Environ. Sci. Technol. 2006, 40, 3558-3564
Regressing Gas/Particle Partitioning Data for Polycyclic Aromatic Hydrocarbons YUSHAN SU,† YING DUAN LEI,† F R A N K W A N I A , * ,† M A H I B A S H O E I B , ‡ A N D TOM HARNER‡ Department of Chemical Engineering and Applied Chemistry and Department of Physical and Environmental Sciences, University of Toronto at Scarborough, 1265 Military Trail, Toronto, Ontario, Canada M1C 1A4 and Science and Technology Branch, Environment Canada, 4905 Dufferin Street, Toronto, Ontario, Canada M3H 5T4
Polycyclic aromatic hydrocarbons (PAHs) were measured in the rural atmosphere of Southern Ontario, Canada from October 2001 to November 2002. Sixty seven pairs of gaseous and particle-bound concentrations of PAHs were determined concurrently in a forest and a clearing. The gas/particle partitioning behavior of the PAHs was investigated by fitting the original Junge-Pankow equation to the fraction in the particle phase φ for each set of measured data, either allowing the slope m to deviate from -1 (two-parameter model) or not (one-parameter model). This fitting procedure was judged more robust than linear logarithmic regressions involving the gas/particle partition coefficient, because the latter is sensitive to the applied blank correction, tends to ignore a significant amount of analytical information, and gives undue weight to more uncertain data points. The experimental data fit was good for both nonlinear models, and discrepancies between experimental data and models and between models are mostly related to sampling/experimental artifacts. In particular, samples taken close to the freezing point appear to suffer from blow-off artifacts. Applying slopes m different from -1 appears only justified if it can be assured that a second parameter indeed provides a better fit and that this better fit is not due to experimental, analytical, or statistical artifacts. The magnitude of the differences in the model fitting parameters between sampling events is consistent with the reported variability in the nature and concentration of atmospheric particles. Statistical tests on the regression results indicate that the gas/particle partitioning was not significantly different between the forest and the clearing.
Polycyclic aromatic hydrocarbons (PAHs) are a class of potentially carcinogenic and ubiquitous global pollutants that have been detected in numerous environmental media and geographic regions (1-4). Although PAHs can be emitted to the environment as a result of natural combustion processes (e.g., forest fires and volcanoes), human activities
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Theory The G/P partitioning behavior of PAHs is commonly characterized with one of two parameters: the fraction of the total amount of a PAH in air that is sorbed to particles φ, or the particle/air partition coefficient KP′. The dimensionless φ is calculated from the measured gaseous (CG in ng‚m-3 of air) and particle-bound (CP in ng‚m-3 of air) concentrations using the following equation:
φ ) CP/(CG + CP)
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 40, NO. 11, 2006
(1)
whereas the dimensionless G/P partition coefficient KP′ is simply derived from this equation:
KP′ ) CP/CG
Introduction
* Corresponding author phone: (416)287-7225;
[email protected]. † University of Toronto at Scarborough. ‡ Environment Canada.
are believed to dominate global PAH emissions, because high atmospheric concentrations of PAHs are usually observed in urban and industrial areas where vehicle traffic, aluminum smelting, residential heating, and other activities emit PAHs into the atmosphere (4, 5). An understanding of the distribution of PAHs between the atmospheric gas and particle phase is a key component in improving our understanding of their environmental fate and effects, especially for PAHs of intermediate volatility, because they are inhaled (6), degraded (5), deposited (7), and scavenged (8) differently depending on whether they exist in the gas phase or bound to particles. This distribution is controlled by the interplay of various factors, including ambient temperature, the concentration and chemical composition of the atmospheric particles, and compound volatility (7, 9-12). In the past two decades, the gas/particle (G/P) partitioning of PAHs has been extensively examined and mechanisms of adsorption, absorption, or a combination of both are usually employed to explain the experimental findings (9, 11-15). As part of a larger project aimed at quantifying the uptake of PAHs in a deciduous forest, high volume air samples were taken between 2001 and 2002 in a rural region of southern Ontario, Canada. In total, gaseous and particle-bound PAHs were separately analyzed in 67 air samples, providing a large and temporally resolved data set suitable for investigating PAH G/P partitioning. Here it served, in particular, to evaluate the relative merit of various approaches relating the G/P behavior of PAHs to their volatility. Because air sampling was conducted concurrently in an open clearing and under a forest canopy, it was further hoped that a comparison of the G/P partition behavior at these two sites may yield insight into similarities and differences caused by different types of surface cover. Differences in G/P partitioning would be expected if differences in the concentration or composition of particles exist between forest and clearing, or if rapid uptake of gaseous compounds in the forest canopy results in locally constrained increases in the particle-bound fractions.
(2)
The two parameters are related through the following:
φ ) KP′/(1 + KP′)
(3)
When the total suspended particle concentration (TSP in µg‚m-3) is known, it is further possible to calculate a G/P partition coefficient KP in unit of m3 of air‚µg-1 of particles:
KP ) KP′/TSP ) (CP/TSP)/CG 10.1021/es052496w CCC: $33.50
(4)
2006 American Chemical Society Published on Web 04/22/2006
where (CP/TSP) is the particle-bound concentration in units of ng‚µg-1 of particles. The extent of particle sorption is related to a chemical’s volatility, the latter often expressed with the help of the vapor pressure of the sub-cooled liquid PL (Pa) or the octanol-air partition coefficient KOA. One of the earliest approaches to describing the G/P partitioning equilibrium of PAHs, known as the Junge-Pankow model, relates φ to PL using the following:
φ ) A/(PL + A)
(5)
The parameter A in this equation is sometimes interpreted as the product of two terms c and θ. θ is the surface area of particles in a unit volume of air (cm2‚cm-3) and c (Pa‚cm) is a substance-specific factor depending on ambient temperature, compound, sorption sites, and the heats of desorption from surface and vaporization from the liquid compound (7, 10, 14). This interpretation of A was based on the assumption that partitioning of the PAH to the particles is a surface adsorption process. This is very often not the case (11, 13, 14, 16-18), and so we prefer here to use A instead of c‚θ. KP is also often related to PL using a regression of the following form:
log(KP/(m3‚µg-1)) ) m‚log(PL/Pa) + b
(6)
where m and b are empirical constants (9-10, 19-21). The mechanistic interpretation of b depends on whether the interaction of PAHs with the particles is assumed to be adsorptive or absorptive. For adsorption, b is determined by particle specific surface area and the heat of desorption of the PAH, whereas for absorption, b is related to the organic matter content of the particles fOM (10-11). By substituting eq 4 into eq 6, we obtain the following:
log KP′ ) m‚log(PL/Pa) + b′
(7)
suggesting that we can also regress the logarithm of the dimensionless partition coefficient KP′ against log(PL/Pa), in which case the total suspended particle concentration (TSP) is subsumed in the intercept b′ (b′ ) b + log TSP). To better understand the difference between eqs 5 and 7, we can substitute eq 7 into eq 3, which yields the following:
φ ) 10m‚log(PL/Pa)+b′/(1 + 10m‚log(PL/Pa)+b′)
(8)
For m ) -1, eq 8 can be simplified:
φ ) 10b′/(PL + 10b′)
(9)
This is simply another version of eq 5. In other words, the Junge-Pankow eq 5 is a special case of eq 7, where the slope m is assumed to be -1:
log KP′ ) -log(PL/Pa) + b′
(10)
It has been argued that in the absence of sampling artifacts and nonequilibrium conditions between gas and particle phase, m should indeed be -1 (11-12). In controlled field experiments (i.e., conducted under constant temperature and relative humidity conditions) at three different locations, regression results indicated that m is close to -1 for both PAHs (-1.09) and polychlorinated dibenzodioxin and dibenzofuran (-1.05) (22). However, it has also been shown that m can theoretically deviate from -1 even under equilibrium conditions and the absence of sampling artifacts (17, 23). Equivalent equations based on KOA have been proposed and used (13, 14, 16). Here we use PL instead of KOA-based regressions because the two approaches are essentially
TABLE 1. Average Concentrations and Their Range (in pg‚m-3) for Different PAHsa fluorene phenanthrene fluoranthene pyrene benz[a]anthracene chrysene benzo[b]fluoranthene benzo[k]fluoranthene benzo[a]pyrene indeno[123,cd]pyrene dibenz[ah]anthracene benzo[ghi]perylene Σ12PAH a
gaseous
particle-bound
2600 (230-23 000) 5200 (470-46 000) 1300 (BDL - 9000) 1800 (89-13 000) 55 (BDL - 440) 150 (BDL - 840) 32 (BDL - 200) 11 (BDL - 74) 5.2 (BDL - 100) 4.9 (BDL - 58) 0.21 (BDL - 7.9) 9.3 (BDL - 86) 11 000 (1300-70 000)
3.6 (BDL - 25) 32 (BDL - 300) 63 (2.6-590) 92 (3.3-650) 80 (0.086-1100) 120 (0.050-830) 470 (1.2-3000) 140 (0.31-700) 200 (BDL - 2400) 310 (1.7-2700) 41 (BDL - 480) 300 (2.1-2400) 1800 (11-15 000)
BDL indicates below method detection limit.
equivalent (24), and measured temperature-dependent KOA values are only available for a small number of PAHs. The different types of regression equations discussed above are summarized in Table S1 (Supporting Information). Note that both φ and log KP′ can be normalized by TSP and/or fOM provided this information is available for the sampling events. The respective equations are included in Table S1 for completeness.
Experimental Section Air Sampling. High volume air samplers were used to simultaneously sample gaseous and particle-bound PAHs in air at a deciduous forest and at a clearing located within 3 km of each other close to Borden, Ontario, which is approximately 75 km N of Toronto and 25 km S of Georgian Bay. Air was sampled at both sites every 12 days from October 2001 to December 2002 during 35 sampling events for a total of 67 sets of gaseous and particle-bound PAH data. A map (Figure S1) and dates for all 35 sampling events (Table S2) are included in the Supporting Information. A volume of air (750-900 m3) was pumped through two glass fiber filters (GFFs) and two polyurethane foam (PUF) plugs in series over 24 h. The particle-sorbed PAHs were trapped on the first of the two GFFs and the gaseous PAHs were absorbed by the PUFs. Sample Extraction, Cleanup, and Analysis. GFFs were Soxhlet-extracted overnight by dichloromethane, whereas petroleum ether was used for the PUFs. Extracts were reduced in volume and cleaned and fractionated on silicic acid/ alumina columns. Mirex was added as an internal standard. Extracts were analyzed for 15 PAHs (naphthalene, acenaphthylene, acenaphthene, and the ones listed in Table 1) by gas chromatography-mass spectrometry using electron impact ionization and selected ion monitoring mode. Pulsed splitless injection onto a DB-5MS column was employed. Details on the procedure used for sampling, cleanup, and instrumental analysis, including GC temperature program and target and qualifier ions, are given in the Supporting Information. Quality Assurance/Quality Control. Analytes were identified by retention time matching with those of individual standards running under identical instrumental conditions. Only target/qualifier ion ratios within (20% of those of the standards and peaks with signal-to-noise ratio above 3 were quantified. Field blanks were collected during each sampling event and were subject to the same extraction and cleanup procedures as the samples. Method detection limits (MDLs, listed in Table S3, Supporting Information) were defined as mean blank plus 3 time standard deviation. Laboratory procedure blanks were also collected periodically, and analytes in all of them were either nondetectable or systematically lower than in the field blanks. Recoveries (listed in Table S3), tested by spiking PAHs onto pre-cleaned PUFs, VOL. 40, NO. 11, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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ranged from 79% to 92% for PAHs. All reported data were blank corrected provided they exceeded the MDLs. However, no data were adjusted for recovery. More detail on QA/QC procedures can be found in the Supporting Information. One-third of the back PUF and GFF samples, collected during different seasons, were extracted separately in order to test for chemical break-through. Apparent break-through for three low molecular weight PAHs (i.e., naphthalene, acenaphthylene, and acenaphthene) occurred since concentration of these low molecular weight PAHs in the back PUF could be as high as in the front PUF. Fluorene and phenanthrene also exhibited some, but relatively low, breakthrough. The highest fraction of the totally sampled amount that was found in the back PUF was 30% for fluorene and 15% for phenanthrene. None of analytes was detected in the back GFF, indicating the absence of a filter adsorption artifact. Data Analysis. Values of φ and log KP′ were calculated from measured gaseous and particle-bound concentrations using eqs 1 and 2, respectively. In separate fitting procedures using Origin 6.1, all 67 measured gas and particle concentration data sets were fitted individually to the nonlinear oneparameter eq 5, the nonlinear two-parameter eq 8, the linear one-parameter eq 10, and the linear two-parameter eq 7. Please note that by not normalizing the data to θ or fOM, we avoid making any assumptions as to the nature of the sorption process. The sub-cooled liquid vapor pressure for the PAHs at the average temperature of the sampling period were calculated using PL and ∆vapH data from ref. 25. Temperature was recorded continuously at half hour intervals by a meteorological station located at the forest site. The 24-hr average temperature, used in the data analysis, varied over 30 K during the year of sampling (Table S2).
Results Table 1 lists the average atmospheric concentrations of individual PAHs and total PAHs (Σ12PAH) during the entire sampling period. Fluorene, phenanthrene, fluoranthene, and pyrene are major atmospheric PAHs at the sampling site. Mean total concentration of gaseous and particle-bound Σ12PAHs were 11 000 pg‚m-3 and 1800 pg‚m-3 during the yearlong sampling period. The experimentally determined φ and log KP′-values for all 67 data sets are listed in Tables S4 and S5 of the Supporting Information. The results of the nonlinear φ-based regressions (A and R2 for eq 5, m, b′, and R2 for eq 8) for all 67 data sets are summarized in Table S6 (Supporting Information). The equivalent information for the linear log KP′-based regressions (eqs 7 and 10) can be found in Table S7 (Supporting Information). The measured data points and regression lines are plotted for each of the 35 sampling events in Figures S3 and S4.
Discussion Comparison of Nonlinear φ-Based Models and Linear log KP′-Based Models. Equations 5 and 10, and also eqs 7 and 8, are mathematically equivalent (i.e., one can deduce one from the other) and they assume exactly the same dependence of G/P partitioning on PL. However, despite mathematical equivalence, the fitting procedures are not identical and give different regression results (Tables S6 and S7). A detailed comparison of the results obtained by nonlinear (eqs 8 and 5) and linear regressions (eqs 7 and 10) on the same blank-corrected data set is facilitated by the plots in Figure 1. Panels A to F relate the regression parameters correlation coefficient R2, number of data points n, slope m and its relative standard deviation (RSD), and intercept b′ and its RSD that are obtained by using the two parameter eqs 8 vs 7. Panels G-I compare the R2, log A (or b′) and its RSD obtained by using the two one-parameter eqs 5 vs 10. 3560
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Similarity between two types of models can be evaluated by how close data points are to the 1:1 line in these panels. Correlation coefficients R2 obtained from the nonlinear two-parameter eq 8 (always higher than 0.69 and above 0.95, 53 out of 67 times) are significantly higher (p < 0.001) than those from the linear two-parameter eq 7 (mostly above 0.85, but can also be as low as 0.51) (Figure 1A). The primary reason for this is the larger number of data points available for the nonlinear regression (Figure 1B), since φ is defined when either CG or CP is 0, whereas log KP′ is not. The slope m obtained with the φ-based model often adopts lower values than in the log KP′-based model (Figure 1C), indicating that it varies more widely to better fit the measurements. Remarkably, the geometric mean slope m obtained using nonlinear eq 8 is identical to the theoretical value of -1.00, whereas the geometric mean of m is -0.68 when using linear eq 7. As will be discussed below, some very low values of m are likely an artifact. Since m and b′ are inter-correlated (see below), it is not surprising that the fitting parameter b′ of the nonlinear model also adopts lower values (Figure 1D). The RSDs of the fitting parameters m and b′ are similar between the two models (Figure 1E and 1F). Regression results for the two one-parameter models (eqs 5 and 10) are compared in Figure 1G-I. R2 values obtained with the φ-based eq 5 are always above 0.62 and above 0.95 in 44 out of 67 regressions. They are consistently much higher than those for the log KP′-based eq 10 (Figure 1G). Some of the latter R2 values are actually negative (e.g., sampling event 13 at the forest site), which indicates that fixing the slope m to -1 is inappropriate. Figure 1H shows that there is no significant difference (p > 0.1 in a paired t-test) between the intercepts log A or b′ obtained with regression eqs 5 and 10. However, Figure 1I indicates consistently a much higher RSD of b′ in the log KP′-based equation than the RSD of the log A from the φ-based regression. In summary, it is by no means unimportant whether linear logarithmic eqs 7 and 10 involving KP′ or eqs 8 and 5 involving φ are used for fitting field data. Specifically, we argue here that the use of φ is preferable over the use of log KP′. The first reason is that φ can still be calculated when either CG or CP is 0, whereas log KP′ cannot be defined for compounds that are either completely in the gas phase or completely bound to particles. Since CG and CP are typically set to 0 whenever concentrations are below the detection limit, this is actually quite common and means that regressions based on log KP′ generally ignore a lot of useful analytical information. The second reason is that the regressions involving KP′ give considerable weight to data points involving low concentrations above the detection limit in either gas or particle phase. This is problematic as these small concentration values tend to be more uncertain (see next paragraph), and so the KP′ values derived from them are also less reliable. On the other hand, KP′ regressions ignore data points involving φ values of 0 and 1, even though they very often have a low uncertainty. One may argue that concentrations above the MDL that fulfill all QA/QC criteria should not have a higher uncertainty than concentrations well above that limit. However, higher uncertainty of concentrations close to the detection limit could simply arise from the procedures used for blank correction (i.e., whether measured concentrations are blank corrected or not), or from the formula used for calculating blank concentrations. To illustrate that a nonlinear regression involving φ is more robust in this respect than a linear log KP′ based regression, we fitted the field data to eqs 8 and 7 twice, once with blank correction (case A) and once without blank correction (case B). Figure S2 in the Supporting Information compares the regression results for cases A and B for both the nonlinear (eq 8) and the linear (eq 7) twoparameter model. When nonlinear eq 8 is used, case A and B yield virtually identical coefficients of correlation R2, slopes
FIGURE 1. Comparison of regression results by using the nonlinear (eq 8) and linear (eq 7) two-parameter model (A-F), and using the nonlinear (eq 5) and linear (eq 10) one-parameter model (G-I). Triangles (4) and squares (0) correspond to data measured at clearing and forest, respectively. The X-axis represents fitting parameters obtained from regressions of log KP′ as a function of log PL (i.e., log KP′) f (logPL), eqs 8 and 7), whereas Y-axis indicates those generated by regressions of O as a function of log PL (i.e., O ) f (PL), eqs 5, 9, and 10). m, and intercepts b′ (i.e., nearly all data points fall on the 1:1 line in Figures S2A-II-S2E-II), i.e., blank correction does not affect the regression results significantly (p > 0.1). However, when the linear log KP′-based eq 7 is employed, larger discrepancies of regression parameters for case A and B are observed (Figures. S2A-II-S2E-II) and m and b′ are significantly higher (p < 0.0001) when using data without blank correction. This proves that typical uncertainties in low concentrations can significantly influence G/P regression results when the linear log KP′-based equation are used, but such uncertainties have no such effect on nonlinear regressions based on φ. Concentrations without blank correction were only used for illustration here. All other regressions are based on blank-corrected data. In brief, it is believed that nonlinear regressions based on φ perform better than linear regressions based on log KP′. The latter usually rely on fewer data points, lead to lower correlation coefficients R2 and sometimes more uncertain regression parameter, and also appear to be quite sensitive to the blank correction procedure. We believe that this issue has not been sufficiently appreciated in previous analyses of G/P partitioning data sets, which tend to prefer log KP′-based linear approaches. In the following, we only refer to the results of φ-based nonlinear regressions.
FIGURE 2. Examples of observed gas/particle partitioning behavior of the PAHs during sampling events no.1 (A) and no.13 (B) (triangle for clearing, square for forest). The regression results of the oneparameter model (eq 5, solid lines) and two-parameter model (eq 8, dotted lines) are also included. Unusually Large and Small Slopes m. Figure 2 shows two examples of φ-log PL plots which include the experimental data points from forest and clearing, and the regression lines obtained from the two φ-based eqs 5 and 8. The steepness of the S-curve described by eq 5 is always the same, and the value of A determines where this curve falls along the log PL axis. The steepness of the S-curve described by eq 8 changes with the value of m, whereas b′ again shifts the curve along VOL. 40, NO. 11, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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the log PL axis. If m is above -1, then the S-curve is shallower than with eq 5, whereas an m below -1 indicates a steeper S-curve. Figure 2A gives an example of a sampling event (no. 1), when the G/P partitioning behavior was not only very similar in clearing and forest, but when the two model equations also resulted in very similar fitting curves. This is the case even though m in eq 8 is -0.77 ( 0.08 and thus significantly above -1. Figure 2B, on the other hand, provides an example of an event (no. 13) where the sample from clearing and forest show different G/P partitioning, and where the fitting curves for the two φ-based nonlinear models deviate considerably from each other. Specifically, several PAHs of very low volatility were found to a surprisingly large extent in the gas phase in the forest sample, requiring a high slope m of -0.45 for an optimized fit. In the clearing, on the other hand, benz[a]anthracene was strongly particle-sorbed despite its relatively high vapor pressure, which yielded a low slope m of -1.31 in the two-parameter regression. From these and many other examples in Figure S3, we can deduce the following: (1) Unexpectedly high gas-phase fractions for low volatility PAHs, such as for the forest sample during event 13 (Figure 1B) occurred several times (i.e., sample no. 10, 11, and 14 at the clearing; sample no. 13, 16, 23, and 35 in the forest, refer to Figure S3). In these cases, the slope m is generally quite high (above -0.60). Such behavior would be consistent with blow-off artifacts, i.e., relatively low-volatile PAHs being desorbed from the particles while being on the GFFs. Interestingly, this behavior mostly occurred when the daily average temperature and the last half-hour average temperature were on either side of the freezing point (see Table S2), i.e., when temperatures changed on the sampling day and were close to 0 °C. One possible explanation of such observations is that the GFF collects frozen ice particles, which releases adsorbed PAHs to the gas phase upon melting. PAHs have a very high affinity for the ice surface (26). Incidentally, high m-values are not caused by the opposite effect, i.e., volatile PAHs did not occur in unreasonably high fractions in the atmospheric particle phase. (2) Unusually low m values of less than -2 occurred nine times (i.e., sample no. 24, 28, 29, and 31 at clearing; sample no. 17, 25, 28, 29, and 31 at forest, Figure S3). A closer inspection of the φ vs log PL plots for these events reveals that this occurs when PAHs with relatively similar vapor pressure show widely divergent G/P distributions, necessitating a very steep curve for a good fit. For example, during sampling event 28, the two benzoflouranthenes with a log PL of around -5.4 were measured predominantly in the gas phase, whereas benzo[a]pyrene with a marginally lower log PL of -5.6 was 100% particle-bound. This seems unreasonable and suggests measurement artifacts, e.g., an error in the measurement of the gas-phase component of benzo[a]pyrene. (Incidentally, a log KP′-based regression is not affected by this artifact, because the data point for benzo[a]pyrene is ignored.) (3) Even though the parameter m is often quite different from -1 (Table S6), a close inspection of the φ vs log PL plots (Figure S3) shows that the actual fitting curve is only very marginally different from the one obtained with the single parameter eq 5. Within the measurement uncertainty, the fit of eq 5 was, in most cases, judged comparable to that of eq 8. Considering the often quite substantial uncertainty in fieldderived φ-values, we believe that relatively minor deviations of m from -1 (e.g., -0.60 > m > -2) should, therefore, not be over-interpreted. In summary, we believe larger deviations (m > -0.60 and m < -2) to be most likely the result of measurement artifacts (27-28), because they unreasonably suggest either significant gas-phase concentrations of very involatile substances or large differences in the G/P behavior of PAHs of similar 3562
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FIGURE 3. Correlation between the fitting parameters b′ and m (n ) 51). 16 excluded data points are indicated by open symbols (4), some of which may not appear on the plot, because they lie beyond the scales displayed here. volatility. The plots of φ vs log PL allow passing judgment as to whether such an artifact occurred during a particular sampling event. Figure 2A is an example of good fits between model and experimental data points (i.e., sampling event no. 1). In contrast, Figure 2B serves as an example that a good fit could not be achieved between experimental data and models (i.e., sampling event no. 13). After evaluating all sampling events, 16 experimental data points with m > -0.60 or m < -2 were excluded from further analysis (i.e., sampling event no. 10, 11, 14, 24, 28, 29, and 31 at the clearing; 13, 16, 17, 23, 25, 28, 29, 31, and 35 at the forest). 51 sets of data were retained. Comparison of Nonlinear Two- and One-Parameter Model. When examining these selected data sets in Figure S3, the difference between the two S-shaped curves in each plot is very small. This implies that the nonlinear oneparameter eq 5 with slope m -1 describes the field data as well as the nonlinear two-parameter eq 8, if sampling and measurement artifacts are accounted for. Recall also that the R2 for the regressions involving eq 5 were only marginally smaller than those for eq 8 (Table S6 and Figure 1 A and G). It has been shown previously that b and m are correlated (20, 29). Since b′ equals b + log TSP, we should also expect a relationship between b′ and m. Figure 3 plots b′ against m for the 51 selected experimental data points. The strong regression between b′ and m (R2 ) 0.78, p-value < 0.001) highlights that these two fitting parameters are not independent from each other, lending further support to the suggestion that the one-parameter model should be comparable to the two-parameter model in interpreting the G/P partitioning of PAHs. A simpler model is inherently preferable over a more complex model, if it performs comparably (30). Although we recognize that two parameters may provide additional theoretical insight into the partitioning mechanisms (1011, 20-21), we suggest that a two-parameter approach (eq 8) should only be used for describing G/P partitioning data, i.e., the slope m should only be allowed to deviate from -1 if it can be assured that it indeed provides a better fit and that this better fit is not due to experimental, analytical, or statistical artifacts. With regard to the latter, we note that a one-parameter model based on log KP′ (eq 10) would have been dismissed right away on account of the poor R2 and highly uncertain intercept b′ (Figure 1G and I). In other words, whereas the one- (eq 5) and two-parameter (eq 8) φ-based regressions are comparable, the two-parameter log KP′ (eq 7) appears to perform much better than the one-parameter log KP′ (eq 10). The linear log KP′-based regressions (eqs 7 and 10) amplify the differences between the one- and twoparameter model, and thereby, conceal that differences in slope m in the range -0.6 to -2 are not very substantial
FIGURE 4. Correlation of the fitting parameters m (A), b′ (B), and log A (C) describing the gas/particle partitioning behavior of PAHs at a forest and a nearby clearing (19 trustworthy data points (2) and 14 excluded data points (4)). The dotted lines correspond to differences between the two sites by a factor of 1.5. when displayed in φ vs log PL plots. We presume that the nonlinear one-parameter model (i.e., slopes m ) -1, eq 5) has not received the attention it deserves because past studies have relied largely on log KP′-based regressions. Variability in Parameter A of Nonlinear One-Parameter Model. A ranges from 6.0 × 10-7 to 1.9 × 10-4 (Table S6), i.e., nearly over two and an half orders of magnitude. This means that chemicals whose temperature-adjusted PL differs by 2.5 orders of magnitude can have the same sorbed particle fraction φ on different sampling occasions. Although this appears to be a rather large range, such variations are easily explained by the variability in the concentrations and properties of the particles in the atmosphere. A is directly related to the capacity of the particle phase for PAHs. In case of adsorptive partitioning, this capacity is often expressed as the available surface area θ, (10), whereas in the case of bulk phase partitioning into aerosol organic matter, it depends on the concentrations of the particles TSP, and their organic matter content fOM, (14). Bidleman (7) suggested that θ varies over more than an order of magnitude from 4.2 × 10-7 cm2‚cm-3 in clean continental background air to 1.1 × 10-5 cm2‚cm-3 in urban air. Similarly, TSP varies over a large range, e.g., from 15 to 162 µg‚m-3 in urban air (14) and from 10 to 300 µg‚m-3 at different atmospheric background sites (22). TSP values as low as 0.65-2.5 µg‚m-3 have been reported for Arctic air (2). fOM has also been reported to vary widely in different urban, suburban, and rural locations (2.4-27%, if organic matter is assumed to consist of 74% organic carbon) (22). Neither TSP, fOM nor θ was recorded at Borden during the sampling period, preventing a more detailed exploration into what controls the variability in parameter A. Comparison of Gas/Particle Partitioning at the Forest and Clearing. After eliminating 16 sets of measurements due to the possibility of artifacts, 19 sampling events remain for which reliable fits could be obtained at both forest and clearing. These were employed to investigate whether the G/P partitioning of the PAHs is the same at the two sites. Fitting parameters obtained from a sample taken at the clearing are plotted against the fitting parameter from the sample taken simultaneously at the forest. Figures 4A-C includes such correlations for m, b′, and log A, respectively. Similarity between the G/P partitioning behavior at the two sampling sites is expressed by how close these points lie to the diagonal 1:1 line. Considering the uncertainty of these fitting parameters, the G/P partitioning of the PAHs at the two sites is quite similar, and even identical for some events. In particular, deviations from the 1:1 line occur in either direction, and deviations above and below the 1:1 line are of similar frequency and extent. Differences in the fitting parameters between the two sites tend to be less than a factor of 1.5. Paired Student’s t-tests with a two-tailed distribution show that there is no significant difference between the forest
and clearing site for m (p > 0.1), b′ (p > 0.1), and log A (p > 0.1), further confirming the similarity of the G/P partitioning behavior of PAHs at the two sites.
Acknowledgments We are grateful to Bondi Gevao and John Deary for help with collecting samples and to Ralf M. Staebler for providing temperature data. The study was supported by the Canadian Foundation for Climate and Atmospheric Sciences.
Supporting Information Available Summary of different regression equations (Table S1). Field sampling information (Figure S1, Table S2). Detailed description of the experimental procedures (Table S3). Measured particle-bound percentages φ and log KP′ for all 35 sampling events (Tables S4 and S5). Regression results using two different nonlinear (Table S6) and two different linear models (Table S7). Figure S2 comparing regression results using measurements with and without blank correction. Figure S3 relating φ with log PL for all sampling events. Figure S4 relating log KP′ with log PL for all sampling events. Discussion of relationship between log A and b′ (Fig. S5). This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review December 13, 2005. Revised manuscript received March 22, 2006. Accepted March 24, 2006. ES052496W
