Laboratory Measurements of Thermodynamics of Adsorption of Small

Nov 25, 2005 - The adsorption isotherms of a series of aromatic hydrocarbons on n-hexane soot were measured as a function of temperature and partial p...
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Environ. Sci. Technol. 2006, 40, 179-187

Laboratory Measurements of Thermodynamics of Adsorption of Small Aromatic Gases to n-Hexane Soot Surfaces DANIEL G. AUBIN AND JONATHAN P. ABBATT* Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6

The adsorption isotherms of a series of aromatic hydrocarbons on n-hexane soot were measured as a function of temperature and partial pressure in a coatedwall flow tube coupled to an electron-impact mass spectrometer. The specific surface area was determined for each of the samples by measuring the BET isotherm of Kr at 77 K. The gas-to-surface uptakes were fully reversible with the extent of adsorption increasing with decreasing temperature and increasing partial pressures. At low partial pressures, the isotherms were well modeled by the Langmuir isotherm for all experimental conditions, and the adsorption was found to saturate at one monolayer of coverage at ≈2 × 1014 molecule cm-2. For the less volatile species, evidence for multilayer adsorption was observed and the BET isotherm was used instead. The experimental enthalpies of adsorption were consistently higher than the enthalpies of vaporization for all compounds. A linear freeenergy relationship was developed between the Langmuir equilibrium constant for adsorption and the compound’s (subcooled) liquid vapor pressure, providing validation for the use of such relationships in assessing gas-particle partitioning of aromatic hydrocarbons to soot aerosols in the environment. The experimental results were compared to the Junge-Pankow gas-to-aerosol partitioning model.

1. Introduction There are numerous processes controlling the fate and transport of chemicals in the environment such as wet and dry atmospheric deposition and advection in the atmosphere, oceans, lakes, and rivers, as well as chemical reactions and biodegradation (1). In the atmosphere, the fate and transport of a chemical will depend greatly on the extent to which it partitions between the gas and particulate condensed phases, both solid and liquid. The extent of this partitioning will depend on the equilibrium partitioning constant and the kinetics of the process (2). Besides affecting the potential for long-range transport, gas-to-particle partitioning will also modify the surface and the bulk physical-chemical properties of the aerosols (3). For example, surface active species may affect the rate of uptake and evaporation to and from the particle surface, the rate of particle scavenging, and the transport of reactive molecules, such as OH and NO3, to the particle surface (4). Currently there are several gaps in our understanding of gas-to-particle partitioning. For example, it is still not clear * Corresponding author phone: 416-946-7359; e-mail: jabbatt@ chem.utoronto.ca. 10.1021/es050800f CCC: $33.50 Published on Web 11/25/2005

 2006 American Chemical Society

whether absorption into the bulk or adsorption onto the surface is the dominant process for different aerosol types (4). Additional uncertainties arise from the relative importance of organic matter and black carbon (BC) and/or soot to the sorption process, the effect of relative humidity, and the effect of competitive uptake in the atmosphere. In fact, the use of different partitioning models leads to differing conclusions about the fate for chemicals, and for polycyclic aromatic hydrocarbons (PAH) in particular (5). PAHs are an important class of chemical pollutants in the environment. Many of them and their degradation products are known or suspected carcinogens (4). They are formed from incomplete burning or pyrolysis and are released into the air as highly complex mixtures of polycyclic organic matter (4). Due to their large range in vapor pressures and hydrophobicities, PAHs are multimedia compounds ubiquitous in the atmosphere, aerosols, soils, and sediments. In the atmosphere, their fate and long-range transport will depend on their partitioning behavior. In the gas phase, they may react with atmospheric oxidants such as OH and NO3, whereas on particles they can have a wide range of reactivities, depending on particle composition (6, 7), and are subject to loss via wet and dry deposition. Soot aerosols are ubiquitous in the environment and have been observed to comprise tens of percent of the total aerosol carbon in both rural and urban areas (8-10). Like PAHs, they are formed from the incomplete combustion of carbonaceous fuels, and they have an average global source strength estimated to be as high as 24 Tg year-1 (11, 12). Aside from one study that used solid material scraped from the inside of a furnace as surrogate material for atmospheric aerosols, to date there have been very few controlled laboratory studies (13, 14) on the adsorption of gas-phase PAHs to soot. Indeed, there have only been a limited number of controlled field studies done as well (1517). In this regard, we believe this is the first paper to study the uptake of aromatic hydrocarbons onto soot with a known specific surface area and as a function of temperature and partial pressure. By so doing, we can better elucidate the nature of the sorption mechanism and better determine the thermodynamics of the process. n-Hexane soot was chosen as a proxy for BC/soot since it has been studied extensively (18-22), has been shown to be reactive with certain trace atmospheric gases (4), and has a high specific surface area that may be available to participate in the adsorption process. The results from this study are compared with current gasto-particle partitioning theories to better validate their use in atmospheric and environmental modeling.

2. Experimental Section The n-hexane soot samples were prepared by burning the liquid hydrocarbon (EMD Omnisolv, 95.4%) in a burner enclosed in a chimney into which a regulated clean air flow was introduced. Once the air-to-fuel ratio had been adjusted to produce a “sooting” flame, the soot sample was collected on the inside of a 20 cm long, 2.3 cm i.d. Pyrex tube held 5-10 cm above the tip of the flame. The soot sample was deep black, and it was allowed to evenly coat the inside of the tube where up to 0.215 g was deposited. Chemical analysis of the soot using a thermal optical transmission instrument (Sunset Laboratory Inc., Forest Grove, OR) at the Meteorological Service of Canada facility showed that the soot was largely elemental carbon, with an elemental carbon to total organic carbon ratio ranging from 0.86 to 0.94. For a more detailed account of the procedure refer to Fan, Brook, and Mabury (23). VOL. 40, NO. 1, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Diagram of the double jacketed coated-wall flow tube coupled to an electron-impact mass spectrometer. The specific surface area of the soot sample was determined by measuring the BET (Brunauer, Emmett, and Teller) (24) isotherm of Kr at 77 K. In particular, the coated Pyrex tube was placed in a specially constructed stainless steel chamber that could be immersed in liquid nitrogen for the BET analysis. For a more thorough overview of this experimental method refer to Aubin and Abbatt (25). It was found that the specific surface area of the soot was up to 75 times larger than the geometric surface area of the sample. Note that this approach measures the total surface area of the entire soot film, and it differs from all other techniques in the literature where a small sample, hoped to be representative of the whole, has its surface area measured in a commercial unit. Because the entire accessible surface area of the soot sample is measured, the interpretation of the adsorption isotherms is not biased by the presence of any inaccessible soot layers whose surface area might be measured if only a small part of the sample were measured in a commercial instrument. An approach that is now well documented in the literature was used to measure the gas-to-surface uptakes (25-27). In particular, the soot-coated tube was inserted into a doublejacketed flow tube, as shown in Figure 1, through which a flow of 400-450 sccm of a helium carrier gas (high purity grade, Air Products) at 0.77 Torr was established for 10-15 min prior to beginning an experiment. The uptake experiments were conducted from 243 to 315 K by using a lowtemperature circulating bath (Neslab, Model ULT-80). A differentially pumped electron-impact mass spectrometer sampled the composition of the gas exiting the flow tube by monitoring the signal for the most abundant ion. The detection limit (S/N ) 1, 1 s sampling time) for the aromatic hydrocarbons was close to 1 × 10-7 Torr. The adsorbate gas, mixed in a small flow of helium, was added to the flow tube through a movable injector initially positioned with its tip beyond the downstream end of the soot film. In all cases, the flow exiting the injector tip never exceeded 10% of the total flow in the flow tube, which ensured that mixing into the bulk flow was rapid. For benzene and ethylbenzene (ACS grade, Uniscience), the partial pressure in the flow tube was determined from the pressure drop with time from a glass reservoir containing vapors of either of these two compounds diluted in helium. The PAHs, which have low vapor pressures at room temperature, were delivered to the flow tube by passing a flow of He into a cell containing glass beads (solid 4 mm diameter glass beads, Fisher Scientific) coated with the solid PAHs (naphthalene (99%) and acenaphthene (99%) from Acros Organics, and acenaphthylene (80+%) from Alfa Aesar). The flow through this cell was sufficiently small that it was saturated with the PAHs. This was demonstrated by showing that the mass spectrometer signal scaled linearly with the flow and also that the 180

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addition of a second flow cell in series did not lead to an increase in the signal, which indicates that the flow of He was fully saturated with the PAH. The uptake experiments were conducted by pulling the injector back over the soot film by a distance of 5, 10, or 20 cm, the exact value being determined by the need to see a sufficiently large change in the mass spectrometer signal indicative of partitioning to the surface. The tip of the injector was then pushed back to the starting position, beyond the soot-coated Pyrex tube, after the signal from the mass spectrometer had approached a steady-state value. The loss of signal after withdrawing the injector was integrated to determine the amount of the gas lost to the surface, where a criterion of 90% signal recovery was used to determine the point at which the surface was saturated. By referencing this amount to the surface area exposed, an uptake, or surface coverage, was obtained.

3. Results and Discussion 3.1. Sorption Mechanism. The molecular structures of the five compounds that were studied, along with their roomtemperature vapor pressures, are shown in Table 1. The compounds are all aromatic hydrocarbons with no other functional groups, which limits the interactions with the soot surface to van der Waals and hydrogen bonding interactions. Also, the molecules were specifically chosen to span a large range (over 4 orders of magnitude) in vapor pressure and to consist of both liquids (benzene and ethylbenzene) and solids (naphthalene, acenaphthene, acenaphthylene). The temperature range for the uptake experiments was from 243 to 315 K, and the range of partial pressures was from 2 × 10-7 to 2 × 10-4 Torr. Due to the low volatility of acenaphthylene and acenaphthene, the flow cell apparatus limited the experimental conditions to partial pressures between 1 × 10-6 and 1 × 10-5 Torr for these compounds. Also, these two compounds had very large uptakes onto the soot surface, which made it impractical to measure their uptakes below 283 K because it required an excessively long time to reach equilibrium between the gas phase and the soot surface. For example, at 283 K it took over 60 min for acenaphthene to establish an equilibrium between the gas phase and the soot surface for a partial pressure of 1.2 × 10-6 Torr. Figure 2 shows a typical uptake profile for ethylbenzene on n-hexane soot at 283 K. It is representative of all the compounds that were studied. The initial drop in the mass spectrometer signal corresponds to the time where the injector was pulled back over the soot film allowing the ethylbenzene to partition to the surface. The amount of time required for the signal to return to a steady state, indicating that equilibrium between the gas phase and the surface was established, ranged from 2 to 3 s for benzene at 283 K to over 60 min for acenaphthene at 283 K. For the most part, the signal returned to at least 95% of its initial value except when the time required to saturate the surface was excessively long, as in the case of acenaphthylene and acenaphthene, where there could be some drift in the mass spectrometer signal over this time frame. Qualitatively, the uptake profile was composed of two different regimes. The first regime, from 10 to 15 s in Figure 2, consisted of a relatively rapid decrease in the signal followed by a rapid recovery of the signal to near its initial value. In the second regime, from 15 to 30 s in Figure 2 and observed predominantly with the less volatile PAHs, the signal slowly recovered, almost asymptotically, back to its initial value. This second regime may arise from slow “diffusion” into the pores and the underlying layers of the soot film. The rapid surge in the signal after pushing back the injector tip beyond the soot film (observed after 30 s in Figure 2) indicates that the desorption lifetime for the compounds on the soot surface is quite short, e.g. less than 10 s or so for the

TABLE 1. Molecular Structure and Vapor Pressure at 298 K of the Compounds Investigated in This Study

a Vapor pressures for the PAHs are taken from Finlayson-Pitts and Pitts (4), and those for benzene and ethylbenzene are taken from Perry’s Chemical Engineer Handbook (28). The sub-cooled vapor pressures were calculated from eq 11 in the Supporting Information.

FIGURE 2. Mass spectrometer signal as a function of time for ethylbenzene partitioning on a 0.101 g n-hexane soot film at 283 K with a partial pressure of 4.7 × 10-6 Torr.

FIGURE 3. Benzene uptake on a 0.101 g n-hexane soot film fit to the Langmuir isotherm at 283 K (solid circle), 273 K (solid triangle), 263 K (solid square), and 243 K (solid diamond).

conditions in Figure 2. The adsorption and desorption amounts were found to be within 15% of each other, which implies that the uptake process was fully reversible within the time scale of the experiment, i.e., no reactive processes are occurring on the soot surface. Figures 3 and 4 show a series of adsorption isotherms for benzene and ethylbenzene, respectively, on n-hexane soot at several different temperatures. As expected, the uptake increases as the temperature decreases and as the partial pressure increases. To learn something about the partitioning mechanism, the experimental uptake isotherms were fit to a variety of sorption isotherms. As seen in Figures 3 and 4, a good fit was obtained with the Langmuir isotherm (29) (eq 1) where θ is the surface coverage in molecule cm-2, θm is

θ KP ) θm 1 + KP

(1)

the surface coverage required to complete a monolayer, which we take to be 1.9 × 1014 molecule cm-2 (see below), P is the partial pressure of the adsorbate gas over the soot surface, and K is the gas-surface equilibrium constant (Torr-1).

FIGURE 4. Ethylbenzene uptake on a 0.101 g n-hexane soot film fit to the Langmuir isotherm at 283 K (cross), 273 K (solid circle), 263 K (solid triangle), 253 K (solid square), and 243 K (solid diamond). We note that the Freundlich isotherm (30) (eq 2), where a and b are empirical parameters, also gave a good fit in the case of benzene and ethylbenzene at low surface coverages VOL. 40, NO. 1, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 5. Naphthalene uptake on a 0.101 g n-hexane soot film fit to the BET isotherm at 308 K (cross), 303 K (open diamond), 295 K (solid circle), 283 K (solid triangle), 273 K (solid square), and 263 K (solid diamond).

FIGURE 6. Acenaphthylene uptake on a 0.215 g n-hexane soot film fit to the BET isotherm at 315 K (solid circle), 308 K (solid triangle), 298 K (solid square), and 283 K (solid diamond).

(i.e. low adsorbate gas partial pressures and high temperatures); however, the Freundlich isotherm could not fit the

θ ) aP1/b

(2)

experimental isotherms at high surface coverage, especially in the case of the PAHs, where there was a pronounced curvature in the isotherm due to the onset of surface saturation. This is seen quite clearly in Figure 5 for naphthalene. We interpret the good agreement with the Langmuir isotherm for the benzene and ethylbenzene data to be consistent with a reversible adsorption mechanism. Also, we note that observation of a limiting surface coverage is in direct support of uptake driven by adsorption. An absorptive uptake would show no such feature. In particular, we find, primarily from the ethylbenzene data, that the saturated surface coverage occurs at a value of θm ) 1.9 × 1014 molecule cm-2, which represents the average of the θm values measured at different temperatures and on two films. Finally, we note that the Langmuir isotherm, or modifications thereof, has been used successfully to describe the gas-phase partitioning of HNO3 (25), SO2 (31), and NH3 (32) to n-hexane soot as well. Under conditions of high surface coverage, as shown in Figure 5 for naphthalene, one could visually observe the saturation to also occur at roughly 1014 molecule cm-2, although a common value of the saturated surface coverage from a Langmuir fit did not describe the data from one temperature to another. In addition, for the case of naphthalene at low temperatures and high partial pressures (data not shown), saturation followed by condensation on the surface was observed as well, i.e., multilayer formation occurred. For the low vapor pressure species, i.e., naphthalene, acenaphthylene, and acenaphthene, where the uptakes were measured close to surface saturation, we analyzed the data using the BET isotherm (24), which can be thought of as a Langmuir adsorption model that has been modified to take into account multilayer adsorption (see Figures 5-7). Equation 3 shows the linearized form of the BET isotherm where

(CBET - 1)x x 1 + ) nmCBET n(1 - x) nmCBET

(3)

x ) P/P°, P is the pressure of the gas above the surface, P° is the saturation vapor pressure of the gas at the temperature used, n is the number of moles adsorbed, nm is the monolayer capacity which is the number of moles of the adsorbate gas required to form a layer one molecule thick over the entire 182

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FIGURE 7. Acenaphthene uptake on a 0.101 g n-hexane soot fit to the BET isotherm at 308 K (solid triangle) and 298 K (solid square). surface, and CBET is a constant related to the thermodynamics of adsorption. By applying eq 3 to the naphthalene data, we were able to derive a monolayer capacity, nm, which corresponded to 1.9 × 1014 molecule cm-2. In addition, there was no systematic variation in the value of nm with temperature. We note that this specific value for the surface coverage is the same as that obtained from the Langmuir analysis of the ethylbenzene data. For molecules the size of these small aromatics, this surface coverage is very close to what is expected for a monolayer coverage, where the molecules are sitting side-by-side on the surface. This is additional evidence that the mechanism of sorption is surface adsorption and that absorption into the bulk is not occurring to a significant degree. We make note that similar monolayer capacities were determined for PAHs on activated carbon: 2.70 × 1014, 1.98 × 1014, and 1.81 × 1014 molecule cm-2 for naphthalene, acenaphthylene, and fluorene, respectively, by Walters and Luthy (33), and 1.30 × 1014, 1.51 × 1014, 1.40 × 1014, and 1.24 × 1014 molecule cm-2 for o-cresol, nitrobenzene, o-methoxyphenol, and quinaldine, respectively, on activated carbon by Martin and Al-Bahrani (34). For sorption of phenanthrene to combusted lake sediments, Cornelissen and Gustafsson (35) obtained a saturated surface coverage ranging from 2.0 × 1013 to 1.0 × 1014 molecule cm-2. It should be noted that all these values were obtained by measuring the equilibrium distribution for the compound between BC/sediment and water, i.e., using a significantly different experimental technique than that used in this study. The close correspondence between the monolayer capacities obtained for the BC experiments and our own is quite striking, especially

FIGURE 8. van’t Hoff plot for the uptake of ethylbenzene on a 0.101 g n-hexane soot film. The equilibrium constants were obtained by fitting the Langmuir isotherm to the experimental adsorption isotherms. noting that our work involved PAHs with no functional groups and the others used substituted PAHs and aromatics containing nitro, hydroxyl, methoxy, and amine functional groups. 3.2. Adsorption Thermodynamics. Since the Langmuir isotherm includes an equilibrium constant for the adsorption process, experiments at different temperatures allowed us to determine enthalpies of adsorption from a van’t Hoff analysis. Figure 8 shows a van’t Hoff plot for the adsorption of ethylbenzene on soot where the adsorption enthalpy, ∆Hads, is obtained from the slope of the van’t Hoff plot as shown in eq 4 where R is the gas constant.

∆Hads ) -R

(

)

∂(ln K) ∂(1/T)

(4)

The straightforward approach described by eq 4 for derivation of the enthalpy of adsorption was appropriate for benzene and ethylbenzene because these species adsorbed sufficiently weakly that the measured surface coverages were typically well below saturation. However, for naphthalene, acenaphthylene, and acenaphthene this was not possible because the measured adsorption isotherms at lower temperatures were close to monolayer coverage. To derive adsorption enthalpies for these three molecules the BET isotherm was fit to the experimental data, as described above, to obtain a value for the BET constant, CBET, which is related to the enthalpy of desorption, ∆Hdes, and the enthalpy of vaporization, ∆Hvap, as follows (24)

CBET ≈ exp

(

)

∆Hdes - ∆Hvap RT

(5)

Note that the quality of the data for acenaphthylene and acenaphthene were not as high as that of the other compounds studied because their vapor pressures are low and their uptakes were very high and, therefore, long experiments were required (see Figures 6 and 7). Table 2 summarizes all the adsorption enthalpies that were determined for the five compounds. It can be seen that the adsorption enthalpies scale inversely with the vapor pressures, as one would expect. It can also be seen that the adsorption enthalpies are all higher than the enthalpies of vaporization. This suggests that condensation of the compound onto the soot surface is not the driving force for the partitioning to the soot surface and that the compounds have a higher affinity for the soot surface than for the pure bulk compound. Benzene is somewhat of an outlier having a heat

of adsorption not much different in absolute magnitude from its heat of vaporization. 3.3. Linear Free-Energy Relationship (LFER). Since the aromatic hydrocarbons are essentially members of a homologous series, it is possible to develop a linear free-energy relationship using the Langmuir equilibrium constant for binding to the surface. Although benzene and ethylbenzene are not PAHs, we believe it is valid to include them in the LFER since all five compounds can interact with the soot surface only through hydrogen bonding and van der Waals interactions and, therefore, would be expected to behave similarly. The underlying motivation is to predict the extent of adsorptive partitioning for other members of this homologous series, such as higher molecular weight PAHs, that have not been studied experimentally. This can be done if there is a common physical property for the molecules that scales in some way with their adsorptive ability. Using only low partial pressure experimental data at room temperature, where the data are in the linear portion of the Langmuir regime and well below monolayer coverage, we have determined the equilibrium constant for adsorption to the surface and then plotted this quantity versus the molecule’s saturated liquid vapor pressure for room-temperature conditions (Figure 9). We note the suggestion that, under environmental conditions, it is more appropriate to use the sub-cooled liquid vapor pressures in correlations of this type (39), as opposed to the solid vapor pressure, since a gas adsorbing on a soot surface well below its saturation vapor pressure is unlikely to experience intermolecular forces similar to those felt as a solid. Instead, the nearest neighbor interactions to the surface are more likely to be similar to those experienced as a disordered liquid, and the effective vapor pressure would be best described by the sub-cooled liquid vapor pressures. The data in Figure 9 are well correlated, with a correlation coefficient of 0.999, which also justifies the inclusion of benzene and ethylbenzene in the LFER. It has been argued extensively that the slope of the plot of the logarithm of the gas-to-particle partitioning constant Kp, i.e., an operationally defined partition coefficient, should scale within a homologous series with the logarithm of the vapor pressure yielding a slope of -1 (4). On the other hand, Goss and Schwarzenbach (2) have shown that the slopes of similar LFERs derived from field and laboratory data routinely differ from -1 and that shallower slopes are simply an indication of a weaker interaction between the gas and solid surface. However, we emphasize in this work that in the case of Langmuir adsorption in the linear regime one should expect a slope of -1 for a plot of log K versus log P°. This result comes from analysis of the nonlinear formulation of the BET isotherm (eq 6).

CBET x n ) nm (1 - x)(1 + (CBET - 1)x)

(6)

It can be seen that eq 6 simplifies to the Langmuir (eq 1) isotherm when P , P° and CBET . 1, i.e., in the linear regime of the adsorption isotherms:

CBETP n = nm P° - CBETP

(7)

When eq 7 is equated to the right-hand side of eq 1, the following relation is obtained (refer to the Supporting Information).

K=

CBET P°

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TABLE 2. Adsorption Enthalpies of Benzene and Ethylbenzene on Both n-Hexane Soot Films Determined from the van’t Hoff Equation Using the Equilibrium Constants Obtained from Fitting the Langmuir Adsorption Isotherm to the Experimental Dataa adsorption enthalpy (kJ mol-1) soot film

benzene

ethylbenzene

naphthalene

acenaphthylene

acenaphthene

0.101 g 0.215 g average ∆Hvap ∆Hdes-∆Hvap

-35 ( 2 -40 ( 4 -37.5 ( 2.2 -33.8 3.7

-55 ( 1 -56.9 ( 3.1 -55.9 ( 1.6 -42.2 13.7

-88.8 ( 4.5 -87.6 ( 6.9 -88.2 ( 5.1 -71 ( 5 17.2

-89.9 ( 0.3 -89.9 ( 0.3 -77 12.9

-97.1 ( 1.4 -98.0 ( 1.0 -97.5 ( 1.7 -83.4 ( 1.0 14.1

a For naphthalene, acenaphthylene, and acenaphthene the enthalpies of adsorption were determined from the BET isotherm (see text). Note: The enthalpies of vaporization were obtained from the Knovel Critical Tables (36), Osbourn and Douslin (37), and Nass et al. (38).

instead (not shown) was significantly different, being equal to -0.827 with a value of R2 ) 0.997.

4. Atmospheric Implications

FIGURE 9. Plot of the equilibrium constant for adsorption, K, as a function of the liquid vapor pressure of benzene and ethylbenzene and of the sub-cooled liquid vapor pressure of naphthalene, acenaphthylene, and acenaphthene on a 0.215 g n-hexane soot film at 298 K. The values of K (Torr-1) for benzene and ethylbenzene were obtained by extrapolating the equilibrium constants determined at lower temperatures to 298 K using their respective values of ∆Hads. The equation for the linear fit was log K ) -0.994 log P°L + 2.60 with R2 ) 0.999. Therefore the equilibrium constant for adsorption for a homologous series should scale with the reciprocal of the saturated vapor pressure when CBET is approximately constant within that series. This constant is related to the difference, ∆Hdes - ∆Hvap (see eq 5), which remains fairly constant for all molecules studied here except for benzene. To our knowledge, this is the first time that a correlation between the partitioning constant and the molecules’ vapor pressure has been shown to be true in controlled laboratory studies involving soot. As such, it gives more confidence in the use of such correlations for predicting partitioning behavior of aromatic hydrocarbons to soot and elemental carbon in the atmosphere. It should be noted that a single-parameter LFER, such as the one derived here, may not be sufficient for compounds other than aromatic hydrocarbons since a single parameter cannot account for hydrogen bonding and van der Waals interactions separately (40). In the case of aromatic hydrocarbons, their hydrogen bonding interactions will be proportional to their van der Waals interactions, and the resulting single-parameter LFER will display a steeper slope than that of a compound class with a constant hydrogen bonding contribution. Also, we note that the LFER developed here may not be appropriate if the soot surface is coated with sulfates or other materials. We also note that we recently showed that a similar correlation holds for the adsorption of small oxygenated organics to ice surfaces, suggesting that these correlations are indeed valid for a number of surfaces (41). The fact that the slope of our log K versus log P° plot is nearly -1 is in accord with our derivation of eq 8. By contrast, the slope of an analogous plot where the solid vapor pressures were used 184

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Junge (42) derived an adsorptive partitioning model that has been widely used to describe the phase partitioning of organic compounds between the gas phase and the aerosol phase (16, 43-49). Junge’s model was critically reviewed by Pankow (50) and will henceforth be referred to as the Junge-Pankow adsorption model as it is conventionally referred to in the literature. The Junge-Pankow model is only applicable for adsorption, which may not be dominant for some types of particles, such as aged soot or secondary organic aerosols. It has been suggested that these types of aerosols may have an organic liquid-like layer on the surface which will drive the most important sorption process to be absorption (51, 52). However, it is clear from our work that adsorption is the dominant sorption process occurring. Had absorption been significant we may still have seen saturation of the isotherms at some point, but we would not have seen saturation always occurring at the specific value of 1014 molecules/cm2, i.e., the value for a monolayer surface coverage. As above, the Junge-Pankow model is derived from the BET isotherm in the limit of low partial pressures and large BET constants, which is equivalent to the Langmuir isotherm in the linear regime (50). Specifically, it relates the fraction of a compound in a unit volume adsorbed to the aerosol surface (Φ) to its saturated liquid vapor pressure (P°L) and to the total aerosol surface area per unit volume in air (SA, cm2/cm3) as shown below.

Φ)

CJPSA P°L + CJPSA

(9)

The constant CJP (Torr cm) is related to that defined earlier in the BET expression:

CJP ) 106RTNs exp[(∆Hdes - ∆Hvap)/RT]

(10)

where Ns is the number of moles of surface adsorption sites (mol cm-2), T is the temperature (K), R, the gas constant, is 0.0623 Torr m3 mol-1 K-1 (or 8.314 Pa m3 mol-1 K-1), and the factor of 106 converts m3 to cm3. Junge originally proposed that a value of CJP ) 0.129 Torr cm (or 17.2 Pa cm) be used (53), and this value has been applied extensively to organochlorine compounds (45, 49, 54-57) and PAHs (16, 43, 44, 46-48). However, Pankow (50) suggested that if Ns is ∼4 × 10-10 mol cm-2 (in this work we choose to use a value of Ns ) 3.1 × 10-10 mol cm-2 since it is equivalent to our experimentally determined saturated surface coverage of θm ) 1.9 × 1014 molecule cm-2) and ∆Hdes - ∆Hvap ) 6.3 kJ mol-1, the resulting value for the constant is CJP ) 0.097 Torr cm (or 13 Pa cm) at 298 K. The justification for using CJP ) 0.097 Torr cm is based on experimental data obtained by Bidleman et al. (58), later analyzed by Pankow (50), that shows

FIGURE 10. Predicted values of the aerosol surface coverage (Φ) from the Junge-Pankow model under typical urban conditions at 283 K, with SA ) 1.1 × 10-5 cm2 cm-3 and Ns ) 3.1 × 10-10 mol cm-2 with CJP ) 0.129 Torr cm (solid circle), and CJP calculated from eq 10 (open circle) using the experimentally determined enthalpies of adsorption and the literature values for the enthalpies of vaporization (refer to Table 2). ∆Hdes - ∆Hvap ) 6.3 kJ mol-1 for a series of organochlorine pesticides. Pankow also determined from Yamasaki’s (59) field data that CJP for PAHs should be on the order of 1.3 Torr cm (or 173 Pa cm) since an analysis of this data set showed that ∆Hdes - ∆Hvap was, on average, 12.5 kJ mol-1 for the PAHs. This serves to emphasize the fact that the JungePankow model can only be applied to a compound class for which the value of ∆Hdes - ∆Hvap is known and constant throughout the compound class. This is confirmed from our experimental results where ∆Hdes - ∆Hvap for the PAHs and ethylbenzene was roughly 13-17 kJ mol-1 which is, on average, 6.2 kJ mol-1 higher than that for the organochlorines studied by Bidleman and Foreman (58, 60). Our experimental results also support the widely used assumption that, in the case of PAHs, the value of ∆Hdes - ∆Hvap is constant within a homologous series of molecules. Yamasaki’s data show that for three or four ring PAHs, ∆Hdes - ∆Hvap is on the order of 8.3-16.7 kJ mol-1, which is in the range of 13-17 kJ mol-1 that we have determined and confirms that different values for ∆Hdes ∆Hvap are appropriate for different classes of compounds. Figure 10 shows Φ obtained when applying the JungePankow model to urban conditions with 1.1 × 10-5 cm2 cm-3 for the aerosol surface area (53) and by calculating a value of CJP a priori from eq 10 using our experimentally determined enthalpies of adsorption and the literature values for the enthalpies of vaporization (refer to Table 2). We note that there is some uncertainty in the literature values for ∆Hvap, which will lead to a larger spread in the value of ∆Hdes ∆Hvap. For naphthalene, for example, this quantity can vary by 5 kJ mol-1. From Figure 10 it can be seen that the aerosol surface coverage is underpredicted by 1-2 orders of magnitude when the commonly used value of CJP ) 0.129 Torr cm (or 17.2 Pa cm) is used. This underprediction is greatest for the compounds with the lowest vapor pressures, which is the case for the bulk of the PAHs in the environment. Even taking the uncertainties described above into consideration, there would be a significant difference between our predictions and the standard implementation of the Junge-Pankow model. Figure 11 shows the variation in the aerosol surface coverage (Φ), under urban conditions, with the variation in the value of ∆Hdes - ∆Hvap. From Figure 11 it is apparent that the predicted aerosol surface coverage is most sensitive to changes in the value of ∆Hdes - ∆Hvap for moderately volatile molecules (log PL°Torr) ) -7 to -4). The Junge-Pankow model has been applied to PAHs using field data from a wide

FIGURE 11. Variation in the aerosol surface coverage (Φ) at 298 K predicted from the Junge-Pankow model, under urban conditions with SA ) 1.1 × 10-5 cm2 cm-3 of aerosol surface area, as a function of the difference ∆Hdes - ∆Hvap . variety of environmental conditions (16, 43, 44, 46-48). In most cases, the Junge-Pankow model, with CJP ) 0.129 Torr cm (or 17.2 Pa cm), provided a reasonably good prediction of the gas-to-particle partitioning when compared to the field data for the most and least volatile PAHs but not for those with a midrange volatility, i.e., log P°L(Torr) -5.6 to -7.6 (or log P°L(Pa) -3.5 to -5.5). This is because the partitioning behavior of the most and least volatile compounds is relatively insensitive to the value of CJP used in the Junge-Pankow model. This serves to emphasize the point that the appropriate value of ∆Hdes - ∆Hvap for the compound class must be used if one wishes to accurately model the partitioning of semivolatile species when adsorption is the predominant process. In the case where aromatic hydrocarbons are adsorbing to particles containing small fractions of elemental carbon with high concentrations of organic carbon and inorganic species, one would expect the aromatic hydrocarbons to interact less strongly with the particle surface. Therefore the effective adsorption enthalpy will be lower than that measured here and is likely a weighted average of all the constituents in the aerosol that contribute to adsorptive partitioning. We are currently analyzing a series of experiments where the uptake of the aromatic hydrocarbons and PAHs was studied as a function of relative humidity and under conditions of competitive adsorption in order to more closely simulate environmental conditions.

Acknowledgments The authors thank Dr. Xinghua Fan of the Meteorological Service of Canada for his assistance with the elemental carbon and organic carbon analysis of the n-hexane soot samples. Acknowledgment is also made to the donors of the American Chemical Society Petroleum Research Fund for support of this research.

Supporting Information Available Equations used to obtain the sub-cooled liquid vapor pressures used in Figure 9. This material is available free of charge via the Internet at http://pubs.acs.org.

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Received for review April 26, 2005. Revised manuscript received October 17, 2005. Accepted October 20, 2005. ES050800F

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