A Semiempirical Correlation between Enthalpy of Vaporization and

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Environ. Sci. Technol. 2010, 44, 743–748

A Semiempirical Correlation between Enthalpy of Vaporization and Saturation Concentration for Organic Aerosol S C O T T A . E P S T E I N , † I L O N A R I I P I N E N , †,‡ A N D N E I L M . D O N A H U E * ,† Center for Atmospheric Particle Studies, Carnegie Mellon University, Doherty Hall, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, and Department of Physics, P.O. Box 64, FI-00014, University of Helsinki, Helsinki, Finland

Received August 14, 2009. Revised manuscript received November 13, 2009. Accepted November 24, 2009.

To model the temperature-induced partitioning of semivolatile organics in laboratory experiments or atmospheric models, one must know the appropriate heats of vaporization. Current treatments typically assume a constant value of the heat of vaporization or else use specific values from a small set of surrogate compounds. With published experimental vaporpressure data from over 800 organic compounds, we have developed a semiempirical correlation between the saturation concentration (C*, µg m-3) and the heat of vaporization (∆HVAP, kJ mol-1) for organics in the volatility basis set. Near room temperature, ∆HVAP ) -11 log 10C *300 + 129. Knowledge of the relationship between C* and ∆HVAP constrains a free parameter in thermodenuder data analysis. A thermodenuder model using our ∆HVAP values agrees well with thermal behavior observed in laboratory experiments.

Introduction Phase partitioning between the condensed and vapor phases governs organic-aerosol (OA) concentrations in the atmosphere because most compounds emitted as primary organic aerosol (POA) or formed from oxidation of atmospheric precursors as secondary organic aerosol (SOA) are semivolatile (1-3). The identity and properties of all individual OA constituents are largely unknown, and only OA bulk properties are tracked in atmospheric models. The volatility basis set (VBS) (2-4) can be used to accurately model the partitioning behavior of a multicomponent OA mixture by separating aerosol and vapor mass into logarithmically spaced saturation concentration (C*) bins. C* is the saturation concentration in the vapor phase: it depends on temperature, chemical identity, and molecular interactions. The C* of an individual compound “i” is formally defined as: Ci∗ )

CivapCOA Ciaer

(1)

where C ivap is the concentration of species “i” in the vapor phase, COA is the total OA concentration, and C aer i is the aerosol concentration of species “i”. * To whom correspondence should be addressed. E-mail: [email protected]; phone: (412)-268-4415; fax: (412)-268-7139. † Carnegie Mellon University. ‡ University of Helsinki. 10.1021/es902497z

 2010 American Chemical Society

Published on Web 12/21/2009

To implement the VBS in atmospheric models (5), experimental oxidation experiments are used to determine the OA distribution after the oxidation of a specific volatile precursor, thus constraining the C* distribution of a particular reaction (6). However, partitioning behavior in the atmosphere is difficult to predict without adequate knowledge of the volatility response to temperature changes (the heat of vaporization, ∆HVAP). Current experimental procedures obtain ∆HVAP values by fitting the change in aerosol mass with temperature. Confounding experimental factors, along with the inability to isolate the ∆HVAP from other parameters also obtained from fitting, lead to significant uncertainties. As we will demonstrate, empirical ∆HVAP—determined from the temperature transformation of bulk SOA, which is often referred to as the effective ∆HVAP—do not produce accurate partitioning within the VBS. Experiments that measure the bulk temperature response of OA find physically unrealistic effective ∆HVAP values of less than 40 kJ mol-1 (7, 8), while measurements of individual OA surrogates find ∆HVAP values in excess of 100 kJ mol-1 (9, 10). The effective ∆HVAP work well for two-component models; however, the more realistic individual ∆HVAP values should be used in the VBS (2). Incomplete knowledge of the ∆HVAP for OA is a significant source of uncertainty in models (11). Though measurements of ∆HVAP for low-volatility compounds are difficult, a significant body of data exists on the thermal response for individual SOA surrogates (10, 12-15). However, the VBS lumps many compounds into individual volatility “bins” defined by a C* at 300 K (C *300). Our objective is to identify the appropriate ∆HVAP for each volatility bin. Then we will propose a framework to implement these individual ∆HVAP values into VBS partitioning theory, specifically tailored to constrain ∆HVAP values for each C* bin in the VBS. Large, oxidized compounds have low C *300 because of their chemical structure and bonding, and they have high ∆HVAP for the same reasons; in general one expects a strong correlation between C *300 and ∆HVAP. Here we will present a correlation between these variables for direct implementation into the VBS. This correlation will constrain a free parameter in the analysis of smog-chamber experiments and will also allow us to more accurately model OA thermal behavior.

Theoretical Basis The Clausius-Clapeyron equation relates the ∆HVAP and the C* of a chemical species (16). If we make the reasonable assumption that the ∆HVAP is constant over small temperature ranges, we can integrate the traditional Clausius-Clapeyron expression (6). Use of C* units, µg m-3, instead of vapor pressures, yields an expression for the C*(T2) of a species at a new temperature, T2, with the reference temperature, Tref, and volatility C*(Tref).

[( )(

R ln

T2 Tref

C*(T2) C*(Tref)

)]

(

) ∆HVAP

1 1 Tref T2

)

(2)

∆HVAP is the difference between the enthalpy of the vapor and the liquid state, and R is the ideal gas constant. All temperatures are absolute. The (subcooled) liquid state is generally assumed to be relevant for compounds forming a solution in the complex mixtures typical of ambient OA (17). The C* at a temperature of T is frequently given with the empirical Antoine equation: C* )

Mς10A-B/ RT

(T+C)

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where M is the molecular weight, ζ is the activity coefficient (assumed to be unity for a single component), and the Antoine expression, 10(A-B/(T+C)), is in units of pressure. The Antoine parameters are the variables A, B, and C. We obtained Antoine parameters for oxygenated organics containing only carbon, hydrogen, and oxygen from Yaws (18), Cappa et al. (10), and Riipinen et al. (15). Solid-phase vapor pressures were converted to liquid phase as outlined in Prausnitz et al. (19): ln PLVAP ) ln PSVAP +

(

)

(

)

∆Cp Tt ∆Sfus Tt -1 -1 + R T R T ∆Cp Tt ln R T

()

(

1 1 300K T2

)

vs ln

[( )( T2 300K

C*(T2) C*(300K)

)]

(4)

(5)

We determined ∆HVAP for C *300 ranging from 10-4 to 1011 µg m-3 in logarithmically spaced bins. This method allows us to find reasonable ∆HVAP from both large and small temperature transformations between 270 and 330 K for representative compounds. The results did not change when a different set of randomly selected temperatures were used. We shall also discuss the effects of neglecting the (T2/300 K) term in eq 5. ∆HVAP as a Function of C* and T. In general, ∆HVAP depends on temperature; we thus developed a more rigorous estimation procedure as well. As before, we start with expressions for C* (5) and ∆HVAP (6) from the ClausiusClapeyron equation, using the unit conversion constants K1, K2, and K3: C* )

MK1ς10A-B/(T-K3+C) RT

∆HVAP )

744

9

K2RT2B (T - K3 + C)2

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T)

(C - K3)(∆HVAP - √K2∆HVAPRB)

(8)

(K2RB - ∆HVAP)

We then take the logarithm of eq 6 and substitute D ≡ log10 (Mς) + A to obtain:

where PLVAP and PSVAP are the liquid and solid vapor pressures, respectively, ∆Sfus is the change in entropy upon fusion, Tt is the triple point temperature in absolute units, and ∆Cp is the difference between the liquid and solid heat capacities. The paucity of ∆Cp data, along with the relative similarity of the last two terms, encourages us to estimate the liquid vapor pressure with the first two terms, following Cappa (10). Experimental data on the change in entropy upon fusion and the triple point temperature were obtained from the NIST Chemistry WebBook (20). Our goal is to use experimental data for atmospherically relevant compounds to estimate ∆HVAP for OA at a given initial C* and T. We shall present two treatments: The first treatment models the ∆HVAP when temperature transformations are relatively small—less than 30 K in either direction from 300 K—and assumes that the ∆HVAP is linearly correlated with log10(C*). The second, more rigorous treatment is applicable for all temperature transformations between 275 and 425 K. This treatment uses an analytically derived expression to correlate the ∆HVAP and C* and places a higher weight on chemical species which appear in OA more frequently. ∆HVAP as a Function of C*. To prevent bias in the size of the temperature transformation, we picked 1000 randomly assigned temperatures between 270 and 330 K for T2. We only selected species with Antoine parameters valid between 270 and 330 K; 222 compounds met this requirement. A table of these compounds can be found in the Supporting Information. We grouped compounds in log space according to C *300. We also rearranged eq 2 to give a linear form with ∆HVAP as the slope. R-1

where K1 ≡ 133.332 × 106 Pa µg g-1 mmHg-1, K2 ≡ 2.302, K3 ≡ 273.15 K, M [)] g mol-1, R [)] J mol-1 K-1, and T is in Kelvin. The Antoine expression 10(A-B/(T-K3+C)) is in units of mmHg. For reasons that will become evident later, we solve eq 7 explicitly for temperature:

(6) (7)

log10 C* ) D -

( )

B RT - log T - K3 + C K1

(9)

Inserting eq 8 into eq 9 yields an expression relating log10 C* directly to ∆HVAP without an explicit dependence on temperature:

((

log10 C* ) log10

K1(K2RB - ∆HVAP)

R ∆HVAP - √K2∆HVAPRB (C - K3) B +D ∆HVAP - √K2∆HVAPRB (C - K3) +1 (K2RB - ∆HVAP)

((

)

)

)

)

-

(10)

We used eq 10 to fit a set of log10(C*) values obtained from eq 6 and a set of ∆HVAP values obtained from eq 7 at a constant temperature. ∆HVAP is the independent variable, and log10(C*) is the dependent variable. We found the parameters B, C, and D with a weighted least-squares optimization algorithm for temperatures ranging from 275 to 425 K. At each temperature, we only used compounds with valid Antoine coefficients at the temperature of interest. We used 821 different compounds containing only carbon, hydrogen, and oxygen. A table of the compounds used, their functional groups, and their Antoine coefficients is provided in the Supporting Information (320 compounds did not exhibit a temperature dependence for ∆HVAP because they were previously fit to a form of the Antoine equation where the parameter C ) 273 K). The optimization minimized the total sum of the squares of the product of each compound’s residual and its respective weighting factor. We weighted compounds according to their functional groups to simulate a typical SOA mixture: 0.4 for acids and hydroperoxides, 0.15 for ketones, 0.10 for aldehydes, and 0.05 for alcohols. These factors were determined by a cursory evaluation of the typical composition of SOA. The exact weights do not significantly influence the results; however, without any weighting, the results would be biased. For example, the large number of alcohol groups in the database (not prevalent in SOA) could skew the fitting procedure. Conversely, the database only contains eight dicarboxylic acids, whereas they occur frequently in SOA. A larger weighting on the dicarboxylic acids ensures that they play a significant role in the data fitting. The prevalence of each of these functional groups in the database is presented in the Supporting Information.

Results and Discussion ∆HVAP as a Function of C *300. The results of our “simple” fitting (eq 5) are shown in Figure 1. Compounds are grouped according to their C *300 values. Only every other C* decade is shown on the plot. The slope of each of the lines corresponds to ∆HVAP (J mol-1) for a given C *300 bin. As expected, ∆HVAP is larger for less volatile species: low saturation concentrations and high heats of vaporization indicate that it is difficult for a molecule to evaporate. These parameters are strongly related to the molecular properties

C*(T) ) C*(300K)exp

FIGURE 1. Plot of 222 compounds undergoing 500 randomly selected temperature transformations from 300 K with final temperatures between 270 and 330 K. The slope of these data sets is an average ∆HVAP for each C *300 bin.

FIGURE 2. (a) Linear fit of average heats of vaporization calculated in Figure 1. The approximation comes from fitting the data to a simplified form of eq 5 by eliminating the T2/300 K term. (b) 300 K plot of ∆HVAP values vs log10 C* values. The solid curve indicates the best fit line obtained with a weighted least-squares optimization. Data are labeled according to their functional groups. The dashed black line comes from the ∆HVAP(C*) treatment. of individual compounds: for instance, highly polar molecules tend to be more tightly bound to the condensed phase than less polar molecules. There is very little overlap in ∆HVAP for different C *300 bins, confirming that individual (and large) ∆HVAP should be assigned for C *300 bins in the range typical of atmospheric condensed-phase organics. To obtain a systematic relation, we plot the average ∆HVAP as a function of log10 C* in Figure 2a. In addition, we show ∆HVAP obtained after neglecting the T2/300 K in eq 5 (the “approximate” solution). Figure 2a shows that this approximation yields results almost identical to the full solution. Linear fits are satisfactory. For the “full solution” (the complete form of eq 2): ∗ + 131 ∆HVAP ) -11 log10 C300

(12)

where ∆HVAP [)] kJ mol-1 and C* [)] µg m-3. For the “approximate” solution: ∗ ∆HVAP ) -11 log10 C300 + 129

(13)

Therefore, for 270 < T < 330 K, we recommend using a simple Arrhenius form to calculate C*(T):

(

∆HVAP 1 1 R 300K T

(

))

(14)

with ∆HVAP ) 129 kJ mol-1 for C *300 ) 1 µg m-3, with a slope of -11 kJ mol-1 per decade. In the original formulation of the VBS, Donahue et al. (2) assumed a ∆HVAP of 100 kJ mol-1 for C* ) 1 µg m-3, with a slope of 6 kJ mol-1 per decade: here we find higher but roughly comparable values. This relation is too simple to model the temperature dependence of ∆HVAP over a wider temperature range, but it is appropriate for most air-quality applications in the boundary layer. For example, a temperature transformation between 270 and 275 K should use a smaller ∆HVAP than a temperature transformation from 325 to 330 K. For more accurate expressions which depend on the temperature range of interest, refer to the “∆HVAP(C*,T)” treatment below. ∆HVAP as a Function of C* and T. We fit ∆HVAP vs log10(C*) data for temperatures between 275 and 425K using eq 10. Results for 300 K are shown in Figure 2b. As with the previous “∆HVAP(C*)” treatment, the vaporization enthalpy shows a clear decreasing trend with increasing C*. The “approximate” relationship from Figure 2a is reproduced in Figure 2b. Both forms reproduce the 300 K data, but the ∆HVAP(C*,T) treatment allows for a better fit of the data across the entire temperature range; this is because it can adapt to the increased curvature present at different temperatures. We also examined a mixture consisting of 1350 non-alkyne compounds containing only hydrogen and carbon as a surrogate for POA. The ∆HVAP(C*,T) fit produced similar results to the SOA fit. Values did not differ by more than 10 kJ mol-1, well within the uncertainty of the analysis. In addition, we sorted compounds by their oxygen to carbon (O:C) ratio. No appreciable trend was observed between O:C and the functional dependence of ∆HVAP and C *300. While it is possible that our inability to find a trend is due to the lack of highly oxidized compounds in the SOA data, this result is not surprising: we are concerned with ∆HVAP over a subcooled liquid, and variation in C *300 is driven only by changes in ∆HVAP or the change in entropy upon vaporization (∆SVAP); for these amorphous systems, large differences in ∆SVAP are unlikely, so a tight relationship with ∆HVAP is reasonable. At this point, it appears reasonable to assign values of ∆HVAP within the VBS based on C *300 alone. The fitting results at temperatures ranging from 275 to 425 K for the SOA surrogate compounds with eq 10 are presented in Figure 3. This figure relates C*(T), values at a given temperature (shown with the colored curves), to the ∆HVAP at that temperature. According to the plot, a SOA mixture at 300 K would have a ∆HVAP corresponding to the y coordinate of each C* isopleth at 300 K, with the vertical cut being the curve shown in Figure 2b. For example, ∆HVAP(300) ) 107 kJ mol-1 for C*(300) ) 100 µg m-3. If we warm the mixture to 320 K, compounds with higher ∆HVAP will move to a given C*; for example, ∆HVAP(320) ) 123 kJ mol-1 for C*(320) ) 100 µg m-3. The black curve tracks the C*(T) ) 100 µg m-3 isopleth. The 95% confidence intervals (shown for C*(T) ) 100 µg m-3) grow in the extrapolation region (shaded gray). The uncertainty is significant above a ∆HVAP of 200 kJ mol-1 and therefore does not permit for an accurate prediction in that range. In Figure 3 we also show the ∆HVAP(T) of pure malonic acid (green dots). The C*(280) of malonic acid is 1 µg m-3 with ∆HVAP of 117 kJ mol-1 (indicated by the leftmost diamond). The C*(390) of malonic acid is 106 µg m-3 with a ∆HVAP of 104 kJ mol-1 (indicated by the rightmost diamond). The literature values of 126 kJ mol-1 and 101 kJ mol-1 at 280 and 390 K, respectively, from Riipinen et al. (15) compare well with our predictions. This treatment requires an iterative procedure when transforming SOA from T1 to T2 but provides more accuracy than the explicit ∆HVAP(C*) treatment exhibited in Figure 2a. VOL. 44, NO. 2, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Predicted C*(T) vs T and ∆HVAP relationship. The black curve indicates the C*(T) ) 100 µg m-3 curve. Black dashed lines indicate the 95% confidence interval for the C* ) 100 µg m-3 curve. The gray shaded area is the region of extrapolation wherein there are no experimental data. C* isopleths indicate the ∆HVAP for each C*(T) at that temperature. The green dots indicate how a single component, malonic acid, appears in this space between 280 K and 390 K. The blue spade shows the location of a C34 alkane (tetratriacontane). Blue dashed lines indicate the lower limits of the dissociation energy for typical bonds found in OA. This analysis is not performed at temperatures below 275 K due to the lack of low-volatility Antoine coefficients. Therefore, a linear extrapolation is used at temperatures below 275 K. A lookup table of ∆HVAP values as a function of log10(C*) and temperature from 200 to 425 K is presented in the Supporting Information. In addition, fitting parameters for eq 10 from 275 to 425 K are also included. We have chosen the form of Figure 3 in order to discuss thermodenuders (TD), which are widely used for determining volatilities of atmospheric aerosol (21-23). Since the basic operating principle of a thermodenuder is the measurement of aerosol mass before and after heating, the saturation concentrations and vaporization enthalpies of the aerosol constituents affect the output of a TD experiment significantly; to determine C *300 from TD data, one must know ∆HVAP. A simple phenomenology is that thermodenuders have a cutoff value of C* (dependent on residence time and other instrument parameters) above which material will evaporate. For illustration, we use C*(T) ) 100 µg m-3 (shown with a heavy black curve in Figure 3). For example, at 330 K (57 °C) the C *300 ) 1 µg m-3 bin will have risen to C*(330) ) 100 µg m-3. As this is the least volatile bin with significant material from the R-pinene + ozone reaction (7), it makes sense that R-pinene SOA evaporates completely near this temperature (21) (see below). Figure 3 also shows four important limits related to bond dissociation. The lower limit of published bond dissociation enthalpies for C-C (24), C-O (24), O-O (24, 25), and C-H (24) bonds are shown with horizontal dash-dot lines. If the ∆HVAP of a compound exceeds the dissociation enthalpy for the weakest bond in the compound, thermal decomposition is likely to precede evaporation. This can become a concern for thermodenuders. Figure 3 indicates that decomposition is unlikely to be a problem for POA, where strong C-C bonds dominate (e.g., Grieshop et al.) (23); however, it suggests that much greater care should be taken when considering oxygenated compounds, where weaker bonds may lead to pyrolysis. Mass loss in a TD with pyrolysis will not be a simple measure of volatility, and the hotter the TD, the greater the risk. Real-World Examples. Many models employ a low, constant “effective” ∆HVAP of 30 kJ mol-1 to reproduce the relatively modest observed temperature dependence of SOA. We can compare this approach to our experimentally 746

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constrained values with several partitioning basis set diagrams (2, 4). For this analysis, we use a volatility distribution for SOA from R-pinene ozonolysis, with 100 µg m-3 of SOA at 300 K, based on parameters from Donahue et al. (3) (Figure 4). Figure 4a shows the phase partitioning at 300 K, with condensed-phase material shaded in green. A constant ∆HVAP of 30 kJ mol-1 (Figure 4b) yields significantly more SOA than our ∆HVAP(C*,T) treatment (Figure 4c) when the SOA is heated from 300 to 320 K (heating shifts the bins to the right, toward higher volatility). The enhanced volatility of the low C* bins is also evident. Our bin-specific ∆HVAP values lead to a much stronger temperature dependence than the constant ∆HVAP of 30 kJ mol-1; however, the overall change in SOA mass is not large below about 315 K. The overall change in SOA with temperature for these two cases is shown in Figure 5; the VAP , is the slope of each “effective” heat of vaporization, ∆HEFF VAP curve. Using realistic ∆H for each bin (the red solid curve), the effective ∆HVAP near 300 K is 33 kJ mol-1, as shown. This value is in reasonable agreement with bulk ∆HVAP EFF measurements of SOA. However, using an effective ∆HVAP of 30 kJ mol-1 on the basis-set distribution (the blue dashed curve) puts the SOA in double jeopardy and grossly underestimates the temperature dependence. The enthalpies are critical for thermodenuders. The effect of using a constant vaporization enthalpy of 30 kJ mol-1 versus the ∆HVAP(C*,T) treatment is demonstrated for a theoretical TD experiment in Figure 6, extending well beyond the phenomenology presented above. The theoretical evaporation in the TD was calculated with a mass-transfer model described by Riipinen et al. (3). We model the fraction of aerosol mass remaining (MFR) after warming to temperature TTD for 30 s for a set of temperatures from 300 to 400 K. The initial aerosol mass and volatility distribution are the same as in Figure 4, with an initial temperature 300 K. The other properties of the aerosol are the same as used by Riipinen et al. (26). We treat a range of mass accommodation coefficients between 1.0 and 0.01 for all species, since no quantitative measurements exist of the mass accommodation coefficients for R-pinene SOA constituents. The constant value of 30 kJ mol-1 results in considerably smaller mass loss than the more realistic ∆HVAP values presented above. Also, the temperature dependence of the

FIGURE 6. Theoretical mass output of a thermodenuder experiment for r-pinene SOA, assuming the same volatility distribution as in Figure 4 and a constant vaporization enthalpy of 30 kJ mol-1 or ∆HVAP(C*,T). The shaded area bounds the mass fraction remaining, which was calculated with an accommodation coefficient of 0.01 and an equilibrium assumption. The residence time in the TD was assumed to be 30 s, and the aerosol is monodisperse with a diameter of 200 nm. The cyan experimental data is from Lee et al. (27). The initial mass loadings before heating for the 50% RH/low NOx, the low RH/low NOx, and the low RH/high NOx were 107, 74, and 45 µg m-3, respectively.

FIGURE 4. (a) Typical distribution of SOA mass in partitioning basis set treatment at 300K. Shaded bars indicate the condensed mass. White bars indicate the mass of vapors. The arrow points to the log10(C*) in which the mass is 50/50 partitioned between the condensed and vapor phase. (b) Original SOA distribution after undergoing a temperature transformation to 320 K with a ∆HVAP of 30 kJ mol-1. (c) Original SOA distribution transformed to 320 K with a ∆HVAP as a function of C* and T.

FIGURE 5. Arrhenius plot of organic-aerosol concentration as a function of temperature with a constant ∆HVAP and a ∆HVAP dependent on temperature and C* derived from this work. The x axis is (1/T). An effective heat of vaporization can be calculated from the slope of these curves. MFR is different in the two cases. The shape of the MFR(TTD) thermal profile obtained with ∆HVAP(C*,T) closely resembles data from Lee et al. (27) for R-pinene SOA, as shown in Figure 6; however, the thermal profile for a constant ∆HVAP ) 30 kJ mol-1 is markedly too shallow. Lee et al. (27) corrected for this difference by changing the effective mass accommodation coefficient during the course of evaporation. It should be noted that the direct comparison to the data of Lee et al.

(27) is not straightforward: in each individual TD experiment, different gas-phase compositions and total aerosol concentrations were used; the model runs, however, were conducted using the volatility distribution from Donahue et al. (3) and a total aerosol loading of 100 µg m-3, which are consistent with the results shown in Figure 4. These differences should, however, mostly affect the overall magnitude of the predicted MFR and not its temperature dependence. During our determination of ∆HVAP(C*) and ∆HVAP(C*,T), we assumed ideal mixing behavior. Uncertainty is introduced when we assume that activity coefficients are identically one. On the basis of the current state of the science, we are unable to accurately constrain activity coefficients for complex SOA mixtures. However, the volatility distributions used in the calculations have been derived while making the same assumption (see Donahue et al. (3)), thus being consistent with the approach taken in this work. In addition, assuming that activity coefficients are unity is not an unreasonable assumption to make in mixtures of similar constituents (4, 10, 28). Also, the laboratory SOA experiments coupled with the thermodenuder model that we used to assert the applicability of our correlation have been fitted to laboratory data on SOA yields, which may already capture the nonideality of the mixture. Recommendations. The correlation between ∆HVAP and C* presented in this paper is effective when constraining volatility partitioning calculations. We recommend the simpler ∆HVAP(C*) treatment when making small temperature changes (less than 30 K) about 300 K. For all other temperature transformations, we recommend using the ∆HVAP(C*,T) treatment. These correlations produce more realistic partitioning behavior over the previous standard of using a constant ∆HVAP. With knowledge of the typical O-O bond dissociation energies, we recommend caution (and more research) in the interpretation of high-temperature thermodenuder measurements of SOA.

Acknowledgments This research was supported by the Electric Power Research Institute grant EPP25369C12290 and the Dreyfus Foundation. VOL. 44, NO. 2, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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Supporting Information Available (i) Table of compounds and their Antoine coefficients used for ∆HVAP(C*,T). (ii) Compounds used for ∆HVAP(C*,T). (iii) Functional groups for compounds used in ∆HVAP(C*,T). (iv) Lookup table for ∆HVAP(C*,T) ranging from 200 K to 425 K and 10-4 µg m-3 to 10-8 µg m-3. (v) Fitting parameters for ∆HVAP(C*,T) ranging from 275 K to 425 K. (vi) Prevalence of functional groups in ∆HVAP(C*,T) SOA fitting. This material is available free of charge via the Internet at http:// pubs.acs.org.

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