Environ. Sci. Technol. 2001, 35, 1164-1172
Modeling the Formation of Secondary Organic Aerosol. 1. Application of Theoretical Principles to Measurements Obtained in the r-Pinene/, β-Pinene/, Sabinene/, ∆3-Carene/, and Cyclohexene/Ozone Systems J A M E S F . P A N K O W , * ,† JOHN H. SEINFELD,‡ WILLIAM E. ASHER,§ AND GARNET B. ERDAKOS† Department of Environmental Science and Engineering, Oregon Graduate Institute, P.O. Box 91000, Portland, Oregon 97291-1000, Department of Chemical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, and Applied Physics Laboratory, University of Washington, Seattle, Washington 98195
Secondary organic aerosol (SOA) forms in the atmosphere when volatile parent compounds are oxidized to form lowvolatility products that condense to yield organic particulate matter (PM). Under conditions of intense photochemical smog, from 40 to 80% of the particulate organic carbon can be secondary in origin. Because describing multicomponent condensation requires a compound-by-compound identification and quantification of the condensable compounds, the complexity of ambient SOA has made it difficult to test the ability of existing gas/particle (G/P) partitioning theory to predict SOA formation in urban air. This paper examines that ability using G/P data from past laboratory chamber experiments carried out with five parent hydrocarbons (HCs) (four monoterpenes at 308 K and cyclohexene at 298 K) in which significant fractions (61100%) of the total mass of SOA formed from those HCs were identified and quantified by compound. The model calculations were based on a matrix representation of the multicomponent, SOA G/P distribution process. The governing equations were solved by an iterative method. Input data for the model included (i) ∆HC (µg m-3), the amount of reacted parent hydrocarbon; (ii) the R values that give the total concentration T (gas + particle phase, ng m-3) values for each product i according to Ti ) 103 Ri∆HC; (iii) estimates of the pure compound liquid vapor pressure p°L values (at the reaction temperature) for the products; and (iv) UNIFAC parameters for estimating activity coefficients in the SOA phase for the products as a function of SOA composition. The model predicts the total amount Mo (µg m-3) of organic aerosol that will form from the reaction of ∆HC, the total aerosol yield Y () Mo/∆HC), and the compound-by-compound yield values Yi. An impediment in applying the model is the lack of literature data on p°L values for the compounds of interest or even on p°L values for other, similarly low-volatility compounds. This was 1164
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overcome in part by using the G/P data from the R-pinene and cyclohexene experiments to determine p°L values for use (along with a set of 14 other independent polar compounds) in calculating UNIFAC vapor pressure parameters that were, in turn, used to estimate all of the needed p°L values. The significant degree of resultant circularity in the calculations for R-pinene and cyclohexene helped lead to the good agreement that was found between the Yi values predicted by the model, and those measured experimentally for those two compounds. However, the model was also able to predict the aerosol yield values from β-pinene, sabinene, and ∆3-carene, for which there was significatly less circularity in the calculations, thereby providing evidence supporting the idea that given the correct input information, SOA formation can in fact be accurately modeled as a multicomponent condensation process.
Introduction The oxidation of volatile organic compounds (VOCs) in the atmosphere can lead to low-volatility products that can condense and thereby lead to increased levels of suspended particulate matter (PM) (1-5). The fraction of the PM that is formed by this path is referred to as “secondary organic aerosol” (SOA). Since SOA can influence visibility, atmospheric chemistry, human and ecological health, and planetary albedo, continued development of a fundamental and predictive understanding of SOA formation is needed. Organic PM in the atmosphere is generally very complex, and in any given circumstance, it is likely that the identification and quantification of many compounds are necessary to account quantitatively for the organic aerosol mass. Typically, less than 20% of the total organic mass can be identified (6-14). While a direct differentiation between primary and secondary organic PM is difficult, a number of approaches have been developed to provide this distinction indirectly (15-22). Such efforts have indicated that under conditions of intense photochemical smog, from 40 to 80% of the particulate organic carbon can be secondary in origin (18-21). Parent organic compounds that are capable of yielding SOA-forming products generally possess at least six carbon atoms (5). For example, when cyclohexene undergoes photooxidation, some of the resulting C6 products are of very low volatility (e.g., adipic acid) and can partition to the PM phase in significant amounts. The oxidation of organic compounds with fewer than six carbon atoms usually does not lead to much SOA: the vapor pressures of the products are generally too high. The fractional mass yield (Y) of SOA produced from the oxidation of a parent gaseous hydrocarbon (HC) is defined as
Y)
Mo ∆HC
(1)
where Mo (µg m-3) is the mass concentration of SOA produced from the reaction of ∆HC (µg m-3) worth of gaseous HC. Although many laboratory studies (e.g., refs 4 and 23-35) have measured SOA yields from various specific parent HCs * Corresponding author phone: (503)748-1080; fax: (503)748-1556; e-mail:
[email protected]. † Oregon Graduate Institute. ‡ California Institute of Technology. § University of Washington. 10.1021/es001321d CCC: $20.00
2001 American Chemical Society Published on Web 02/14/2001
TABLE 1. Characteristics of Experimentally Measured Yield (Y) Values and Associated Explanations observaton
explanation
Y ) 0 is possible when ∆HC is very low in each given case, a critical value of ∆HC is required to produce Mo > 0 and Y > 0 once ∆HC is large enough to yield nonzero values of Mo and Y, further increases in ∆HC will cause Mo and Y to increase
all condensable products possess some volatility; thus, Y can equal zero when levels of the condensable products are very low once encough condensable products have accumulated, the system can become saturated for that mix of products; formation of additional condensable products allows aerosol condensation to begin formation of increasing amounts of condensable products causes increases in (i) Mo; (ii) fractions of condensable products that partition to the SOA phase; and (iii) overall yield Y
(e.g., cyclohexene, xylenes, and monoterpenes such as Rand β-pinene), even in such simple systems it has proven a significant challenge to obtain a relatively complete molecular identification and quantification of the products making up those yields: the oxidation pathways are complex and lead to multiple products, and the products are highly polar, difficult to identify, and difficult to determine. Nevertheless, two laboratory investigations (34, 35) have succeeded in identifying and quantifying appreciable fractions of the organic compounds in SOA produced from relevant HCs (see below). For purposes of specifics in discussion here, let us assume for the moment that the photooxidation of some parent hydrocarbon HC leads to just two final products P1 and P2:
HC + oxidants f p1P1 + p2P2
(2)
where p1 and p2 are molar stoichiometric coefficients. We further assume that the volatilities of P1 and P2 are sufficiently low that they can condense to form SOA. Reaction 2 is not meant to represent a fundamental reaction since some initial products may only be transitory in the system. The earliest studies of SOA yields were interpreted based on the assumption that each parent HC is characterized by a particular fixed value of Y that is set by the stoichiometric coefficients of its condensable oxidation products. For the case of reaction 2, the notion of fixed Y values carries with it the requirement that P1 and P2 are of such low volatility that essentially 100% of any P1 and P2 produced will condense. For that case, for every µg/m3 of HC that reacts, a certain fixed concentration of SOA equal to
Mo )
[( )
(
)
1 µg 1 mol of HC × × µg m3 MWHC × 106 mol of P1 µg of P1 p1 × MWP1 × 106 + mol of HC mol of P1 mol of P2 µg of P2 p2 × MWP2 × 106 mol of HC mol of P2
) ( ) (
(
p1 × MWP1 MWHC
+
)
Y)
p1 × MWP1 MWHC
) R1 + R2
+
p2 × MWP2 MWHC
(Y fixed)
(5)
(Y fixed)
(6)
In the general case of n condensable products instead of just two, the notion of a fixed Y value leads to n
Y)
∑R
i
(Y fixed)
(7)
i
In actuality, laboratory SOA yield data are not consistent with the notion of fixed Y values. Rather, the data indicate that (i) when only a very small amount of parent HC has reacted, Y can be zero; (ii) as more product material accumulates, Y values can become greater than zero; and (iii) further increases in products lead to further increases in Y (see Table 1). Although the formation of SOA from the simultaneous condensation of multiple products is more complex than the condensation behavior of a single component, a single-component system is analogous insofar as (i) no condensation will occur so long as the gas phase pressure of the component remains below the saturation vapor pressure; (ii) the condensation yield will rise above zero once the amount of the compound per unit volume of air exceeds the saturation concentration; and (iii) the condensation yield will then continue to increase as more of the compound is added. As discussed by Pankow (2), once a multicomponent system contains enough condensable material to form aerosol, equilibrium gas/particle (G/P) partitioning (viz. condensation) is governed by the equation for absorptive gas/liquid partitioning in a potentially nonideal system, namely
pi ) Xiζip°L,i
)]
(3)
p2 × MWP2 MWHC units: (µg of P1 + P2)/m3 (4)
will always form where each MW is a molecular weight and p1 × MWP1/MWHC and p2 × MWP2/MWHC are the mass stoichiometric factors R1 and R2 for the production of P1 and P2 from HC. The conditions under which R factors do tend to remain constant have not been determined for SOA systems of interest. Nevertheless, this is not an unreasonable first assumption, and recent laboratory investigations (34, 35) are not inconsistent with it. Since eq 3 gives Mo per µg/m3 of reacted HC, the notion of Y being fixed for reaction 2 leads to
(8)
where pi is the gas-phase pressure of species i, Xi is the mole fraction of species i in the aerosol phase, ζi is the activity coefficient of species i in the aerosol phase, and p°L,i is the compound’s vapor pressure as a pure liquid (subcooled if necessary) at the temperature of interest. Rearrangement of eq 8 yields a simple expression for Xi/pi, which can be viewed as a form of G/P partition coefficient in a multicomponent system:
Xi 1 ) pi ζip°L,i
(9)
Equation 9 emphasizes the importance of p°L,i and ζi in controlling G/P partitioning in SOA systems. A low value of p°L,i translates into a large value of the partition coefficient Xi/pi and therefore a high tendency for compound i to be found in the aerosol phase. The p°L values for photooxidation products of interest span at least 5 orders of magnitude and extend down to very low values (e.g., 10-7 Torr): it is the low vapor pressure products that condense most easily to form VOL. 35, NO. 6, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 2. Average Percent Mass Balance for Mo by Summation of Individual Product Compounds Identified (Dry Conditions) parent HC
av % of final Mo identified
av final Mo (µg m-3)
Na
ref
R-pinene β-pinene sabinene ∆3-carene cyclohexene
100 89 100 61 91
53 15 18 63 49
3 2 1 1 6
34 34 34 34 35
a
N, number of experiments.
SOA. A low ζi (compound i is “comfortable” in the aerosol phase) also favors condensation. For the cases of interest here, ζi values typically lie in the range 0.3 < ζi < 3. Since low p°L values are exceedingly difficult to measure, the p°L values of most SOA-relevant compounds are not known. The fact that many such compounds are solids as pure compounds at ambient temperatures complicates matters further because difficult to measure p°S values still need to be adjusted to obtain subcooled p°L values. (Note that, even when SOA components are solids as pure compounds at an ambient temperature, the mutual depression of melting points that occurs in a mixture can allow such a mixture to be a liquid at equilibrium at that temperature.) A manipulation (2) of the concentration units in eq 9 leads to the G/P partitioning constant in the standard Kp form:
Kp,i )
(ng/µg)particle phase 3
)
(ng/m )gas phase
Fi/TSP 760RTfom ) 6 Ai 10 MW ζ p°
(10)
om i L,i
where Ai (ng m-3) is concentration in the gas phase; Fi,om (ng m-3) is concentration in the largely organic material (om) aerosol phase; TSP (µg m-3) is total suspended PM concentration; R is ideal gas constant; T (K) is temperature; fom is weight fraction of the TSP that comprises the absorbing om phase; MWom (g mol-1) is number-averaged molecular weight of the absorbing om phase. The calculations of both fom and MWom include any water in the om phase. Each ζi is a function of the aerosol composition and T (i.e., ζi ) ζi(X1, X2, ..., Xn; T)); each p°L,i (Torr) is a strong function of T. In an SOA system
Mo ) fom × TSP
(11)
The aerosols considered in this paper are assumed to be dry and free of any P-phase water. Dividing both sides of eq 10 by fom gives (4)
Kp,om,i )
(ng/µg)om phase 3
(ng/m )gas phase
)
Fi/Mo 760RT ) 6 Ai 10 MW ζ p°
(12)
om i L,i
so that
Fi ) MoKp,om,i Ai
(13)
Yield values therefore tend to increase as the amounts of products increase because there is more aerosol into which partitioning can occur: increasing the concentration of aerosol favors the particle phase for all condensable products, regardless of their value of Kp,om. Odum et al. (4) utilized the above concepts of multicomponent G/P partitioning to develop a framework for parametrizing the trend of increasing Y values with increasing Mo. When applied over all condensable products of signifi1166
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cance, the result for the overall yield Y is
Y)
∑Y ) ∑R i
i
i
(
i
Kp,om,iMo
1 + Kp,om,iMo
)
(14)
where Yi is the individual contribution to the SOA yield from compound i
Yi )
Mi ∆HC
(15)
with Mi (µg m-3) being the contribution to Mo from component i. The total amount Ti of compound i in the atmosphere will be distributed between the gas and particle phases so that
Ti ) Ai + Fi ) 103Ri∆HC
(16)
The factor of 103 accomplishes a unit conversion to ng m-3. Comparing eq 14 with eq 7 reveals that Kp,om,iMo/(1 + Kp,om,iMo) is the fraction of Ri that actually condenses to form aerosol, i.e.
(
)
Fi Kp,om,iMo ) 1 + Kp,om,iMo Ai + Fi
(17)
The above framework has been found effective in describing SOA yield data for experiments conducted in laboratory smog chambers using a wide variety of parent HC compounds (4, 28-31, 35). Each of those experiments was adequately described by fitting Y vs Mo data under the assumption that two hypothetical average product compounds P1 and P2 were formed. One of the products is an average for the lower vapor pressure compounds; the other is an average for the remaining, higher vapor pressure compounds. (Yield data are generally not fit well by assuming a single product, and the assumption of three products does not improve the fits significantly.) In a two-product fit, there are four fitting parameters: two R values and two Kp,om values. While assuming two products of averaged properties allows good fits to laboratory yield data, it remains a semiempirical way of parametrizing SOA formation and does not provide a means by which more complicated, real systems can be modeled predictively. For that, a product-specific model is needed that accounts for the formation of SOA from all of the important individual products based on (i) the structures and R values for the products; (ii) the p°L values for the products at the T of interest; and (iii) a means to estimate the compound-dependent SOA phase ζi values as a function of the SOA composition (viz., the Xi values) and at the T of interest. A numerical scheme can then be used to solve the simultaneous equations governing the equilibrium distribution of the products. A major goal of the dry chamber experiments of Yu et al. (34) and Kalberer et al. (35) was to identify and quantify as much of the SOA mass that formed as possible. In some of the experiments, much of the Mo mass could be accounted for (Table 2). The identities of the products found and quantified are given in Tables 3-7. The goal of this paper is to use those experimental SOA yield results as a basis against which the multicomponent G/P partitioning model can be compared. Indeed, if those experimental data are accurate and if eq 10 correctly describes the partitioning, then accurate knowledge of the relevant p°L values combined with a reliable method to estimate ζ values must lead to agreement between the distribution results derived predictively and those derived experimentally.
Modeling Numerics. Equation 20 of Pankow (2) is a matrix representation of multicomponent SOA G/P equilibrium. It relates the
TABLE 3. Measured and Predicted Aerosol Product Yields in the r-Pinene/O3 System (Dry Conditions) aerosol yield Yi × 100 (%)
predicted/measured
exp 6/9/98b
p°L (Torr)a
product
10-1
1.74 × 4.63 × 10-2 2.29 × 10-4 8.17 × 10-6 7.50 × 10-6 2.22 × 10-6 2.10 × 10-6 2.03 × 10-6 1.00 × 10-12
norpinonaldehyde pinonaldehyde hydroxy pinonaldehydes norpinonic acid and isomers norpinic acid pinonic acid pinic acid hydroxy pinonic acid X (total unidentified mass)d
exp 6/9/98b
results for three expts
rb
measdc
pred
RYi
av, R h Yi
SD, σRY
0.0208 0.1458 0.0762 0.1129 0.0012 0.0568 0.0661 0.0397 0.0167
0.2 0.4 1.4 5.9 0.1 2.1 5.3 1.9 1.2
0.0001 0.002 0.3 5.5 0.1 4.4 5.3 3.1 1.2
0.0004 0.01 0.19 0.93 0.64 2.10 1.00 1.65 1.00
0.0003 0.003 0.11 1.37 0.68 2.02 1.42 1.17 1.00
0.00 0.00 0.07 0.56 0.10 0.13 0.58 0.42 0.00
total yield, Y × 100% Mo (µg m-3) RY ) 1.07 (6/9/98b), R h Y ) 1.09, σRY ) 0.07
18.6 65.1
i
19.9 70.0
a Predicted by UNIFAC vapor pressure method at 308 K. b Arithmetic average of measured R values calculated for the three experiments. Measured values are from Yu et al. (34). d Product X represents the total amount of unidentified aerosol mass, including two products identified only as A13 and A14 by Yu et al. (34). Product X was assumed to consist of a compound with 2 CH3, 2 CH2, 2 CH, 1 C, 1 CH3CO, and 1 COOH UNIFAC functional groups; MWX ) 184 g mol-1. An R value for product X was calculated individually for each experiment. The vapor pressure of X is such that essentially all the available mass will partition into the aerosol phase. c
set of Fi values to the corresponding set of Ai values, i.e., it relates the vector Fˆ to the vector A ˆ . Pankow (2) used that relation to demonstrate that (i) the various Fi values are interdependent; (ii) a change in any Ti will affect all Fi; and (iii) the equilibrium G/P distributions of all of the components (as well as the total concentration of SOA, Mo) can be determined by solving that equation iteratively. Equation 20 of Pankow (2) leads directly to the conclusion that a given photooxidation circumstance with a vector Tˆ of total concentrations for the products will produce a specific vector Yˆ of values Yi. The input data for the algorithm are ∆HC and the vector of Ri values with
Tˆ ) 103 R ˆ ∆HC
(18)
On the basis of eq 20 of Pankow (2), the relationship between Fˆ and Tˆ is
[]
F1 Mo 760RT F2 ) 6 × . 10 MWom Fn
[
(ζ1p°L,1)-1 1 + Kp,om,1Mo
0 (ζ2p°L,2)-1
0 .
1 + Kp,om,2Mo .
.
.
.
.
.
. -1
.
.
.
(ζnp°L,n) 1 + Kp,om,nMo
]
[] T1 T2 . Tn
(19)
For any Tˆ and guess value of Mo, eq 19 can be solved iteratively to determine the corresponding solution Fˆ . In each iteration, the ζi values are needed and can be estimated using UNIFAC (36, 37). After solving eq 19, it is not necessarily true that the resulting Fi will sum to give the guess value of Mo, i.e., it is not necessarily true that the result will satisfy
∑F ) 10 M 3
i
i
The quantity
o
(guess)
(20)
n
)|
∑F - 10 M 3
i
o
(guess)|
(21)
i)1
was therefore selected as an optimization parameter, and the calculation model developed here utilized an optimization scheme that varied the guess value Mo in search of ) 0. Note that eq 21 always admits the trivial solution Mo ) 0, Fˆ ) 0. It is important to note that when the optimization finds only this solution, SOA aerosol will not form for the conditions of interest. Input r Values. The photooxidation reaction pathways of parent HCs are not known in sufficient detail to allow Ri values to be predicted reliably, even for relatively simple parent HCs such as cyclohexene. Therefore, the Ri values for the products formed from the five reactive HCs considered here were determined directly from the corresponding measured yield data. When data from multiple experiments for the same parent HC were available (as with R-pinene), the arithmetic averages of the Ri values were used. The Ri values used are summarized in Tables 3-7. Input p°L Values. If a product was not detected in the SOA phase or was found there only in trace amounts, it was assumed that the compound did not partition at all to the SOA phase (p°L too high), and/or it was not produced in sufficient amounts to be important. For most of the other products in Tables 3-7, experimentally determined values of p°L could not be found in the literature. The needed p°L values were estimated by adapting Jensen et al.’s (38) application of UNIFAC principles for estimating p°L values. The resulting “UNIFAC-p°L” method (39) estimates p°L by (i) summing the contributions to the total free energy G of the molecule from each of its functional groups (as expressed using the 108 available groups in the Dortmund UNIFAC database (40)) and then (ii) applying a correlation of G vs log p°L. The G for each particular UNIFAC group is calculated using four coefficients determined by an optimization procedure operating on a basis set of compounds that have known structures and p°L values. The basis set should be representative of the compounds of interest. Jensen et al.’s (38) UNIFAC-p°L method included up to six additional coefficients per group that accounted for how p°L is affected by detailed structural differences between molecules. The UNIFAC-p°L method used here did not use these additional coefficients because the basis sets were not large enough to represent all possible structural variations. When constructing the basis sets, little data could be found in the literature for compounds with oxygenated functionVOL. 35, NO. 6, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 4. Measured and Predicted Aerosol Product Yields in the β-Pinene/O3 System (Dry Conditions) aerosol yield Yi × 100 (%) exp 6/11/98b product hydroxy pina ketones norpinonic acid and isomers norpinic acid hydroxy norpinonic acid pinonic acid pinic acid hydroxy pinonic acid X (total unidentified mass)d
p°L (Torr)a 10-1
1.09 × 8.17 × 10-6 7.50 × 10-6 6.93 × 10-6 2.22 × 10-6 2.10 × 10-6 2.03 × 10-6 1.00 × 10-12
predicted/measured exp 6/11/98b
results for two expts
rb
measdc
pred
RYi
av, R h Yi
SD, σRY
0.0923 0.1400 0.0039 0.0129 0.0085 0.0431 0.0054 0.0099
0.74 1.7 0.17 0.14 0.14 1.2 0.25 0.15
0.0005 4.9 0.15 0.48 0.56 3.0 0.37 0.15
0.001 2.88 0.89 3.40 4.00 2.49 1.47 1.00
0.0003 1.62 0.57 1.84 2.36 1.57 1.03 1.00
0.00 1.78 0.44 2.21 2.32 1.31 0.63 0.00
total yield, Y × 100% Mo (µg m-3) RY ) 2.13 (6/11/98b), R h Y ) 1.33, σRY ) 1.14
4.5 18.9
i
9.6 40.4
a Predicted by UNIFAC vapor pressure method at 308 K. b Arithmetic average of measured R values calculated for the two experiments. c Measured values are from Yu et al. (34). d Product X represents the total amount of unidentified aerosol mass, including the product identified as 3-oxopinaketone by Yu et al. (34). Product X was assumed to consist of a compound with 2 CH3, 2 CH2, 2 CH, 1 C, 1 CH3CO, and 1 COOH UNIFAC functional groups; MWX ) 184 g mol-1. An R value for product X was calculated individually for each experiment. The vapor pressure of X is such that essentially all the available mass will partition into the aerosol phase.
TABLE 5. Aerosol Product Yields in the Sabinene/O3 System (Dry Conditions)
product 2-(2-isopropyl)-2-formylcyclopropyl methanoic acid hydroxysabina ketones sabina ketone norsabinonic acid and isomers norsabinic acid sabinic acid pinic acid S10 (exact structure unknown) X (total unidentified mass)d
p°L
aerosol yield, Yi × 100 (%)
predicted/measured
exp 6/15/98a
exp 6/15/98a
rb
measdc
pred
RYi
1.75 × 10-1
0.0030
0.13
0.000002
0.00002
2.93 × 10-2 9.49 × 10-3 8.17 × 10-6 7.50 × 10-6 2.10 × 10-6 2.10 × 10-6 2.03 × 10-6 1.00 × 10-12
0.4729 0.0793 0.0588 0.0032 0.0164 0.0191 0.0021 0.0001
0.53 0.43 1.4 0.09 0.53 0.39 0.03 0.01
0.0005 0.004 0.8 0.04 0.60 0.70 0.08 0.01
0.0009 0.01 0.55 0.49 1.13 1.79 2.73 1.00
(Torr)a
total yield, Y × 100% Mo (µg m-3) RY ) 0.63 (6/15/98a)
3.5 17.6
2.2 11.1
a Predicted by UNIFAC vapor pressure method at 308 K. b Measured R values for the single experiment. c Measured values are from Yu et al. (34). d Product X represents the total amount of unidentified aerosol mass, including the product identified as 3-oxosabinaketone by Yu et al. (34). Product X was assumed to consist of a compound with 2 CH3, 2 CH2, 2 CH, 1 C, 1 CH3CO, and 1 COOH UNIFAC functional groups, MWX ) 184 g mol-1. The vapor pressure of X is such that essentially all the available mass will partition into the aerosol phase.
TABLE 6. Aerosol Product Yields in the ∆3-Carene/O3 System (Dry Conditions) aerosol yield, Yi × 100 (%)
predicted/measured
exp 6/15/98b
exp 6/15/98b
product
p°L(Torr)a
rb
measdc
pred
RYi
C5 (exact structure unknown) caronaldehyde hydroxy caronaldehydes nor-3-caronic acid and isomers C4 (exact structure unknown) 3-caronic acid 3-caric acid pinic acid hydroxy 3-caronic acid X (total unidentified mass)d
>10 2.97 × 101 5.38 × 10-2 5.55 × 10-3 4.77 × 10-3 1.46 × 10-3 2.10 × 10-6 2.10 × 10-6 2.03 × 10-6 1.00 × 10-12
0.0261 0.1050 0.0433 0.0288 0.0061 0.0568 0.0260 0.0164 0.0162 0.0514
0.25 0.83 0.25 0.68 0.54 2.1 1.8 0.46 1.0 5.1
0.000000 0.000001 0.0004 0.002 0.0001 0.02 1.8 1.15 1.1 5.1
0.000000 0.000002 0.002 0.004 0.0003 0.01 1.01 2.51 1.11 1.00
total yield, Y × 100% Mo (µg m-3) RY ) 0.72 (6/15/98b)
13.0 63.3
9.3 44.9
a Predicted by UNIFAC vapor pressure method at 308 K. b Measured R values for the single experiment. c Measured values are from Yu et al. (34). d Product X represents the total amount of unidentified aerosol mass. Product X was assumed to consist of a compound with 3 CH3, 1 CH2, 2 CH, 1 C, 1 CH2CO, and 1 COOH UNIFAC functional groups, MWX ) 184 g mol-1. The vapor pressure of X is such that essentially all the available mass will partition into the aerosol phase.
alities and the low p°L values (10-5-10-7 Torr) that characterize the SOA products of interest. It was therefore necessary to use some of the data from the SOA chamber experiments 1168
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to obtain some basis set compounds with p°L values sufficiently low that the sets spanned the whole p°L range of interest. This necessity introduced varying degrees of cir-
TABLE 7. Aerosol Product Yields in the Cyclohexene/O3 System (Dry Conditions) aerosol yield, Yi × 100 (%) exp 5/13/99b product 2-hydroxy-pentanoic acid 4-hydroxy-butyraldehyde oxalic acid malonic acid 1,4-butanedial 4-oxo-butanoic acid succinic acid glutaraldehyde 5-oxopentanoic acid glutaric acid adipaldehyde 6-oxohexanoic acid adipic acid 2-hydroxyglutaric acid 2-hydroxyadipic acid X (total unidentified mass)d
p°L (Torr)a 10-3
1.52 × 1.24 × 10-3 2.03 × 10-4 1.59 × 10-4 1.54 × 10-4 1.45 × 10-4 9.64 × 10-5 7.82 × 10-5 7.49 × 10-5 5.09 × 10-5 3.62 × 10-5 3.53 × 10-5 2.47 × 10-5 1.40 × 10-7 7.76 × 10-8 1.00 × 10-12
predicted/measured exp 5/13/99b
results from six expts
rb
measdc
pred
RYi
av, R h Yi
SD, σRY
0.0158 0.0303 0.0703 0.0969 0.0061 0.0963 0.0096 0.0060 0.0688 0.1064 0.0262 0.0714 0.0406 0.0331 0.0187 0.0505
0.1 0.2 1.3 0.64 0.0 0.3 0.2 0.01 0.56 0.2 0.01 0.48 0.1 1.2 1.7 5.7
0.01 0.01 0.1 0.34 0.0 0.4 0.1 0.03 0.5 1.1 0.2 0.90 0.7 3.2 1.8 5.7
0.08 0.07 0.11 0.54 0.55 1.15 0.34 2.05 0.89 5.60 41.18 1.88 5.12 2.69 1.07 1.00
0.10 0.05 0.23 0.95 0.81 1.67 0.58 1.65 2.34 3.62 35.63 3.22 2.63 3.01 1.82 1.00
0.14 0.04 0.21 0.77 1.13 1.42 0.42 1.26 2.50 3.79 53.39 3.16 2.93 2.83 1.51 0.00
total yield,Y × 100% Mo (µg m-3) RY ) 1.20 (5/13/99b), R h Y ) 1.21, σRY ) 0.32
12.8 36.4
i
15.3 43.6
a Predicted by UNIFAC vapor pressure method at 298 K. b Arithmetic average of measured R values calculated for five of six experiments. Experiment 5/17/99b was neglected in computing the average. Four of six experiments were used in calculating the average R value for product X (see footnote d). c Measured values are from Kalberer et al. (35). d Product X represents the total amount of unidentified aerosol mass. Product X was assumed to consist of a compound with 2 CH2 and 2 COOH UNIFAC functional groups, MWX ) 118 g mol-1. An R value for product X was calculated individually for each experiment. No R values were calculated for the 6/19/99 experiments in which all of the aerosol mass was identified. The vapor pressure of X is such that essentially all the available mass will partition into the aerosol phase.
cularity in the model calculations, ranging from significant circularity to relatively little (see below). Basis set 1 (Table 8) was used for predicting the p°L values at 308 K for the cyclic products formed from R-pinene, β-pinene, sabinene, and ∆3-carene. It included 14 straightchain multifunctional oxygen-containing compounds plus the eight identified R-pinene SOA phase products. The p°L values for the 14 straight-chain compounds and for one R-pinene product (pinonaldehyde) were obtained from the literature and were corrected from p°S to p°L values as necessary. The p°L values for the other R-pinene products were extracted as average estimates based on the experimental Kp,om values (as determined from the measured Fi, Ai, and Mo of Yu et al. (34)) and application of eq 12 with the measured Fi (including that for the unidentified mass as represented by compound X, see below) to calculate MWom and the ζi (by UNIFAC). Applying the UNIFAC-p°L method to the monoterpene products gave the input p°L values in Tables 3-6. The p°L value predicted for pinonaldehyde by the UNIFAC-p°L method was 0.046 Torr, which is within about a factor of 2 of the value (0.10 Torr) measured by Hallquist et al. (45). Basis set 2 (Table 8) was used for predicting the input p°L values at 298 K for the straight-chained products from cyclohexene. It included the same group of 14 compounds in basis set 1 plus all of the identified cyclohexene SOAphase products except glutaric acid, which was retained as a method validation compound. For adipic acid, a value for p°L was available in the literature (44) and was used to estimate the corresponding basis set p°L value based on the ∆Hfus of adipic acid (43). For the remaining cyclohexene products (except glutaric acid), basis set p°L values were extracted from the experimental Kp,om values as described for the R-pinene products in basis set 1. All of the input p°L resulting from the application of the UNIFAC-p°L method for the cyclohexene products are given in Table 7. For glutaric acid, the method with basis set 2 yielded p°L ) 5.1 × 10-5 Torr at 298 K. This is in good agreement with the value of 3.2 × 10-5 Torr obtained based on the literature p°S value for glutaric acid (44) and an estimate of ∆Hfus of glutaric acid (43).
Unidentified SOA MasssCompound “X”. For most of the experimental runs considered, a portion of Mo could not be identified. Since all condensable compounds are coupled in their G/P behavior, inclusion of this mass in Mo was needed if the model was to place enough of each of the identified compounds in the SOA phase (see eq 13). This was accomplished by assigning (see Tables 3-7) a single compound “X” the following properties: (i) all of the unidentified portion of Mo; (ii) a p°L value that is sufficiently low that the model would place essentially 100% of X in the SOA phase for a wide range of Mo values that bracket the equilibrium solution value of Mo; (iii) a value for MWX that is representative of the products formed from the parent HC; and (iv) a mix of functionalities representative of the products formed. While the third and fourth assignments were necessary to allow calculation of the mole fraction-dependent MWom and ζi values, the model results were not very sensitive to these assignments: within a group of similar compounds, the quantities MWom and ζi are relatively weak functions of composition. Initial Guess Values. The model was applied to each of the SOA chamber experiments carried out with each of the five parent HCs. For each experiment modeled, the initial guess for Mo was the final Mo value determined experimentally. For the composition of each SOA phase, if n ) total number of condensable products found (including compound X), then for the SOA phase, the initial guess was that each mole fraction Xi ) 1/n. The corresponding initial value of MWom was calculated based on these Xi values, the known MW values of the products, and the assumed MWX. For all of the iterations, UNIFAC (36, 37) was used to calculate the composition-dependent ζi values, and fom was taken to be unity. Once all of the model parameters were initialized, a nonlinear optimization subroutine (46) was used to seek ) 0 by varying Mo. As implied above, updated values of MWom, ζi, and Kp,i were calculated for each iteration in the optimization.
Modeling Results Overview. Tables 3-7 compare the yield results predicted by the model to those measured experimentally in the VOL. 35, NO. 6, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 8. Basis Set Compounds Used with UNIFAC Vapor Pressure Prediction Model p°L(Torr) compound 4-methyl-3-penten-2-one 2-propenoic acid propanoic acid 1-pentanol 2-methyl-2-propenoic acid 2-methyl-propionic acid 4-hydroxy-4-methyl-2-pentanone butanoic acid 2,3-butanediol 1,2-propanediol 1,4-butanediol 2-butene-1,4-diol (cis) 1,2-pentanediol adipic acid pinonaldehyde norpinonic acid hydroxy pinonaldehyde pinonic acid pinic acid norpinic acid norpinonaldehyde hydroxy pinonic acid adipaldehyde 4-oxobutanoic acid 5-oxopentanoic acid malonic acid glutaraldehyde 6-oxohexanoic acid 2-hydroxypentanoic acid butanedial succinic acid oxalic acid 4-hydroxybutanaldehyde 2-hydroxyglutaric acid 2-hydroxyadipic acid a
basis set
T ) 298 K
T ) 308 K
eq used to calculate p°L
ref
1, 2 1, 2 1, 2 1, 2 1, 2 1, 2 1, 2 1, 2 1, 2 1, 2 1, 2 1, 2 1, 2 1, 2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
1.09 × 3.93 × 100 3.67 × 100 2.44 × 100 1.81 × 100 1.80 × 100 1.69 × 100 9.35 × 10-1 1.80 × 10-1 1.27 × 10-1 1.03 × 10-2 6.42 × 10-3 3.36 × 10-4 6.69 × 10-6 naa na na na na na na na 4.23 × 10-4 1.35 × 10-4 8.89 × 10-5 8.13 × 10-5 5.96 × 10-5 5.71 × 10-5 5.36 × 10-5 3.70 × 10-5 2.89 × 10-5 2.20 × 10-5 1.80 × 10-5 2.31 × 10-6 2.24 × 10-6
1.91 × 7.42 × 100 6.96 × 100 5.14 × 100 3.88 × 100 3.54 × 100 3.15 × 100 1.93 × 100 4.13 × 10-1 3.07 × 10-1 2.60 × 10-2 1.82 × 10-2 1.34 × 10-3 2.00 × 10-5 1.03 × 10-1 8.87 × 10-6 7.12 × 10-6 5.22 × 10-6 4.57 × 10-6 3.37 × 10-6 1.92 × 10-6 1.83 × 10-6 na na na na na na na na na na na na na
modified Antoine modified Antoine modified Antoine modified Antoine modified Antoine modified Antoine modified Antoine modified Antoine modified Antoine modified Antoine modified Antoine modified Antoine Clausius-Clapeyron Clausius-Clapeyron Clausius-Clapeyron eq 12 and data (34) eq 12 and data (34) eq 12 and data (34) eq 12 and data (34) eq 12 and data (34) eq 12 and data (34) eq 12 and data (34) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35) eq 12 and data (35)
41 41 41 41 41 41 41 41 41 41 41 41 42 43, 44 45 na na na na na na na na na na na na na na na na na na na na
101
101
na, not available.
associated chamber experiments. For each of the parent HCs, the comparisons are carried out for an individual SOA run and also as averaged for the set of experiments conducted with that HC. Tables S1-S5 (Supporting Information) provide the comparisons for all of the individual experiments. Degrees of Circularity (Expectation of Perfect Agreement) in the Model Results. It would be fully circular to just use measured Fi, Ai, and Mo values to extract p°L values from SOA formation experiments and then take those p°L values and the measured Ti () Fi + Ai) values to predict the measured Fi/Ai distributions, the Mo values, and the measured Yi values. Model results obtained in that manner would be expected to be in perfect agreement. The degree of circularity in the model results obtained here varied, from relatively significant for R-pinene and cyclohexene, to less for β-pinene, to little for sabinene and ∆3-carene. As noted, for R-pinene, the input p°L for the model runs were obtained from the UNIFAC-p°L method as applied using basis set 1. The model results are therefore partially circular in their derivation, though by no means totally so because basis set 1 included experimental p°L values for pinonaldehyde and the 14 compounds not related to the monoterpene products. Moreover, as noted above, the UNIFAC-p°L method gave p°L ) 4.6 × 10-2 Torr at 308 K for pinonaldehyde, which is within a factor of 2 of the experimental value of 0.10 Torr determined by Hallquist et al. (45). For β-pinene, application of the model was less circular than for R-pinene: while the input p°L values were again developed using basis set 1, two of the β-pinene products were not R-pinene products. For sabinene and ∆3-carene, application of the model involved little circularity because 1170
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there is little overlap between basis set 1 on one hand and the products identified from sabinene and ∆3-carene on the other. For cyclohexene, the degree of circularity approached that in the R-pinene results: the input p°L values were developed using basis set 2, which involved most of the cyclohexene products plus the group of 14 compounds. However, the basis set 2 value for p°L for adipic acid (a cyclohexene product) was obtained from the literature and not backed out of the chamber data of Kalberer et al. (35). Many of the group of 14 compounds are similar in structure to the cyclohexene products. The fact that the UNIFAC-p°L method with basis set 1 came well within a factor of 2 of the literature-derived value of p°L ) 5.1 × 10-5 Torr (298 K) for the method validation compound glutaric acid (see above) is also reassuring. r-Pinene Results. The degree of circularity in the R-pinene model runs would require at least modest agreement with the experimental results. In fact, the overall agreement is very good. The average predicted/measured total yield ratio (R h Y) is 1.09 ( 0.07. The average predicted/measured individual h Yi < 2.1 for all but three yield ratio R h Yi falls in the range 0.6 < R products. For the three compounds norpinonaldehyde (minor), pinonaldehyde (minor), and hydroxypinonaldehyde, the model significantly underpredicted the yields. For the 6/9/98b experiment, the RYi values for these three compounds were 0.0001, 0.002, and 0.3, respectively. As is discussed below, for all five parent HCs, the model underpredicted the measured yields for all products with p°L > 10-4 Torr; a possible explanation is discussed below. β-Pinene Results. For the two β-pinene experiments, with R h Y ) 1.3, good overall agreement on the total yield values
FIGURE 1. Average predicted/measured yield ratios of SOA compounds in the five experimental systems as a function of product compound vapor pressure. was obtained. The fact that the Yi values for the high p°L products from β-pinene were underpredicted did not have a large effect on the overall Y values because those products (e.g., the hydroxypinaketones) did not contribute significantly to total SOA yield; however, the model underpredicted Yi. For the products with p°L < 10-4 Torr, RYi was found to range from 4.0 for pinonic to 0.89 for norpinic acid. The relatively large overprediction of Yi for the former does not significantly affect the predicted total yield because this compound is not a major constituent of this aerosol. Sabinene Results. For the overall yield, R h Y ) 0.63, an important positive result given that the degree of circularity in the modeling is low for the sabinene calculations. As with R- and β-pinene, the model underpredicted Yi for the high p°L products, in this case hydroxysabinaketone, sabinaketone, and 2-(2-isopropyl)-2-formylcyclopropylmethanoic acid. The predicted Yi values for the lower p°L products pinic acid, sabinic acid, norsabinic acid, norsabinonic acid, and S10 are in reasonable agreement with the measured Yi values; the R h Yi values for these five components averaged 1.3. ∆3-Carene Results. For the overall yield, R h Y ) 0.72. The model also did a good job in predicting Yi values for the ∆3-carene products with lower vapor pressures. As with the other parent HC experiments, however, the model underpredicted the measured Yi for the high p°L products. Cyclohexene Results. Overall, R h Y ) 1.21 ( 0.32 for the six experiments. The cyclohexene R h Yi values show the same pattern observed in the monoterpene data, namely, R h Yi ≈ 1 for the lower vapor pressure compounds, and R h Yi , 1 for products with relatively high vapor pressures.
General Comments Figure 1 is a plot of average R h Yi values for all of the individual products from the different parent HCs, where the averages are as computed across the different experiments for each parent HC. Figure 1 shows that the model represents the data well (R h Yi ≈ 1) for compounds with low log p°L values. Since most of those compounds are also relatively abundant in the SOA phases studied, this agreement is the source of the general agreement in the total aerosol yields (RY ≈ 1). Although Figure 1 illustrates good agreement at low log p°L, it also indicates an apparently increasingly severe underprediction (R h Yi < 1) as log p°L increases. These results
may point to the consequence of denuder sampling artifacts. In particular, as discussed by Kamens et al. (47), use of denuder/filter/sorbent systems to quantify G/P partitioning can lead to an overestimation in Yi for high vapor pressure compounds because small amounts of gas-phase material that escape collection in the front denuder portion of the system will be ascribed to the particle phase, thus overestimating some Fi and therefore some Yi values. Since the magnitude of this effect on the Fi/Ai ratio would increase as Fi/Ai naturally decreases with increasing log p°L, there is a real potential that currently such Yi values can be predicted more accurately than they can be measured. Moreover, it is important to again note that this may not represent a significant problem for efforts to predict total SOA yields because high volatility compounds are not expected to contribute significantly to the SOA mass. Indeed, the fact that the underpredictions are so severe at very high log p°L values lends support to the presence of this artifact in the data: it is very hard to rationalize a significant presence in the SOA phase of a compound with p°L ) 0.1 Torr. We conclude that a straightforward mathematical approach now exists for modeling SOA formation in the atmosphere. While this approach requires a detailed understanding of the identities, amounts, and properties of the condensable products that are formed by photooxidation, current progress in determining the pathways of these reactions coupled with improved information on product vapor pressures (including improved abilities to predict such) indicate that predictive estimation of SOA formation in the atmosphere is an increasingly realistic goal.
Acknowledgments This work was supported by U.S. Environmental Protection Agency Grant R826371-01-0.
Supporting Information Available Five tables (S1-S5) showing the comparisons for individual experiments (7 pages). This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)
Schuetzle, D.; Rasmussen, R. A. J. Air Pollut. 1978, 28, 236-240. Pankow, J. F. Atmos. Environ. 1994, 28A, 185-188. Pankow, J. F. Atmos. Environ. 1994, 28A, 189-193. Odum, J. R.; Hoffmann, T,; Bowman, F.; Collins, D.; Flagan, R. C.; Seinfeld, J. H. Environ. Sci. Technol. 1996, 30, 2580-2585. Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; Wiley: New York, 1998; 1326 pp. Rogge, W. F.; Hildemann, L. M.; Mazurek, M. A.; Cass, G. R.; Simoneit, B. R. T. Environ. Sci. Technol. 1991, 25, 1112-1125. Rogge, W. F.; Hildemann, L. M.; Mazurek, M. A.; Cass, G. R.; Simoneit, B. R. T. Environ. Sci. Technol. 1993, 27, 636-651. Rogge, W. F.; Hildemann, L. M.; Mazurek, M. A.; Cass, G. R.; Simoneit, B. R. T. Environ. Sci. Technol. 1993, 27, 1892-1904. Rogge, W. F.; Hildemann, L. M.; Mazurek, M. A.; Cass, G. R.; Simoneit, B. R. T. Environ. Sci. Technol. 1993, 27, 2700-2711. Rogge, W. F.; Hildemann, L. M.; Mazurek, M. A.; Cass, G. R.; Simoneit, B. R. T. Environ. Sci. Technol. 1993, 27, 2736-2744. Rogge, W. F.; Hildemann, L. M.; Mazurek, M. A.; Cass, G. R.; Simoneit, B. R. T. Environ. Sci. Technol. 1994, 28, 1375-1388. Rogge, W. F.; Hildemann, L. M.; Mazurek, M. A.; Cass, G. R.; Simoneit, B. R. T. Environ. Sci. Technol. 1997, 31, 2726-2730. Rogge, W. F.; Hildemann, L. M.; Mazurek, M. A.; Cass, G. R.; Simoneit, B. R. T. Environ. Sci. Technol. 1997, 31, 2731-2737. Rogge, W. F.; Hildemann, L. M.; Mazurek, M. A.; Cass, G. R.; Simoneit, B. R. T. Environ. Sci. Technol. 1998, 32, 13-22. Kaplan, I. R.; Gordon, R. J. Aerosol Sci. Technol. 1994, 21, 343359. Hildemann, L. R.; Klinedinst, D. B.; Klouda, G. A.; Currie, L. A.; Cass, G. R. Environ. Sci. Technol. 1994, 28, 1565-1576. Turpin, B. J.; Huntzicker, J. J.; Larson, S. M.; Cass, G. R. Environ. Sci. Technol. 1991, 25, 1788-1793.
VOL. 35, NO. 6, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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(18) Turpin, B. J.; Huntzicker, J. J. Atmos. Environ. 1991, 25A, 207215. (19) Turpin, B. J.; Huntzicker, J. J. Atmos. Environ. 1995, 29, 35273524. (20) Lee, W. M. G.; Huang, R. L. J. Environ. Sci. Health 1993, 28, 1565-1579. (21) Castro, L. M.; Pio, C. A.; Harrison, R. M.; Smith, D. J. T. Atmos. Environ. 1999, 33, 2771-2781. (22) Strader, R.; Lurmann, F.; Pandis, S. N. Atmos. Environ. 1999, 33, 4849-4863. (23) Pandis, S. N.; Paulson, S. E.; Seinfeld, J. H.; Flagan, R. C. Atmos. Environ. 1991, 25A, 997-1008. (24) Izumi, K.; Fukuyama, T. Atmos. Environ. 1990, 24A, 1433-1441. (25) Wang, S. C.; Paulson, S. E.; Grosjean, D.; Flagan, R. C.; Seinfeld, J. H. Atmos. Environ. 1992, 26A, 403-420. (26) Wang, S. C.; Flagan, R. C.; Seinfeld, J. H. Atmos. Environ. 1992, 26A, 421-434. (27) Zhang, S. H.; Shaw, M.; Seinfeld, J. H.; Flagan, R. C. J. Geophys. Res. 1992, 97, 20717-20729. (28) Hoffmann, T.; Odum, J. R.; Bowman, F.; Collins, D.; Klockow, D.; Flagan, R. C.; Seinfeld, J. H. J. Atmos. Chem. 1997, 26, 189222. (29) Odum, J. R.; Jungkamp, T. P. W.; Griffin, R. J.; Forstner, H. J. L.; Flagan, R. C.; Seinfeld, J. H. Environ. Sci. Technol. 1997, 31, 1890-1897. (30) Odum, J. R.; Jungkamp, T. P. W.; Griffin, R. J.; Flagan, R. C.; Seinfeld, J. H. Science (Washington, D.C.) 1997, 276, 96-99. (31) Griffin, R. J.; Cocker, D. R.; Flagan, R. C.; Seinfeld, J. H. J. Geophys. Res. 1999, 104, 3555-3567. (32) Kleindienst, T. E.; Smith, D. F.; Li, W.; Edney, E. O.; Driscoll, D. J.; Speer, R. E.; Weathers, W. S. Atmos. Environ. 1999, 33, 36693681. (33) Hallquist, M.; Waengberg, I.; Ljungstroem, E.; Barnes, I.; Becker, K.-H. Environ. Sci. Technol. 1999, 33, 553-559. (34) Yu, J.; Cocker, D. R.; Griffin, R. J.; Flagan, R. C.; Seinfeld, J. H. J. Atmos. Chem. 1999, 34, 207-258.
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(35) Kalberer, M.; Yu, J.; Cocker, D. R.; Flagan, R. C.; Seinfeld, J. H. Environ. Sci. Technol. 2000, 34, 4894-4901. (36) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC: A Group-Contribution Method; Elsevier Scientific Publishing: New York, 1977. (37) Fredenslund, A.; Sorensen, J. M. Group Contribution Estimation Methods. Models for Thermodynamic and Phase Equilibria Calculations; Sandler, S. I., Ed.; Marcel Dekker: New York, 1994. (38) Jensen, T.; Fredenslund, A.; Rasmussen, P. Ind. Eng. Chem. Fundam. 1981, 20, 239-246. (39) Asher, W. E.; Erdakos, G. B.; Pankow, J. F.; Seinfeld, J. H. Unpublished work. (40) Hansen, H. K.; Rasmussen, P.; Fredenslund, A.; Schiller, M.; Gmehling, J. Ind. Eng. Chem. Res. 1991, 30, 2352-2355. (41) Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals, National Standard Reference Data System Parts 1-4; American Institute of Chemical Engineering: Hemisphere, NY, 1989. (42) Knauth, P.; Sabbah, R. Bull. Soc. Chim. Fr. 1988, 5, 834-836. (43) Khetarpal, S. C.; Lal, K.; Bhatnagar, H. L. Indian J. Chem. 1980, 19A, 516-519. (44) Tao, Y.; McMurray, P. H. Environ. Sci. Technol. 1989, 23, 15191523. (45) Hallquist, M.; Wangberg, I.; Ljungstrom, E. Environ. Sci. Technol. 1997, 31, 3166-3172. (46) Frontline Systems. Solver DLL; Boulder, CO. (47) Kamens, R.; Odum, J.; Fan, Z. H. Environ. Sci. Technol. 1995, 29, 43-50.
Received for review June 2, 2000. Revised manuscript received December 4, 2000. Accepted December 12, 2000. ES001321D
