Environ. Sci. Technol. 2008, 42, 7321–7329
Variation in the Sensitivity of Predicted Levels of Atmospheric Organic Particulate Matter (OPM) ,†
JAMES F. PANKOW* AND ELSA I. CHANG‡ Department of Civil and Environmental Engineering, and Department of Chemistry, Portland State University, Portland, Oregon 97207 and Bonneville Power Administration, 905 NE 11th Avenue Portland, Oregon 97232
Received February 3, 2008. Revised manuscript received June 3, 2008. Accepted June 12, 2008.
This study examines the sensitivity in predicted levels of atmospheric organic particulate matter (Mo, µg m-3) to changes in the governing gas/particle partitioning constants and the uI (levels of condensable organic compounds, µg m-3). Mo is given by the difference between ∑ui and the corresponding sum for the gas-phase levels. It is demonstrated that the sensitivity in predicted Mo levels increases rapidly as Mo becomes very small relative to ∑ui : as the ui, decrease, the gas phase becomes increasingly capable of holding the majority of all ui, and small changes in system parameters can cause large relative changes in Mo. These effects are illustrated using predictions for two values of the reacted hydrocarbon concentration (∆HC) for each of three secondary organic aerosol systems for relative humidity (RH) ) 20-80%. Specific structures for the oxidation products allows consideration of the effects of varying activity coefficients and water uptake. At low Mo/∑ui (as may be found in the atmosphere away from sources and at warm temperatures), relatively small errors in model input parameters (e.g., vapor pressures, vaporization enthalpies, activity coefficient parameters, and the ui values for low volatility compounds) will be amplified into large errors in the predicted Mo values.
1. Introduction Current efforts to model organic particulate matter (OPM) in the atmosphere do not lead to reliable predictions of ambient OPM levels (1, 2), and it has been suggested (3) that levels in the atmosphere can be significantly underpredicted. Essentially, all these calculations are based on the simplified “two-product” (2p) model approach of Odum et al. (4) in which each parent hydrocarbon (HC) that can lead to secondary organic aerosol (SOA) is considered to produce as many as two lumped products. Each such product is assumed to be formed according to a stoichiometric formation factor Ri, and to possess a gas/particle (G/P) partitioning constant Kp,i (m3 µg-1) for absorption into a single OPM phase. With ∆HC (µg m-3) giving the reacted amount of the parent HC, the total amount ui (µg m-3) formed for each lumped product is assumed to be given by ui ) Ri∆HC. Each product is then considered subject to temperature-dependent condensation * Corresponding author e-mail:
[email protected]. † Portland State University. ‡ Bonneville Power Administration. 10.1021/es8003377 CCC: $40.75
Published on Web 09/04/2008
2008 American Chemical Society
according to the theory of Pankow (5, 6), with ui thereby distributed over the G and P phases with ui (µg m-3) ) Fi + Ai
(1)
where Fi (µg m-3) is the P-phase portion and Ai (µg m-3) is the G-phase portion. (In prior work, we have used the symbols Ti, Fi, and Ai which carry the units ng m-3.) When multiple parent HCs are considered, Odum et al. (7) extended the 2p model by assuming that the various Kp,i values for the products from a mix of N parent HCs may be used without significant concern for effects due to dissimilarities among the partitioning organic compounds, or for the effects of water uptake into the OPM. For example, for the ozone oxidation of a mixture of cyclohexene and m-xylene at temperature T (K), the assumption would be that OPM produced from a mixture of the two can be modeled using fitted values of Ri and Kp,i for chamber experiments at a temperature T* (K) with (a) cyclohexene alone; and (b) m-xylene alone. It is generally assumed that the Ri are independent of temperature, and that the Kp,i can be adjusted from T* to T using assumed molar vaporization enthalpies for the products. When water uptake is ignored and absorption into the OPM phase is assumed to occur into a single phase, Pankow and Barsanti (8) refer to the result as the N•2p approach. Consideration of the equation of Pankow (5) for Kp,i for multicomponent absorptive partitioning (see eq 8 below) indicates that the N•2p approach assumes similarity in both the polarity and molecular weight (MW) characteristics of all the various lumped 2p compounds. With those assumptions, for OPM formed from all relevant mixes of the products, then all ζi (mole-fraction-scale activity coefficients, dimensionless) are ∼1, and the MW (mean MW of the absorbing particle phase, g mol-1) will remain approximately constant. It is the conceptual and computational simplicity of the N•2p approach that has led to its wide application in predicting OPM levels in the atmosphere. There will, however, be many situations in which variation in the ζi and in MW (as due to water uptake), and/or the possibility of phase separation in the P phase cannot be ignored. When those complexities are added, the result has been designated the N•2pζ,MW,θ approach (8). Following Erdakos and Pankow (9), θ is the phase index for when phase separation does occur. θ ) R refers to the phase that is relatively more aqueous, more polar, and more hydrophilic; θ ) β refers to the converse. Chang and Pankow (10) compare predicted values of the PM concentrations for Mo (total organics, µg m-3) as obtained by the N•2p and (N•2p)ζ,MW,θ approaches for the O3 oxidation of R-pinene over a range of relative humidity (RH) values. Comparisons are also made for Mw (water, µg m-3) and for MTPM () Mo + Mw, µg m-3). When Fi >Ai for the important condensable i, then large differences tend to be found in the output from the two approaches, and moreover the predictions of the N•2pζ,MW,θ approach tend to be sensitive to RH. In this work, we develop a general approach for considering the sensitivity of predictions of Mo, Mw, and MTPM to variation of Kp,i values as they might be affected by changes in system variables such as T and RH, or by errors in the parameters that determine the relevant Kp,i (e.g., vapor pressure, activity coefficients, and enthalpy of vaporization). The effects of errors in the ui are also considered. While the context of this study is the prediction of organic PM levels in the atmosphere, most of the equations developed apply equally well to inorganic aerosols. VOL. 42, NO. 19, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Governing Equations. Background. The fractions in the P- and G-phases are given by (11): fp,i ≡
Fi ui
(0 < fp,i < 1)
(2)
fg,i ≡
Ai ui
(0 < fg,i < 1)
(3)
The exclusive use of the symbol < in the ranges given in eqs 2 and 3 presumes the presence, in the real atmosphere, of at least some P-phase material so that it is never possible that fp,i ) 0 (fg,i ) 1). In a truly single-component system, the ranges are 0 e fp,i < 1 and 0 0, the value is small), then predictions of Mo will be highly sensitive to variation in the inputs used in Mo calculations: Mo is being computed as the difference between two similar numbers. Type I and Type II Sensitivity. Two types of model input are (I) thermodynamic; and (II) mass balance. In a single o (T) function component case, the single type I input is the pL,i o (T) )1/Ao(T). Type I sensitivity is then caused that gives Kp,i i by natural changes or uncertainty in T, or uncertainty in o (T). In multicomponent systems, in addition to effects pL,i o (T) functions, Type I sensitivity can involving the various pL,i be caused by changes in P-phase composition (e.g., as due to RH effects). Type II sensitivity can be caused by variation or uncertainty in ui values due to variable and incompletely understood sources, formation and/or degradation reactions, and dilution.
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Type I Sensitivity in a Single Component System: Glycerol Example. The consequences of Type I sensitivity in a singlecomponent system can be illustrated using a glycerol case for which it has been accurately measured that uglycerol ) 455.2 µg m-3 at 20 °C. Assuming perfect accuracy for o (T) from Yaws (14), then 455.2 µg m-3 corresponds pL,glycerol exactly to gas/liquid saturation at 20 °C (14). For temperatures from 20 °C down to 1 °C (and including the effects on uglycerol due to a contracting gas volume because of Charles’ Law), condensation leads to Mo values (liquid glycerol) of 0-449.9 µg m-3 (see Table S1 in the Supporting Information). Consider o (T) being too low for all T now the consequences of pL,glycerol by 15% (propensity to condense slightly too high). With uglycerol ) 455.2 µg m-3 at 20 °C, then for 20-1 °C the predicted Mo range would be 68.3-455.4 µg m-3, respectively. All of these values are too high, but the most problematic is that for 20 °C: instead of Mo ) 0 µg m-3, the prediction is Mo ) 68.3 µg m-3, and the error is large both absolutely (+68.3 µg m-3) and relatively (+∞%). However, as T decreases and most of the glycerol is driven into the liquid phase, the prediction error decreases toward zero. Multi-Component Systems: General. When multiple absorbing compounds are present in the atmosphere, the equilibrium gas/particle (G/P) partitioning constant Kp,i(m3 µg-1) for absorption of i into a single in P phase is (5)
fp,i )
Kp,iMTPM 1 + Kp,iMTPM
(10)
fg,i )
1 1 + Kp,iMTPM
(11)
When multiple components condense and the summation is limited to organic compounds, Mo ≡
∑f
p,iui ≡
i
∑ F ≡ ∑ (u - A ) i
i
i
(12)
i
i
By consideration of eq 9, the multiple component version of eq 7 is Mo )
∑ (u - K1 i
i
) ∑(
Fi ) M p,i TPM
i
ui - Ci/
Fi MTPM
)
(13)
It is the factor Fi /MTPM that allows any i in a multicomponent system to always contribute positively to Mo, even when ui o )-1 ) C/,o . The role of the factor F /M , (Kp,i i TPM in eq 13 is i identical to the role of xi in eq 4. (When all i share the same MW, then Fi /MTPM ) xi.)
Type I Sensitivity in Multi-Component Systems: General. When one Kp,i value changes, it is likely that others will also be changing, e.g., as due to the effects of changing T or PM composition. The sensitivity of Mo in a multicomponent system to changes in system conditions that lead to coupled changes in Kp,i for all i may be examined as follows. Consider init; and (b) a system for which (a) Mo ) 0 when all Kp,i ) Kp,i the Kp,i may increase according to init Kp,i ) 10ainKp,i
(14)
dKp,i init ) 2.303aiKp,i ) 2.303ai10ainKp,i dn
(15)
init. Equations 14 and 15 assume that When n ) 0, all Kp,i ) Kp,i (1) the independent variable n is linked to system condition(s) that cause all Kp,i to increase with increasing n; and (2) ai is a compound-dependent parameter that allows the strength of the dependence on n to vary by compound. When Kp,i values increase due to decreasing T, then n is given by eq 23; when Kp,i values change due to changing MW, then n is given by eq 25. A parametrization connecting n with changes in the ζi would not be straightforward. Using fp,i as given by eq 10 and Mo as given by the first equality in eq 12, then eqs 14 and 15 with the assumptions that dMTPM/dn ≈ dMo/dn and that the ui are independent of n give
dMo ≈ dn
2.303
[
1-
∑auf
i p,ifg,i
i
i
1 MTPM
]
∑uf
(16)
i p,ifg,i
i
The relative change in Mo with changing n is given by dMo ⁄ Mo 1 × ≈ dn Mo
2.303
[
1-
∑auf i
i p,ifg,i
i
1 MTPM
∑uf
]
(17)
i p,ifg,i
i
The contributions to dMo/dn made by two compounds with the same fp,i will differ only according to their ui values. The same comment applies to d(Mo/Mo)/dn. At the point of incipient PM formation, Mo ≈ 0, and so for this condition of ultimate relative sensitivity, (dMo/Mo)/dn approaches ∞. With a single component i, then, MTPM ) Mo ) uifp,i. The denominator in eq 16 thus equals (1 - fg,i) ) fp,i. Just prior to incipient PM formation, fg,i ) 1, and so at n ) 0, dMo ) 2.303aiui dn
FIGURE 1. (a) Mo vs n for the generic case example with u3 ) init ) 0.194 m3 µg-1, Kinit ) 6.81 × 10-3, u2 ) u1 ) 5 µg m-3; Kp,3 p,2 init) 2.39 × 10-4; and a ) 1, a ) 0.8, and a ) 0.6. and Kp,1 3 2 1 Equivalent temperature values given on upper x-axis. (b) dMo/dn vs n (see part a for assumptions). (c) (dMo/Mo)/dn vs n (see part a for assumptions).
(18)
Differentiation of eq 7 leads to the same result since (1) by o ) ) 2.303a /Ko,init; and (2) n ) 0 is eq 15, at n ) 0, d(-1/Kp,i i p,i o,init ) u . set such that Mo ) 0, so by eq 7, 1/Kp,i i In a multicomponent system, by eqs 16 and 17, each organic compound i will contribute to dMo/dn and (dMo/ Mo)/dn based on the value of uifp,ifg,i. For each i, this term maximizes when fp,ifg,i ) 0.5 × 0.5. As the terms for the various i sequentially maximize, the numerator and the bracketed denominator in eqs 16 and 17 act together to create a series of maxima in the plots of dMo/dn and (dMo/Mo)/dn vs n. (See Figure 1b and c below.) For the bracketed denominator, as each uifp,ifg,i term increases then decreases, the result is a decrease, then an increase. For the first maximum(a), i.e., when MTPM is small because only small portions of the most condensable compounds have condensed, then the bracketed denominator will be small and thus very influential on the values of both dMo/dn and (dMo/Mo)/dn. This skews the first maximum(a) in both quantities significantly toward the origin. By eq 17, for (dMo/Mo)/dn, the action of 1/Mo
accentuates this effect (infinitely as Mo f 0). As n and MTPM increase, the fg,i sequentially approach 0, the denominator approaches unity, and the influence of the denominator dampens out. Overall, if the maxima are well separated init are well separated, the height of each will because the K p,i depend on the corresponding value of aiui. In the “volatility basis set” view of Donahue et al. (13), there will be a peak for each bin j in the set, with the height of the peak related to aj, and to uj, the total mass concentration in bin j. As fp f 1 for all “bins” so that Mo f∑j uj, then dMo/dn f 0. The form of dMo/dn vs n as given by eq 16 is similar to that of buffer intensity vs pH for a mixture of multiple monoprotic acid/base pairs (16). For each HA/A- pair, the buffer intensity includes a term of the form 2.303 ATRHARA-. The quantities RHA and RA- are fractions, so this term has the same form as 2.303uifp,ifg,i. Role of Temperature in Type I Sensitivity. When the heat of vaporization (∆Hvap,i, kJ mol-1) for each i is assumed to be independent of T, then by the Clausius-Clapeyron equation, VOL. 42, NO. 19, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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o,init pL,i o pL,i
(
∆Hvap,i 1
) 10 2.303R
1 T Tinit
)
(19)
o,init is the vapor pressure at temperature Tinit, and po where pL,i L,i is the vapor pressure at T. By eq 8, the primary effects of T on Kp,i may be considered according to
(
∆Hvap,i 1
Kp,i ) 10 2.303R
1 T Tinit
)K
init p,i
(20)
The strength of the T-dependence in eq 20 is determined by ∆Hvap,i. As a specific type of ai, we introduce aH,i so that ∆Hvap,i ) aH,i100 kJ mol-1 100
Kp,i ) 10aH,i 2.303R
(
1 1 T Tinit
)K
init p,i
(21) (22)
-1
The use of 100 kJ mol in eq 21 is convenient as well as relevant. Comparison of eqs 14 and 22 gives n≡
(
1 100 kJ mol-1 1 2.303R T Tinit
)
(23)
When aH,i ) 0.50, 0.75, and 1.0, then ∆Hvap,i ) 50, 75, and 100 kJ mol-1, respectively. For aH,i ) 1.0, cooling from Tinit ) 293 init; for a K to T ) 283 K leads to Kp,i ≈ 4Kp,i ∆H,i ) 0.5, the init. When ∆H corresponding change is weaker, Kp,i ≈ 2Kp,i vap,i cannot be assumed to be constant with changing T, more complex representations than eqs 19 and 23 will be needed. The derivation of eqs 16 and 17 assumes that the ui are independent of n. That assumption is not strictly valid when n is given by eq 23 because the ui are volume-based concentrations, and gas volume depends on T according to Charles’ Law. That dependence, nevertheless, is much weaker than the dependence for Kp,i given in eq 22. Therefore, other than its consideration in the glycerol example, that dependence is neglected in this work. Role of MW and an Associated Influence of Water in Type I Sensitivity. In a single-component system, T is the only variable that affects a Kp,i value. In a multicomponent system, in addition to the effects of changing T, the Kp,i values are affected by variations in all of the xi in the PM (due to varying MW and ζi). Inorganic constituents fall into a special category in this regard because while they are not included in the summations in eqs 16 and 17, they affect the Kp,i, fp,i, and fg,i for all compounds. Water is of great interest in this regard: (1) it is ubiquitous in the atmosphere and thus is always absorbed into OPM to some extent; (2) it can be present at high thermodynamic activities (even low RH values can represent significant water concentrations); (3) its low molecular weight (18 g mol-1) means that absorption of even a relatively small amount of water can reduce MW by amounts that can have significant effects on the Kp,i; and (4) it possesses high polarity and so can have strong effects on the ζi of both hydrophilic and hydrophobic compounds. Though absorption of a given amount of water into a particular P phase will affect each ζi differently, the portion of the effect on each Kp,i due to changes in MW will be the same, i.e., according to (MW )-1. Thus, if aMW, i is defined as the version of ai for effects due to changing MW, then aMW, i t 1 for all i so that at constant T for this effect, init init ) (MWinit/MW)Kp,i Kp,i ) 10nKp,i
(24)
10n ≡ MW init/MW n ≡ log10 MW init/MW
(25)
For n )...-0.097, -0.046, 0.0, 0.041, 0.079..., 10n )...0.8, 0.9, 1.0, 1.1, 1.2,... Generic Multi-Component Examples: Mo as a Function of n. General. As n increases, each fp,i (and thus Mo) will 7324
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 19, 2008
FIGURE 2. Mo vs n for generic cases 2 and 3. Equivalent init and a values as temperature values given on upper x-axis. Kp,i i in Figure 1. increase. While changes in MW offer limited range for changes in n, changes in T can easily cause Kp,i values to change by multiple orders of magnitude. Indeed, the lumped surrogate secondary compounds considered by Chang and Pankow (10) have ∆Hvap,i values at T ≈ 300 K as high as 100 kJ mol-1 (ai ) 1). Second, wide T variations exist within the troposphere, e.g., Tinit ) 313 K (40 °C) to T ) 223 K (-50 °C.) For this range, with ∆Hvap,i ) 100 kJ mol-1, there is a 7 orders of magnitude increase in Kp,i (aH,in ) 7). init For three condensable organic compounds, we assign Kp,3 init ) 6.81 × 10-3, and K init ) 2.39 × 10-4, ) 0.194 m3 µg-1, Kp,2 p,1 o < po 0 and curve B predicts Mo ) 0, the percent error is -∞. For n slightly greater than 1.8, the error is large: Mo is greatly affected in this region by the low level of u3. As n increases and the Mo level becomes dominated by larger amounts of components 2 and 1, the error asymptotically approaches -5% () -u3 × 100/(u2 + u1)).
Besides variation in T, another driver of type II error is dilution. Figure 4assumes that the Figure 3 system is held at n ) 3 (T ) 263 K), and subjected to increasing dilution. When the dilution factor (D) ) 1 (no dilution), the error is -12%: because Mo (as given by curve A) is dominated by component 2, neglecting component 3 (curve B) causes only a small amount of error. As D increases, all fp,i decrease. However, fp,2 drops faster than fp,3. This makes component 3 an increasingly important contributor to Mo, so neglecting it becomes increasingly problematic. When D reaches ∼9, failure to consider component 3 (curve B) would suggest Mo ) 0, when in fact Mo ) 0.2 µg m-3: the percent error goes to -∞. For D > 40, although both curves A and B give Mo ) 0 so that the error (B - A) becomes 0, in the real atmosphere some amount of low volatility compounds will always keep Mo > 0. Overall, Figure 4 illustrates that dangers exist when high Mo chamber results are extrapolated to the ambient atmosphere wherein Mo is likely to be much lower. Type I Sensitivity in Three SOA Example Systems. Model. PM concentrations were predicted using both the conventional N•2p approach to obtain Mo () MTPM), as well as the N•2pζ, MW ,θ approach to obtain Mo, Mw, and MTPM. The latter was implemented using the set of SOA computation algorithms described by Chang and Pankow (10), e.g., computation of ζi, values by the WCP.1 method. The SOA computations could have been carried out using any of the other algorithm sets that allows appropriate consideration of ζi and MW effects. (Examples are those discussed in refs 19–22). Any such set will lead to the conclusion reached below: at low ∆HC, eq 13 requires that Mo will be found to be very sensitive to changes in RH because changing RH will affect the Kp,i. This remains true even if the possibility of phase separation is neglected. (Koo et al. (21) and Bian and Bowman (22) do not allow for phase separation.) Three single-parent HC systems were considered at T ) 301 K over a range of RH: (1) R-pinene/O3; (2) isoprene/OH; and (3) C16 n-alkane/OH. Each system was considered at a high and low value of ∆HC. The sources of the Ri values (most are chamber-derived) are given elsewhere (10). Both the R-pinene/O3 and isoprene/OH systems were considered to lead to two lumped products; the C16 n-alkane/OH system VOL. 42, NO. 19, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Secondary Organic Aerosol Predictions at Two Relative Humidities for Three Parent Hydrocarbons at Two Levels Using the N•2pζ, MW, θ Approach Following Implementation Described by Chang and Pankow (10) r-pinene/O3
lumped product properties MW (g mol-1) (see ref 10) * (chamber) (see ref 10) Kp,i
Ri (see ref 10)
S3 S4 S3 S4 S3 S4
m-3)
ui (µg m-3) ∑ui (µg m-3)
Fi (µg m-3) Ai (µg m-3) fp,i fg,i ζi Kp,i (m3 µg-1) (Kp,i)-1 ) Ci* (µg m-3)
Product S3 S4
Product S3 S4 S3 S4 S3 S4 S3 S4 S3 S4 S3 S4 S3 S4
(dMo/Mo)/dna (%) (b) Results - Lower ∆HC ∆HC (µg m-3) ui (µg m-3) ∑ui (µg m-3)
m-3)
fp,i fg,i ζi Kp,i (m3 µg-1) (Kp,i)-1 ) Ci* (µg m-3) (dMo/Mo)/dn (%)a a
7326
20% 147 4.27 151 0.24 152
80% 152 40.2 192 0.74 63.7
81.0 66.4 3.36 2.42 0.96 0.96 0.040 0.035 1.50 1.39 0.159 0.181 6.29 5.52 9
83.6 68.1 0.82 0.76 0.99 0.99 0.010 0.011 1.08 1.29 0.529 0.466 1.89 2.15 2
Product S10 S11 S10 S11 S10 S11 S10 S11 S10 S11 S10 S11 S10 S11
r-Pinene/O3
Product S3 S4
Product S3 S4 S3 S4 S3 S4 S3 S4 S3 S4 S3 S4 S3 S4
S25
287
S25
0.0229 (298K)
S25
1.17
Isoprene/OH
C16 n-Alkane/OH
675
675
Product S10 S11
84.4 68.9 153
C16 n-alkane/OH
136 218 0.0086 (295K) 1.62 (295K) 0.232 0.029
Product S25
157 19.5 177 80% 163 98.5 262 0.83 39.6
64.4 19.3 92.2 0.23 0.41 0.99 0.59 0.012 0.89 1.44 0.00788 0.936 127 1.07 180
144 19.5 12.6 0.03 0.92 1.00 0.080 0.002 0.43 1.68 0.0434 2.17 23.0 0.46 17
20% 728 0.94 729 0.021 295
80% 733 4.46 737 0.092 275
Product S25
728
733
S25
63.5
59.2
S25
0.92
0.93
S25
0.080
0.075
S25
1.000
1.006
S25
0.0157
0.0168
S25
63.6
59.6
20
19
Isoprene/OH
C16 n-Alkane/OH
60 Product S10 S11
3.75 3.06 6.81 20% 1.53 0.0445 1.57 0.24 151
80% 5.35 1.42 6.77 0.74 63.7
0.76 0.77 2.99 2.29 0.20 0.25 0.80 0.75 1.62 1.31 0.161 0.214 6.21 4.68 720
2.98 2.37 0.77 0.69 0.79 0.77 0.21 0.23 1.08 1.30 0.572 0.507 1.75 1.97 60
Product S10 S11 S10 S11 S10 S11 S10 S11 S10 S11 S10 S11 S10 S11
60 Product S25
13.9 1.74 15.6
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 19, 2008
70.0 70.0
20% 0.80 0.025 0.83 0.26 160
80% 4.88 2.47 7.34 0.81 43.6
0.047 0.76 13.9 0.98 0.003 0.43 0.996 0.56 1.14 0.97 0.0041 0.93 244 1.08 320
3.23 1.65 10.7 0.09 0.23 0.95 0.77 0.05 0.42 1.36 0.0411 2.43 24.3 0.41 190
20% 6.46 0.0083 6.47 0.021 295
80% 10.8 0.066 10.8 0.092 275
Product S25
6.46
10.8
S25
63.5
59.2
S25
0.092
0.15
S25
0.91
0.85
S25
1.000
1.006
S25
0.0157
0.0168
S25
63.6
59.6
2200
1300
All ai assumed equal to 1 because changes in Mo are being caused largely by changes in MW . 9
792 792
20% 83.7 4.84 88.6 0.32 107
30
RH ) Mo (µg m-3) Mw (µg m-3) MTPM (µg m-3) xH2O MW (g mol-1) Fi (µg m-3)
S10 S11 S10 S11 S10 S11
675
RH ) Mo (µg m-3) Mw (µg m-3) MTPM (µg m-3) xH2O MW (g mol-1)
Ai (µg
214 174 0.088 (310K) 0.0788 (310K) 0.125 0.102 r-Pinene/O3
(a) Results: Higher ∆HC ∆HC (µg
isoprene/OH
FIGURE 6. r-pinene/O3 system. (a) ∆HC ) 675 µg m-3; (b) ∆HC ) 30 µg m-3 (adapted from Chang and Pankow (10)). Mo, Mw, and MTPM by the N•2pζ, MW, θ approach using the CP-Wilson.1 method (10) for ζi predictions for the assumed products (Figure 5 and Table 1) and water (changes in Kp values going from RH ) 20 to 80% are given for each organic product). For comparison, Mo ) MTPM by the N•2p approach is also given.
FIGURE 7. Isoprene/OH system. (a) ∆HC ) 675 µg m-3; (b) ∆HC ) 60 µg m-3. Mo, Mw, and MTPM by the N•2pζ, MW,θ approach using the CP-Wilson.1 method (10) for ζi predictions for the assumed products (Figure 5 and Table 1) and water (changes in Kp values going from RH ) 20 to 80% are given for each organic product). For comparison, Mo ) MTPM by the N•2p approach is also given.
FIGURE 8. C16 n-alkane/OH system. (a) ∆HC ) 675 µg m-3; (b) ∆HC ) 60 µg m-3. Mo, Mw, and MTPM by the N•2pζ, MW,θ approach using the CP-Wilson.1 method (10) for ζi predictions for the assumed products (Figure 5 and Table 1) and water (changes in Kp values going from RH ) 20 to 80% are given for each organic product). For comparison, Mo ) MTPM by the N•2p approach is also given. was assumed to lead to one lumped product. Surrogate structures were assigned to the five products (Figure 5). Varying ζi and MW were considered to alter chamberderived Kp,i values according to eq 2 of Chang and Pankow (10), i.e., using the form of an expression given by Bowman and Karamalegos (23) as based on Pankow (5). The CPWilson.1 method (10) was used for predicting ζi values as a function of PM composition. Table 1 summarizes the assumed system conditions.
Results The results by the N•2p and N•2pζ, MW,θ approaches at T ) 301 K are given in Figures 6-8 and Table 1. Mo values by the N•2p approach do not account for water uptake, or for the
effects of varying ζi and MW values: for every system, over the entire RH range, Mo () MTPM) remains constant and Mw ) 0. In contrast, the predictions by the N•2pζ, MW,θ approach show dependency of Mo, Mw, and MTPM on RH. A summary of results is given in Table 1. For every system at every RH value considered, the N•2pζ, MW,θ results indicate a single P phase. At the high ∆HC value (675 µg m-3), increasing RH from 20 to 80% causes the predicted Mo values for the R-pinene/O3, isoprene/OH, C16 n-alkane/OH systems to increase by ∼3, ∼90, and ∼1%, respectively (Figures 6a, 7a, and 8a). In each of the figures, the effects of RH on the Kp,i values are placed in terms of eq 14: values of 10ai,n are given for each case as the ratio (Kp,i at RH ) 80%)/(Kp,i at RH ) 20%). In the two systems with small VOL. 42, NO. 19, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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percent increases, at RH ) 20%, Mo is already close to ∑ui, thus not much additional organic condensation is possible. At the lower ∆HC values considered (30, 60, and 60 µg m-3), the increases in Mo for the same RH range are ∼250, ∼500, and ∼70%, respectively (Figures 6b, 7b, and 8b). For the R-pinene/O3 case examined by Seinfeld et al. (24), the relatively low predicted sensitivity for Mo with increasing RH is a result of the fact that a relatively high ∆HC was considered (244 µg m-3): the fp,i values for products with low to o were all greater than 1/3 at the initial RH intermediate pL,i of 0%. The thermodynamic origin of the increases in the Kp,i values driving the increases in Mo in Figures 6–8 may be determined by examining the MW and ζi values in Table 1. For the lower ∆HC cases, for the R-pinene/O3 and C16 n-alkane/OH systems, the effect of MW being reduced (due to water uptake) is more influential than the changes in the ζi. For the isoprene/OH system at the lower ∆HC, reductions in MW and ζS10 are of similar importance. The large percentage increases in Mo for the N•2pζ, MW θ results at the lower ∆HC values can be considered in terms of the high type I sensitivity in Figures 1b and c near n ) 0. The C16 n-alkane/OH results in Figure 8b are particularly striking in this regard. The relatively high hydrophobicity expected for product S25 (Figure 5) results in very little water being absorbed as RH increases from 20 to 80%; at RH ) 80%, Mw is only 0.004MTPM in Figure 8.b. Thus, the activity coefficient ζS25 remains essentially unchanged (ζS25 ) 1.000 at RH ) 20%, and ζS25 ) 1.006 at RH ) 80%), and the 70% increase in Mo as RH increases to 80% is brought about entirely by the 7% decrease in MW from 295 to 275 g mol-1.
Discussion A framework for understanding when predicted Mo levels will be highly sensitive to changes in system conditions has been discussed. Possible laboratory chamber experiments to investigate high sensitivity conditions (due to fg,i ∼ 1) include SOA experiments at (1) low ∆HC values and a range of RH values; (2) moderate ∆HC values and warm chamber temperatures; (3) one temperature and RH, and then subjected to (a) increasing T, and/or (b) dilution. In the ambient atmosphere, field studies examining the predictability of Mo in Lagrangian parcels affected by changing T and D will be of interest, especially at low Mo, warm T, and when affected by primary emissions. In any case, in the ambient atmosphere away from sources and at warm T, it does not seem likely that deterministic (i.e., source- chemistry-, and transport-driven) OPM models of either the N•2p or N•2pζ, MW θ types (with consideration or partitioning of primary emissions) will be able to reliably predict Mo levels to closer than a factor of 3 any time soon.
aH,i
aMW, i
Ai (µg m- 3 ) Aio (µg m-3) cg,i (ng m-3) cp,i (ng µg-1) Ci/ Ci/,o D f fg,i fp,i Fi (µg m-3) HC ∆HC (µg m-3) ∆Hvap,i (kJ mol-1) Kp,i (m3 µg-1) o (m3 µg-1) Kp p,i init K p,i
Mw (µg m-3) Mo (µg m-3) MTPM (µg m-3) MW (g mol-1) MW (g mol-1) MWi (g mol-1) n
N N•2p
Acknowledgments This work was supported by National Science Foundation Grant ATM-0513492, the Electric Power Research Institute, the Cooley Family Fund for Critical Research of the Oregon Community Foundation, and through the support of Steven T. Huff.
N•2pζ, MW ,θ
Appendix A Symbols and Abbreviations ROMAN ai
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compound-specific parameter determining the strength of the dependence of Kp,i on the parameter n as Kp,i changes init from the initial value K p,i 9
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2p OPM pi (atm) o (atm) p L,i
version of the compound-specific parameter ai when changing T is considered responsible for changing Kp,i version of the compound-specific parameter ai when changing MW is considered responsible for changing Kp,i (in this work, aMW,i ) 1 for all i) portion of ui in the gas phase. saturated mass concentration of i in the gas phase (as a single component) concentration of i in the gas phase concentration of i in the particulate matter phase saturation concentration () 1/Kp,i) for particular PM composition and T saturation concentration in a single component system at a particular T () Aio) o ) 1/Kp,i dilution factor according to which each ui is decreased weight fraction of the particulate matter that is the absorbing phase fraction of i that is in the gas phase () Ai/ui ) fraction of i that is in the particulate matter () Fi/ui ) portion of ui in the particulate matter hydrocarbon (parent) reacted amount of parent hydrocarbon enthalpy of vaporization of i gas/particle partitioning constant of i gas/particle partitioning constant for i in a single component system initial value of Kp,i for some specific initial conditions (e.g,, Tinit) mass concentration of water for the particulate matter mass concentration of total organic compounds for the particulate matter mass concentration of total particulate matter ()Mo + Mw in this work) molecular weight mean molecular weight of the absorbing particle phase molecular weight of i system parameter that, with the compound-specific ai, governs exponential change in each Kp,i according to Kp,i ) init 10ai,nK p,i number of parent hydrocarbons (HCs) responsible for forming SOA abbreviation of SOA modeling approach of Odum et al. (7); assumes simple superimposability when N parent hydrocarbons (HCs) produce up to two products per parent HC abbreviation for SOA modeling approach of SOA proposed by Pankow and Barsanti (8); builds on N•2p approach by considering the effects of varying ζi, variable MW and the possibility of phase separation two product organic particulate matter gas-phase pressure of i vapor-pressure of pure i as a liquid (subcooled if necessary)
o,init (atm) p L,i
R RH (%) SOA T (K) T* (K) ui (µg m-3)
xi Greek Ri R β θ ζi
vapor pressure of pure i(subcooled if necessary) at temperature Tinit gas constant () 8.2 × 10-5 m3 atm mol-1 K-1) relative humidity secondary organic aerosol temperature temperature in an SOA chamber experiment total concentration of component i (ui ) Ri∆HC if i is formed by reaction of a parent hydrocarbon (HC) and no source/sink reactions occur) mole fraction of i in a liquid phase
stoichiometric formation factor by which an SOA product is formed according to ui ) Ri∆HC (usually assumed to be independent of T) value of θ for the relatively more aqueous, more polar, and more hydrophilic phase value of θ for the relatively less aqueous, less polar, and less hydrophilic phase phase index for the particulate matter () R, β, etc.) mole-fraction-scale activity coefficient (dimensionless) of i in a liquid phase
Supporting Information Available Table S1. This material is available free of charge via the Internet at http://pubs.acs.org.
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(8) Pankow, J. F.; Barsanti, K. C. Atmos. Environ. 2008. (9) Erdakos, G.B.; Pankow, J.F. Gas/particle partitioning of neutral and ionizing compounds to single- and multi-phase aerosol particles. 2. Phase separation in liquid particulate matter containing both polar and low-polarity organic compounds. Atmos. Environ. 2004, 38, 1005–1013. (10) Chang, E. I.; Pankow, J. F. Organic particulate matter formation at varying relative humidity using surrogate secondary and primary organic compounds with activity corrections in the condensed phase obtained using a method based on the Wilson equation. Atmos. Chem. Phys. Discuss. 2008, 8, 995–1039. (11) Liang, C.; Pankow, J. F. Gas/particle partitioning of organic compounds to environmental tobacco smoke: partition coefficient measurements by desorption and comparison to urban particulate material. Environ. Sci. Technol. 1996, 30, 2800–2805. (12) Denbigh, K. The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering, Cambridge [Eng.], 4th ed.; Cambridge University Press: New York, 1981. (13) Donahue, N. M.; Robinson, A. L.; Stanier, C. O.; Pandis, S. N. Coupled partitioning, dilution, and chemical aging of semivolatile organics. Environ. Sci. Technol. 2006, 40, 2635–2643. (14) Yaws, C. L. Handbook of Vapor Pressure; Gulf Publishing Company: Houston, TX, 1994. (15) Yamasaki, H.; Kuwata, K.; Miyamoto, H. Effects of temperature on aspects of airborne polycyclic aromatic hydrocarbons. Environ. Sci. Technol. 1982, 16, 189–194. (16) Pankow, J. F. Aquatic Chemistry Concepts; CRC Press, Boca Raton, FL, 1991. (17) Kalberer, M.; Paulsen, D.; Sax, M.; Steinbacher, M.; Dommen, J.; Prevot, A. S. H.; Fisseha, R.; Weingartner, E.; Frankevich, V.; Zenobi, R.; Baltensperger, U. Identification of polymers as major components of atmospheric organic aerosols. Science 2004, 12, 1659–1662. (18) Barsanti, K. C.; Pankow, J. F. Thermodynamics of the formation of atmospheric organic particulate matter by accretion reactionssPart 3: Carboxylic and dicarboxylic acids. Atmos. Environ. 2006, 40, 6676–6686. (19) Griffin, R. J.; Nguyen, K.; Dabdub, D.; Seinfeld, J. H. A coupled hydrophobic-hydrophilic model for predicting secondary organic aerosol formation. J. Atmos. Chem. 2003, 44, 171–190. (20) Clegg, S. L.; Kleeman, M. J.; Griffin, R. J.; Seinfeld, J. H. Effects of uncertainties in the thermodynamic properties of aerosol components in an air quality modelsPart I: Treatment of inorganic electrolytes and organic compounds in the condensed phase. Atmos. Chem. Phys. 2008, 8, 1–29. (21) Koo, K.; Ansari, A. S.; Pandis, S. N. Integrated approaches to modeling the organic and inorganic atmospheric aerosol components. Atmos. Environ. 2003, 37, 4757–4768. (22) Bian, F.; Bowman, F. M. A lumping model for composition-and temperature-dependent partitioning of secondary organic aerosols. Atmos. Environ. 2005, 39, 1263–1274. (23) Bowman, F. M.; Karamalegos, A. M. Estimated effects of composition on secondary organic aerosol mass concentrations. Environ. Sci. Technol. 2002, 36, 2701–2707. (24) Seinfeld, J. H.; Erdakos, G. B.; Asher, W. E.; Pankow, J. F. Modeling the formation of seconddary organic aerosol (SOA). 2. The predicted effects of relative humidity on aerosol formation in the R-pinene, β-pinene, sabinene, ∆3-carene, and cyclohexeneozone systems. Environ. Sci. Technol. 2001, 35, 1806–1817.
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