic fraction of seed aerosol and glyoxal oligomer is VOL. 40, NO. 9, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY



FIGURE 5. (A) Time profile of aerosol growth, for two seed aerosol systems (AS and Fs ) 0.75), ∆OM between the two systems, model OMH for the acid system, and the r-pinene decay as predicted by a chemical kinetics solver. The time profile of both experimental ozone concentration and the predicted ozone concentration by a chemical kinetic solver is also illustrated using the 2nd y-scale (ppb). The experiment (data set I in Table 1) was conducted at Fs ) 0.75, Mseed ) 274 µg/m3, %RH ) 10, and ∆ROG ) 850 µg/m3. (B) The corresponding time profile of aerosol yields using eq 1. condensable and not evaporated from the particle phase, the model under-predict OMH as shown in Figure 6B (R2 ) 0.42 and slope ) 0.27). This result indicates that excess heterogeneous acid-catalyzed reactions occur through glyoxal in addition to SOA formation from secondary organic products created from ozonolysis of R-pinene. When the aqueous glyoxal nebulized into the chamber, the aerosol phase glyoxal is polymerized as water evaporates and inert for further particle-phase reactions due to the phase transition to the solidlike polymeric matter. Liggio et al. have reported that higher order oligomers are formed in highly concentrated glyoxal solutions (higher than 1 M aqueous solution) (42, 43). Thus, we also expect that some fraction of glyoxal derivatives (e.g., hydrate and dimer) can be evaporated from seed aerosols to the chamber air before reaching solution higher than 1M. Figure 6B also illustrates the model OMH with inclusion of glyoxal derivatives in the gas phase and the inorganic fraction (inorgnics + inorganic phase water) (f′inor) estimated from experimental seed aerosol data with/without glyoxal in a given experimental condition. The model OMH reasonably agrees with observed OMH (R2 ) 0.70 and slope ) 0.88) (Figure 6B). Glyoxal derivatives is categorized into R3,H-f in the model (Table 3). The study of effects of glyoxal hydrates on aerosol growth is needed for diverse experimental conditions in the future. The model OMH will be also extended to the highly reactive glyoxal as a surrogate SOA product created from photooxidation of aromatic VOCs in the future. From the partitioning point of view, glyoxal oligomer increases the molecular size of medium. Therefore, partitioning processes cause a reduc3020



FIGURE 6. (A) r-Pinene ozone SOA mass produced in the presence of various preexisting seed aerosols (data sets V, VI, and VII in Table 1) consisting of glyoxal (Gly) and inorganic species (AS and Fs ) 0.75). finor is the mass fraction of inorganic components in seed aerosol. (B) Experimental OMH (data set V in Table 1) vs predicted OMH (eq 22) in the presence of preexisting seed aerosol consisting of glyoxal and inorganic species (Fs ) 0.75). Model OMH has been performed both with and without contribution of glyoxal derivatives (e.g., glyoxal hydrate and dimer) in the gas phase. Glyoxal derivatives is categorized into r3,H-f in the model (Table 3). tion of OMP in the presence of polymeric glyoxal, while the real contribution of heterogeneous reactions on apparent SOA mass with glyoxal is higher than that without glyoxal. Future study is needed to characterize the fraction of OMH. Atmospheric Implication. Our study suggested that the formation of OMH is completed within a short time (one minute) in the presence of an acid catalyst. If the acid produced by oxidation of SO2 is not instantly titrated with ammonia, inorganic acid in the atmosphere can catalyze oligomerization and rapidly increase SOA mass. Thus, the significance of acidity effects on heterogeneous aerosol production is dynamic and varies with locations, the history of titration with ammonia, and SOA fraction of total organic aerosol. The evaluation of dynamic acid effects on ambient SOA is, however, limited by current analytical methods for inorganic species because the sampling of ambient particles linked to a chemical ionization chromatography requires several hours to 1 day. Ambient data collected by a shorter time interval is necessary to dynamically evaluate the atmospheric acid effects on SOA formation mechanisms suggested by the laboratory study. To expand the study to atmospheric acidity, model OMH derived with strong and medium particle acidity was extrapolated to weak acidic and neutral inorganic seed particles in this study. The validation of the heterogeneous SOA formation (Figure S3) also evinced that model OMH are applicable for the SOA formation (near 50 µg/m3) with low concentrations of R-pinene (45 ppb) and relatively weak

acidic seed. The SOA mass in the chamber are still higher than concentrations (e 25 µg/m3) in field studies. The atmospheric concentration of sulfate is also lower (