Quantum Mechanical Predictions of the Henrys Law Constants and

Oct 15, 2008 - 150 Academy Street, Newark, Delaware 19716, Delaware. Department of Natural Resources and Environmental Control,. Watershed ...
0 downloads 0 Views 732KB Size
Download PDF
Environ. Sci. Technol. 2008, 42, 8412–8418

Quantum Mechanical Predictions of the Henry’s Law Constants and Their Temperature Dependence for the 209 Polychlorinated Biphenyl Congeners KATHY L. PHILLIPS,† STANLEY I. SANDLER,† R I C H A R D W . G R E E N E , ‡,§ A N D D O M I N I C M . D I T O R O * ,§ Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, 150 Academy Street, Newark, Delaware 19716, Delaware Department of Natural Resources and Environmental Control, Watershed Assessment Branch, 820 Silver Lake Boulevard, Suite 220, Dover, Delaware 19904, and Department of Civil and Environmental Engineering, University of Delaware, DuPont Hall, Newark, Delaware 19716,

Received April 1, 2008. Revised manuscript received August 6, 2008. Accepted August 13, 2008.

The Henry’s law constants (HLCs) for all 209 polychlorinated biphenyl (PCB) congeners were predicted at 25 °C using the quantum mechanical (QM) continuum solvation models COSMOSAC and SM6, and trends were examined. COSMO-SAC HLCs were also predicted for all congeners at 4, 11, 18, and 31 °C. The temperature dependences of the HLCs were used to calculate enthalpy of solvation (∆HS) values. At 25 °C, COSMOSAC and SM6 predicted similar values of the HLC, which are consistent with all but one of the available sets of measurements, and have smaller root-mean-square prediction errors than other models tested. This supports the validity of the QM values, and the recommendation of their use in environmental transport and fate models. Intercongener trends in the HLCs appear to be dominated by the strength of PCBwater polar interactions. The COSMO-SAC predictions between 4 and 31 °C indicate that the temperature dependence of the HLC is similar for all congeners. At low temperatures, the HLC predictions for several heavy congeners are substantially higher than recently reported measurements, supporting claims in the literature that these low-temperature data are inaccurate.

Introduction Atmospheric transport is a key process in the global redistribution of polychlorinated biphenyls (PCBs) (1). The Henry’s law constant (HLC) is a fundamental property describing the exchange between the atmosphere and surface waters. The lack of accurate HLC values poses a major problem in modeling the transport and fate of PCBs in the * Corresponding author phone: (302) 831-4092; fax: (302) 8313640; e-mail: [email protected]. † Department of Chemical Engineering, University of Delaware. ‡ Delaware Department of Natural Resources and Environmental Control. § Department of Civil and Environmental Engineering, University of Delaware. 8412

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 22, 2008

environment, a necessary step for performing risk assessments and developing environmental remediation strategies. HLCs have been measured for selected congeners (2–17), commonly at 25 °C. The largest experimental data sets at this temperature are those of Brunner et al. (11), who measured HLCs for 58 congeners using a concurrent flow technique, and Bamford et al. (13), who used a modified gas-stripping method to measure HLCs for 26 congeners. The totality of data at 25 °C (Figure 1A) are highly scattered, and reported values for some individual congeners differ by up to almost 2 orders of magnitude. Different trends with changes in the number of chlorine substituents (NCl) are apparent in the HLC data. Furthermore, measurements for many congeners are unavailable. Consequently, consensus is lacking on the values of the HLCs, particularly for the heavier congeners. HLCs of PCBs have also been modeled by many groups (11, 14, 15, 18–30). However, most models are fitted to measured HLCs and therefore suffer from the uncertainty in the data. Predictive models for the HLCs of all congeners have been published. Burkhard et al. (20) predicted the HLCs from the ratios of vapor pressures and solubilities calculated by modeling data for selected congeners (Figure 1B). Abraham and Al-Hussaini (29) used chromatographic data to develop a linear free energy relationship for the properties of PCBs (Figure 1C). The SPARC (31) method can be used to predict properties for organic compounds using molecular interaction models based on chemical structure theory, and calibrated using experimental data (32–36) (Figure 1D). These predictions are not in close agreement with each other, nor do they consistently support any set of measured HLCs. (A statistical analysis of the prediction errors is presented subsequently.) Therefore, a lack of consensus remains. Most work on HLCs for PCBs has been performed at ambient temperatures. However, HLC is a highly temperature-dependent property, and transport and fate modeling requires knowledge of HLCs over a range of environmentally relevant temperatures. A small body of work exists on the temperature dependence of HLCs for PCBs, including measurements (12, 13) and calculations (14, 20, 37). However, the results are inconsistent, and uncertainty about the temperature dependence remains. In this study, two quantum mechanics (QM) based continuum solvation models, COSMO-SAC (38–40) and SM6 (41), were employed to predict HLCs for all PCB congeners at 25 °C. COSMO-SAC, the only one of the models that can be applied at different temperatures, was also used to predict HLCs for all congeners over the environmentally relevant temperature range of 4-31 °C. The QM-based methods predict the HLC from a combination of individual solvation terms, each of which offer insight into the effects that give rise to the HLC values and the intercongener trends. Additional insight is gained by examining the QM-determined three-dimensional structure for each congener.

Overview of Models The QM models used in this study are both well established and have been described in detail elsewhere (COSMO-SAC (38–40); SM6 (41)). A brief overview is included here. COSMO-SAC. The Conductor-like Screening Model (COSMO) developed by Klamt and Schu ¨u ¨ rmann (42) is a QMbased model in which the solvent is represented by a homogeneous medium characterized solely by its dielectric constant. Conceptually, such continuum solvation models take a solute molecule from an ideal gas and place it in a 10.1021/es800876w CCC: $40.75

 2008 American Chemical Society

Published on Web 10/15/2008

FIGURE 1. HLCs for PCB congeners at 25 °C. (A) Experimental data: O, Hassett and Milicic (5); 3, Dunnivant et al. (8, 9); 4, Fendinger and Glotfelty (10); +, Brunner et al. (11); 9, Bamford et al. (13); ], Fang et al. (15). Lau et al. (16): x, gas-stripping method (GSM), !, modified GSM, 4, (crossed triangle), integrated GSM. Error bars indicate standard deviation, where reported. (B-D) Predicted values from the literature: (B) ], Burkhard et al. (20); (C) 4, Abraham and Al-Hussaini (29), eq 10 in their paper; (D) 3, SPARC (31). (E, F) Predicted values from this work: (E) O, COSMO-SAC; (F) O, SM6. cavity formed within the dielectric medium. The interface between the cavity and the medium is referred to as the solvent accessible surface. Any charge distribution of the solute will polarize the medium, leading to a charge distribution on the solvent accessible surface, from which the interaction energies of the surfaces can be evaluated (42, 43). The free energy of transfer from the gas phase to the condensed phase is referred to here as the free energy of solvation, ∆GS, and is directly related to the HLC by

( )

jf L ∆GS ) RT exp HLC ) lim xf0 x(55 . 4 × 103) RT

(1)

where HLC is in (Pa m3)/mol, x and jf L(Pa) are, respectively, the mole fraction and fugacity of the solute in the solution, the molar volume of water (55.4 × 103 mol/m3) is a unit conversion factor, R is the gas constant (8.314 J/(mol K)), T (K) is the absolute temperature, and ∆GS is in J/mol. In the COSMO method, which is implemented in several QM packages including DMol3 (44), the surface-charge density calculation is simplified by treating the dielectric medium as a perfect conductor (infinite dielectric constant) (42, 43). An extension to COSMO, the COSMO-Segment Activity Coefficient (COSMO-SAC) model then applies statistical thermodynamics to the surface-charge distribution in the conductor to account for the interactions between the molecule and the solvent. COSMO-SAC, developed by Lin and Sandler (38, 39) and refined by Wang et al. (40), is a variation on the Klamt COSMO-RS (real solvents) model (45, 46). Using the QM-calculated energies, COSMO-SAC can then be used to predict thermodynamic properties, including the

vapor pressure (P vap) and the infinite dilution activity coefficient in water (γW). The mole fraction solubility of any very slightly soluble compound is the reciprocal of γW. The product of P vap (Pa) and γW gives an estimate of the HLC, assuming ideal gas behavior.

(

HLC ≈ PvapγW

1 55.4 × 103

)

(2)

SM6. The Solvation Model 6 (SM6) is a QM-based continuum solvation model developed by Cramer, Truhlar and co-workers, and is implemented in the SMXGAUSS software (47). However, SM6 employs a distinctly different approach to predict the HLC. SM6 partitions ∆GS into three contributions (41) ∆GS ) ∆Eelec + GP + ∆GCDS

(3)

The ∆Eelec term is the change in the internal electronic energy of the solute in moving from the gas phase to the liquid phase at a fixed geometry (41). In this work, gas-phase geometries were used rather than reoptimizing the solute geometry in the liquid phase, because the difference in ∆GS resulting from reoptimization is generally less than the average error in the model, and the model has been parametrized using gas-phase structures (41). The polarization contribution, GP, accounts for the change in the solute free energy because of electrostatic interactions between the charge distribution of the solute and the bulk electric field of the solvent (41, 48). These terms are computed using QM. The term ∆GCDS accounts for all remaining contributions to ∆GS, which include the free energy changes due to electrostatic interactions between the solute and solvent VOL. 42, NO. 22, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

8413

molecules in the first solvation shell (41). These short-range interactions can be attributed to cavity formation (C), dispersion (D), and changes in the solvent structure (S) due to the presence of the solute (48). ∆GCDS is an empirical term that is calculated using atomic surface tensions (41).

Methods Throughout this work, PCB congeners are referred to by their IUPAC names and numbers (Table S1 of the Supporting Information) (49). Predictions were made for all 209 congeners using both COSMO-SAC and SM6. COSMO-SAC. To prepare a starting geometry for each congener, we sketeched the structure using GaussView 3.09 (50), and the gas-phase geometry was optimized with Gaussian 03 (51) using density functional theory (DFT) with the B3LYP functional and the 6-31G(d,p) basis set. A frequency calculation was included to verify that the structure represented a minimum in the potential energy surface. To improve the initial guess of the structure (52), this was followed by a molecular mechanics energy minimization calculation using the Amber (53) force field. The final geometry, together with the gas-phase molecular energy, was obtained from a further DFT gas-phase optimization using DMol3 (44) with the VWN-BP density functional, DNP v4.0.0 basis set, a real space cutoff of 5.50 Å, and a “fine” numerical integration grid. These are the recommended DMol3 settings for COSMO calculations (54) and have been used in parametrization of COSMO-SAC (40, 55). Using the optimized (gas-phase) geometry, a single-point energy calculation in the condensed phase was then performed using DMol3 with the “COSMO solvation” environment and “conductor” as the solvent (other settings were unchanged from the previous step). The molecular weight and an estimate of the liquid density for each congener (required for the vapor pressure calculation) were obtained from ref 56. For all compounds, the COSMO-SAC program, incorporating the calculation method and parameters described in (40, 52), was used to calculate Pvap (Pa) and γW at each temperature of interest. HLC was predicted using eq 2. SM6. For each congener, the Gaussian B3LYP/6-31G(d,p) gas-phase optimized structure (as above) was used. A single-point liquid-phase energy calculation was performed with the SMXGAUSS program (47) running in mode 2, using the SM6 solvation model and the B3LYP/6-31G(d) theory and basis set, with water as the solvent. The HLC was calculated from the ∆GS value at 25 °C using eq 1.

Results and Discussion HLCs at 25 °C. The COSMO-SAC and SM6 HLC predictions at 25 °C (see the Supporting Information, Table S1) are plotted in panels E and F in Figure 1, respectively. These predictions are in close agreement, and both agree well with some of the measurements (Figure 1A) across the whole range of congeners. The agreement between each set of predictions and each data set is quantified by the root mean-square-error of prediction (RMSE) in log(HLC)

RMSE )



n

∑ (y

i,obs - yi,pred)

i)1

n

2

(4)

where y ) log(HLC/((Pa m3)/mol)), “obs” and “pred” refer to the observed and predicted values, respectively, and n is the number of points in the data set. Figure 2 compares the RMSEs for the various predictions and the major data sets (see the Supporting Information, Table S2). The Abraham and Al-Hussaini (29) and Burkhard et al. (20) predictions both agree most closely (i.e., RMSE is smallest) with the 8414

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 22, 2008

FIGURE 2. RMSE in log(HLC) for each set of predictions from each major data set for the PCBs at 25 °C. Experimental data (numbers in brackets {} indicate number of data points): white bars, Dunnivant et al. (8, 9) {17}; diagonal stripes pointing up to right, Brunner et al. (11) {58}; diagonal stripes pointing down to right, Bamford et al. (13) {26}; crosshatch, Fang et al. (15) {12}; horizontal stripes, Lau et al. (16) (GSM {8}, modified GSM {9}, integrated GSM {9}); black bars, overall, excluding Brunner et al. (11) data set {81}. Predictions from the literature: Burkhard et al. (20); Abraham and Al-Hussaini (29); SPARC (31). Predictions from this work: COSMO-SAC; SM6. Dunnivant et al. (8, 9) data, while the COSMO-SAC and SM6 predictions best agree with the Bamford et al. (13) data. The SPARC predictions are not in close agreement with any of the data sets. The data sets comprise different congeners; therefore, caution is warranted in directly comparing the RMSEs for different data sets. For instance, the Dunnivant et al. (8, 9) data do not include any congeners with more than six chlorines, whereas the Bamford et al. (13) data include several heavy congeners for which the experimental uncertainty in the HLC is greatest. Goss et al. (57) claimed that the Bamford et al. (13) HLCs are too high for the heavy congeners, possibly due to congener sorption on the gas bubble surface followed by transfer to the gas phase. However, the Burkhard et al. (20) HLCs are in close agreement with the Bamford et al. (13) measurements for all congeners with seven or more chlorines (panels A and B in Figure 1); the COSMO-SAC and SM6 predictions are slightly higher than these data for several heavy congeners (panels A, E, and F in Figure 1). Therefore, the Bamford et al. (13) HLC values do not appear to be too high for the heavy congeners, as has been claimed (57). There are consistently large deviations between all models and the data of Brunner et al. (11). If those data are excluded, the overall RMSE for each model using the remaining data (the black bars in Figure 2) indicates that the QM models best agree with the remaining data. The overall RMSE is lower for SM6 than for COSMO-SAC, which is not surprising since SM6 uses an empirical correction (∆GCDS), and SM6 is parametrized using HLC data, whereas COSMO-SAC does not rely on any HLC data. The QM values of the HLCs, and in particular, the SM6 values, are therefore recommended. Relationship between HLC and Degree of Chlorination (at 25 °C). The COSMO-SAC and SM6 models both predict an average increase in the HLC as the NCl (or equivalently, the molecular weight) increases (see the Supporting Information, A and B in Figure S1; Figure S1C shows data, for comparison). In both cases, significant variability within each homologue indicates that the HLC also depends strongly on other factors, a result consistent with most experimental data (8, 9, 13, 15, 16), as well as literature predictions (20, 29). As NCl increases, the increase in the COSMO-SAC value of γW outweighs the accompanying drop in Pvap (see the Supporting Information, Figure S1D; eq 2), resulting in the predicted NCl-dependence of the HLCs. Similarly, for SM6,

the GP value increases (becomes less negative) with increasing NCl by an amount greater than the combined decrease in ∆Eelec and ∆GCDS (see the Supporting Information, Figure S1E; eqs 1 and 3). The decrease in Pvap and ∆GCDS values with increasing NCl is at least partially attributable to the increasing molecular size, which is associated with both increasing strength of the dispersion interactions and increased energy costs for cavity formation. The increase in γW and the reduction in the magnitude of GP (|GP|) indicate that, as NCl increases, solute-solvent interactions become less favorable, on average, because of a decrease in stabilizing polarization effects. As a result, there is a greater tendency for the congener to partition into the gas phase. Polar solute-solvent interactions appear to play a principal role in determining the values of the HLCs. In particular, the very high SM6 HLC value for decachlorobiphenyl (PCB 209) results primarily from the small |GP| relative to the values for other congeners. To investigate these polarization effects, the SM6 |GP| values have been examined relative to the dipole moments for the optimized (B3LYP/6-31G(d,p)) structures. On average, |GP| increases (congener-water polar interactions become more favorable and HLC decreases) as the magnitude of the molecular dipole moment (“molecular dipole”) increases (see the Supporting Information, Figure S2), as expected. However, there is substantial variation in the GP values among the congeners that cannot be accounted for by differences in the molecular dipoles. For instance, 3,3′,4,4′,5,5′-hexachlorobiphenyl (PCB 169) and decachlorobiphenyl (PCB 209) both have zero molecular dipole moments due to their symmetric substitution patterns; however, their GP values are -12.0 and -1.3 kJ/mol, respectively. Some of this variation can be explained by the differences in local effects, which Schwarzenbach (28) believes are important in determining molecular interactions. Here, we define a “local dipole” for each ring as the magnitude of the dipole moment for a molecule with the same substitution pattern on one ring but connected to a phenyl ring with no chlorines. For example, the two local dipoles for 2,3′,4trichlorobiphenyl are taken to be the molecular dipoles of 2,4-dichlorobiphenyl and 3-chlorobiphenyl. The sum of the local dipoles for a congener is termed the “total local dipole”. In the case of PCB 169, the local dipoles are relatively strong, leading to enhanced PCB-water interactions. In contrast, PCB 209 lacks strong local dipoles because of the complete chlorination of both rings, which may explain the observed difference in GP. As a measure of the combined molecular and local effects, the average of the molecular dipole and the total local dipole (the “average dipole”) was calculated for each congener (see the Supporting Information, Figure S3 and Table S1). Within most homologues, SM6 predicts an average increase in |GP| as the average dipole increases, which is expected. However, in homologue 1, the average dipole for the three monosubstituted PCBs increases but |GP| decreases as the chlorine position changes from ortho to meta to para. This change in GP cannot be explained by the average dipoles. Within other homologues, the average dipoles account for much of the variation in GP, but other factors also appear to be important. In particular, as for homologue 1, substitution in the ortho position appears to lead to higher |GP| values. It is not clear why ortho-substitution may cause enhanced congener-water polar interactions, but this may relate to changes in the planarity of the biphenyl ring structure (see further discussion below). Relationship between HLC and Substitution Pattern (at 25 °C). SM6 predicts an average increase in HLC within each homologue as the number of ortho-chlorines increases (see the Supporting Information, Figure S4B). This trend (the

“ortho effect”) has also been widely reported in the literature (8, 9, 11, 13, 20). It has been postulated (8, 9, 13) that orthosubstitution leads to sterically hindered structures with reduced rotational freedom at the phenyl-phenyl bond, resulting in a highly noncoplanar arrangement of the phenyl rings that affects the PCB-water molecular interactions. To investigate this hypothesis, we examined the dihedral angle between the phenyl rings in the optimized (B3LYP/ 6-31G(d,p) structure for each congener in relation to the substitution pattern and the SM6 HLC prediction. The dihedral angles (see the Supporting Information, Table S1) are found to be between 37 and 90°, indicating that all congeners are most stable in a nonplanar conformation. This is consistent with experimental findings (58), and appears to be related to the smallest angle at which there is no overlap between adjacent ortho-atoms, reported elsewhere (20) as 39° for congeners with no ortho-substituents. The average angle increases systematically with increasing degree of ortho-chlorination (see the Supporting Information, Figure S5). Variability in angle of up to 12° for congeners with a fixed number of ortho-chlorines is the result of the specific substitution pattern. In particular, substitution in any two adjacent positions on the rings, and/or an uneven distribution of substituents between the rings leads to higher angles. As the angle increases, there is an average increase in the SM6 HLC predictions within each homologue (see the Supporting Information, Figure S6). This is related to the strong positive correlation between the SM6 ∆GCDS value and the angle (or number of ortho-chlorines) for congeners within a homologue (see the Supporting Information, Figure S7C). This result suggests that the ortho effect may be related to the reduced ability of sterically hindered congeners to undergo short-range interactions. However, there is substantial variability in the SM6 HLCs within a homologue that is not accounted for by changes in angle. This can be associated with differences in the ∆Eelec and GP terms (see the Supporting Information, Figure S7C), the sum of which is dominated by long-range solute-solvent interactions. Unlike the SM6 predictions, the ortho effect in the COSMO-SAC predicted HLCs occurs only within some homologues (see the Supporting Information, Figure S4A). The COSMO-SAC Pvap values increase (on average) with increasing ortho-substitution within every homologue (see the Supporting Information, Figure S7A), which is consistent with Pvap measurements (59, 60) and also the conclusions of Burkhard et al. (20). However, the ortho effect is not the dominant trend in the COSMO-SAC HLCs within all homologues since the contribution made by γW (see the Supporting Information, Figure S7B) is also important. Temperature Dependence of HLCs. The temperature dependence of the HLC is quantified by the enthalpy of solvation, ∆HS, that can be obtained from dln(HLC/(RT)) -∆HS ) dT RT2

(5)

where ∆HS is in J/mol. Integrating this equation, assuming ∆HS is constant over the temperature range of interest, yields ∆HS

) + constant ( HLC RT ) RT

ln

(6)

so that ∆HS is obtained from the slope of the linear regression of ln(HLC/RT) against 1/T. HLCs were predicted at 4, 11, 18, 25, and 31 °C using COSMO-SAC (see the Supporting Information, Table S1 and Figure S8). Similar calculations could not be performed with SM6 since this model is only for predictions at 25 °C, and its temperature-dependent extension, SM6T (61), cannot be applied to chlorine-containing compounds. For all congeners, VOL. 42, NO. 22, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

8415

FIGURE 3. Enthalpies of solvation for PCBs determined from HLC values at various temperatures. Experimental data: 3, ten Hulscher et al. (12); 9, Bamford et al. (13). Predictions from the literature: ], Burkhard et al. (20); +, Paasivirta et al. (37). Predictions from this work: •, COSMO-SAC. the COSMO-SAC HLCs increase with increasing temperature, indicating negative ∆HS values, as reported elsewhere (12, 13, 20, 37). COSMO-SAC predicts an increase in Pvap and a decrease in γW with increasing temperature (see the Supporting Information, Table S1). As expected, the temperature dependence of Pvap (average change of 878% per 25 °C) is much greater than that of γW (average change of 40.5% per 25 °C). Figure 3 compares the COSMO-SAC predictions for ∆HS (see the Supporting Information, Table S1) with values from the literature. In a separate evaluation for compounds that are structurally similar to PCBs, a RMSE of 7.2 kJ/mol was determined for the COSMO-SAC ∆HS values (see the Supporting Information, page S8, Figure S9, Table S3). The COSMO-SAC ∆HS values for all congeners differ from each other by less than 10 kJ/mol, indicating that the HLCs of all congeners have similar temperature dependences. Consequently, intercongener trends in the COSMO-SAC HLCs are essentially the same at each temperature. The Burkhard et al. (20) ∆HS values (based on HLC at 0, 15, 25, and 40 °C) likewise span a small range (less than 25 kJ/ mol). However, the COSMO-SAC ∆HS values are smaller in magnitude and have no systematic NCl-dependence, whereas the ∆HS values of Burkhard et al. (20) become more exothermic on average with increasing NCl. These discrepancies may in part be attributed to different treatment of the temperature dependence of γW in the two models. Burkhard et al. (20) used solubility measurements for PCB 4 and biphenyl at different temperatures to estimate an average temperature dependence of γW, taken to be the same for all congeners. Their estimate of a 28.8% decrease in γW between 0 and 25 °C is in good agreement with the COSMO-SAC predictions for PCB 4 (30.6% decrease in γW per 25 °C rise) and other monosubstituted congeners. However, COSMO-SAC predicts strong intercongener variation in the temperature dependence of γW, ranging from a change of 28.9-56.6% per 25 °C. The temperature dependence generally increases with increasing NCl. Underestimating the temperature dependence of γW would result in ∆HS values that are too highly exothermic. ten Hulscher et al. (12) experimentally determined values of ∆HS for three congeners that are similar to the COSMOSAC and Burkhard et al. (20) values. Paasivirta et al. (37) estimated the temperature dependence of the HLC for 11 congeners using an approach similar to that of Burkhard et al. (20), producing comparable results. Bamford et al. (13) reported ∆HS values for 26 congeners determined from the temperature dependence of the measured HLCs that vary from -14.5 to -167 kJ/mol. This large range and the highly negative ∆HS values for several of the 8416

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 22, 2008

heavier congeners are inconsistent with all other values in the literature. Bamford et al. (13) noted that the magnitude of ∆HS should approximate the difference between the enthalpy of vaporization (∆HVAP) and the enthalpy of solubilization (∆HSOL). However their seven most highly exothermic ∆HS values are greater in magnitude than the corresponding ∆HVAP values from the literature, suggesting ∆HSOL values that are more highly exothermic than those reported for any other organic compound (57). Goss et al. (57) pointed out that the Bamford et al. (13) data display a greater range of enthalpy values within a homologue than previously reported for any other set of closely related isomers. Goss et al. (57) proposed that the low temperature HLCs of Bamford et al. (13) may be erroneously high for some congeners as the result of enhanced PCB adsorption to the bubble surface at low temperatures. As temperature is reduced, agreement between the COSMO-SAC and Bamford et al. (13) HLCs at each temperature (see the Supporting Information, Figure S10) systematically worsens, supporting claims that the low temperature measurements are inaccurate. The greatest discrepancies appear in the low temperature measurements for the heavy congeners, for which the predicted COSMO-SAC HLC values are greater than the Bamford et al. (13) values. However, the mechanism proposed by Goss et al. (57) cannot explain the highly negative enthalpies determined by Bamford et al. (13) for the heavy congeners. Although Bamford et al. (62) have defended the accuracy of their data, the COSMO-SAC results together with other work in the literature strongly suggests that the Bamford et al. (13) HLC measurements are inaccurate at low temperatures.

Acknowledgments This research was funded by the National Institute of Environmental Health Sciences through a Superfund Basic Research Program Grant (5R01ES015444). KP is grateful to Shu Wang, Jeffrey Frey, Russell Burnett, Pei Chiu, and Patrick McMahon for assistance.

Supporting Information Available Table S1 lists the PCBs, all HLC values and other properties predicted by COSMO-SAC and SM6, as well as the dipoles and angles; Table S2 lists the RMSE values for log(HLC); Table S3 and Figure S9 contain the results from the evaluation of COSMO-SAC ∆HS values, discussed on page S8 (above the figure); Figure S1 shows the COSMO-SAC and SM6 property predictions as a function of NCl; Figure S2 shows the SM6 |GP| values versus the molecular dipoles; Figure S3 is a plot of |GP| as a function of the average dipole within a homologue; Figure S4 shows the COSMO-SAC and SM6 HLCs as a function of the number of ortho-chlorines for congeners within a homologue; Figure S5 shows the angle versus the number of ortho-chlorines; Figure S6 shows the SM6 HLC predictions as a function of the angle, within a homologue; Figure S7 comprises plots of Pvap, γW, ∆Eelec, GP, and ∆GCDS against the number of ortho-chlorines for congeners within a homologue; Figure S8 shows the COSMO-SAC predictions of selected HLCs at each temperature; and Figure S10 comprises cross plots of the COSMO-SAC predictions with the Bamford et al. (13) measurements of HLC at each temperature. Figures and discussion as PDF; tables in Excel format. This material is available free of charge via the Internet at http://pubs.acs.org.

Literature Cited (1) MacDonald, R. W.; Barrie, L. A.; Bidleman, T. F.; Diamond, M. L.; Gregor, D. J.; Semkin, R. G.; Strachan, W. M.; Li, Y. F.; Wania, F.; Alaee, M.; et al. Contaminants in the Canadian Arctic: 5 years of progress in understanding sources, occurrence and pathways. Sci. Total Environ. 2000, 254 (2-3), 93–234.

(2) Atlas, E.; Foster, R.; Glam, C. S. Air-sea exchange of high molecular weight organic pollutants: laboratory studies. Environ. Sci. Technol. 1982, 16 (5), 283–286. (3) Murphy, T. J.; Pokojowczyk, J. C.; Mullin, M. D., Vapor exchange of PCBs with Lake Michigan: the atmosphere as a sink for PCBs. In Physical Behavior of PCBs in the Great Lakes; Mackay, D., Paterson, S., Eisenreich, S. J., Simmons, M. S., Eds.; Ann Arbor Science: Ann Arbor, MI, 1983; pp 49-58. (4) Coates, J. T. Sorption equilibria and kinetics for selected polychlorinated biphenyls on river sediments. PhD Thesis. Clemson University, Clemson, SC, 1984. (5) Hassett, J. P.; Milicic, E. Determination of equilibrium and rate constants for binding of a polychlorinated biphenyl congener by dissolved humic substances. Environ. Sci. Technol. 1985, 19 (7), 638–643. (6) Oliver, B. G. Desorption of chlorinated hydrocarbons from spiked and anthropogenically contaminated sediments. Chemosphere 1985, 14 (8), 1087–1106. (7) Murphy, T. J.; Mullin, M. D.; Meyer, J. A. Equilibration of polychlorinated biphenyls and toxaphene with air and water. Environ. Sci. Technol. 1987, 21 (2), 155–162. (8) Dunnivant, F. M.; Coates, J. T.; Elzerman, A. W. Experimentally determined Henry’s law constants for 17 polychlorobiphenyl congeners. Environ. Sci. Technol. 1988, 22 (4), 448–453. (9) Dunnivant, F. M.; Elzerman, A. W. Aqueous solubility and Henry’s law constant data for PCB congeners for evaluation of quantitative structure-property relationships (QSPRs). Chemosphere 1988, 17 (3), 525–541. (10) Fendinger, N. J.; Glotfelty, D. E. Henry’s law constants for selected pesticides, PAHs and PCBs. Environ. Toxicol. Chem. 1990, 9 (6), 731–735. (11) Brunner, S.; Hornung, E.; Santl, H.; Wolff, E.; Piringer, O. G.; Altschuh, J.; Bruggemann, R. Henry’s law constants for polychlorinated biphenyls: experimental determination and structure-property relationships. Environ. Sci. Technol. 1990, 24 (11), 1751–1754. (12) ten Hulscher, T. E. M.; van der Velde, L. E.; Bruggeman, W. A. Temperature dependence of Henry’s law constants for selected chlorobenzenes, polychlorinated biphenyls and polycyclic aromatic hydrocarbons. Environ. Toxicol. Chem. 1992, 11 (11), 1595–1603. (13) Bamford, H. A.; Poster, D. L.; Baker, J. E. Henry’s law constants of polychlorinated biphenyl congeners and their variation with temperature. J. Chem. Eng. Data 2000, 45 (6), 1069–1074. (14) Bamford, H. A.; Poster, D. L.; Huie, R. E.; Baker, J. E. Using extrathermodynamic relationships to model the temperature dependence of Henry’s law constants of 209 PCB congeners. Environ. Sci. Technol. 2002, 36 (20), 4395–4402. (15) Fang, F.; Chu, S. G.; Hong, C. S. Air-water Henry’s law constants for PCB congeners: experimental determination and modeling of structure-property relationship. Anal. Chem. 2006, 78 (15), 5412–5418. (16) Lau, F. K.; Charles, M. J.; Cahill, T. M. Evaluation of gas-stripping methods for the determination of Henry’s law constants for polybrominated diphenyl ethers and polychlorinated biphenyls. J. Chem. Eng. Data 2006, 51 (3), 871–878. (17) ten Hulscher, T. E. M.; van den Heuvel, H.; van Noort, P. C. M.; Govers, H. A. J. Henry’s law constants for eleven polychlorinated biphenyls at 20°C. J. Chem. Eng. Data 2006, 51 (2), 347–351. (18) Westcott, J. W.; Bidleman, T. F. Determination of polychlorinated biphenyl vapor pressures by capillary gas chromatography. J. Chromatogr., A 1981, 210 (2), 331–336. (19) Westcott, J. W.; Simon, C. G.; Bidleman, T. F. Determination of polychlorinated biphenyl vapor pressures by a semimicro gas saturation method. Environ. Sci. Technol. 1981, 15 (11), 1375– 1378. (20) Burkhard, L. P.; Armstrong, D. E.; Andren, A. W. Henry’s law constants for the polychlorinated biphenyls. Environ. Sci. Technol. 1985, 19 (7), 590–596. (21) Hawker, D. W. Vapor pressures and Henry’s law constants of polychlorinated biphenyls. Environ. Sci. Technol. 1989, 23 (10), 1250–1253. (22) Sabljic´, A.; Gu ¨ sten, H. Predicting Henry’s law constants for polychlorinated biphenyls. Chemosphere 1989, 19 (10-11), 1503–1511. (23) Dunnivant, F. M.; Elzerman, A. W.; Jurs, P. C.; Hasan, M. N. Quantitative Structure Property Relationships for Aqueous Solubilities and Henry’s Law Constants of PolychlorinatedBiphenyls. Environ. Sci. Technol. 1992, 26 (8), 1567–1573.

(24) Li, A.; Doucette, W. J.; Andren, A. W. Estimation of aqueous solubility, octanol/water partition coefficient, and Henry’s law constant for polychlorinated biphenyls using UNIFAC. Chemosphere 1994, 29 (4), 657–669. ¨ berg, T. Prediction of physical properties for PCB congeners (25) O from molecular descriptors. Internet J. Chem. 2001, 4 (11). (26) Wang, X. D.; Tang, S. L.; Liu, S. S.; Cui, S. H.; Wang, L. S. Molecular hologram derived quantitative structure-property relationships to predict physico-chemical properties of polychlorinated biphenyls. Chemosphere 2003, 51 (7), 617–632. (27) Li, N. Q.; Wania, F.; Lei, Y. D.; Daly, G. L. A comprehensive and critical compilation, evaluation, and selection of physicalchemical property data for selected polychlorinated biphenyls. J. Phys. Chem. Ref. Data 2003, 32 (4), 1545–1590. (28) Schwarzenbach, R. P.; Gschwend, P. M.; Imboden, D. M., Environmental Organic Chemistry, 2nd ed.; John Wiley & Sons: Hoboken, NJ, 2003. (29) Abraham, M. H.; Al-Hussaini, A. J. M. Solvation parameters for the 209 PCBs: calculation of physicochemical properties. J. Environ. Monit. 2005, 7 (4), 295–301. (30) Schenker, U.; MacLeod, M.; Scheringer, M.; Hungerbuhler, K. Improving data quality for environmental fate models: a leastsquares adjustment procedure for harmonizing physicochemical properties of organic compounds. Environ. Sci. Technol. 2005, 39 (21), 8434–8441. (31) Karickhoff, S. W.; Carreira, L. A.; Hilal, S. H. SPARC, version 3.1 (January 2006); http://ibmlc2.chem.uga.edu/sparc/. (32) Karickhoff, S. W.; McDaniel, V. K.; Melton, C.; Vellino, A. N.; Nute, D. E.; Carreira, L. A. Predicting chemical reactivity by computer. Environ. Toxicol. Chem. 1991, 10 (11), 1405–1416. (33) Hilal, S. H.; Carreira, L. A.; Karickhoff, S. W.; Melton, C. M. Estimation of gas-liquid chromatographic retention times from molecular structure. J. Chromatogr. A 1994, 662 (2), 269–280. (34) Hilal, S. H.; Karickhoff, S. W.; Carreira, L. A. Prediction of the vapor pressure boiling point, heat of vaporization and diffusion coefficient of organic compounds. QSAR Comb. Sci. 2003, 22 (6), 565–574. (35) Hilal, S. H.; Karickhoff, S. W.; Carreira, L. A. Prediction of the solubility, activity coefficient and liquid/liquid partition coefficient of organic compounds. QSAR Comb. Sci. 2004, 23 (9), 709–720. (36) Hilal, S. H.; Saravanaraj, A. N.; Whiteside, T.; Carreira, L. A. Calculating physical properties of organic compounds for environmental modeling from molecular structure. J. Comput. Aided Mol. Des. 2007, 21 (12), 693–708. (37) Paasivirta, J.; Sinkkonen, S.; Mikkelson, P.; Rantio, T.; Wania, F. Estimation of vapor pressures, solubilities and Henry’s law constants of selected persistent organic pollutants as functions of temperature. Chemosphere 1999, 39 (5), 811–832. (38) Lin, S. T.; Sandler, S. I. A priori phase equilibrium prediction from a segment contribution solvation model. Ind. Eng. Chem. Res. 2002, 41 (5), 899–913. (39) Lin, S. T.; Chang, J.; Wang, S.; Goddard, W. A.; Sandler, S. I. Prediction of vapor pressures and enthalpies of vaporization using a COSMO solvation model. J. Phys. Chem. A 2004, 108 (36), 7429–7439. (40) Wang, S.; Sandler, S. I.; Chen, C.-C. Refinement of COSMO-SAC and the applications. Ind. Eng. Chem. Res. 2007, 46 (22), 7275– 7288. (41) Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. SM6: a density functional theory continuum solvation model for calculating aqueous solvation free energies of neutrals, ions, and solute-water clusters. J. Chem. Theory Comput. 2005, 1 (6), 1133–1152. (42) Klamt, A.; Schu ¨u ¨rmann, G. COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. J. Chem. Soc., Perkin Trans. 2 1993, (5), 799–805. (43) Klamt, A. COSMO-RS: from Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design; Elsevier Science: Amsterdam, 2005. (44) Cerius2: DMol3, version 4.6, revision 01.0602; Accelrys Software Inc.: San Diego, CA, 2001. (45) Klamt, A. Conductor-like screening model for real solvents: a new approach to the quantitative calculation of solvation phenomena. J. Phys. Chem. 1995, 99 (7), 2224–2235. (46) Klamt, A.; Jonas, V.; Burger, T.; Lohrenz, J. C. W. Refinement and parametrization of COSMO-RS. J. Phys. Chem. A 1998, 102 (26), 5074–5085. (47) Thompson, J. D.; Kelly, C. P.; Lynch, B. J.; Xidos, J. D.; Li, J.; Hawkins, G. D.; Zhu, T.; Volobuev, Y.; Dupuis, M.; Rinaldi, D.; et al. SMXGAUSS, version 3.3; University of Minnesota: Minneapolis, 2006. VOL. 42, NO. 22, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

8417

(48) Cramer, C. J.; Truhlar, D. G., SMx continuum models for condensed phases In Trends and Perspectives in Modern Computational Science, Lecture Series on Computer and Computational Sciences, Maroulis, G., Simos, T. E., Eds.; Brill Academic: Amsterdam, 2006; Vol. 6, pp 112-140. (49) Barney, J., Table of PCB Species by Congener Number, 2003; www.epa.gov/toxteam/pcbid/(Accessed Online 2006). (50) Dennington II, R.; Keith, T.; Millam, J.; Eppinnett, K.; Hovell, W. L.; Gilliland, R. GaussView, Version 3.09; Semichem, Inc.: Shawnee Mission, KS, 2003. (51) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, Revision B.05; Gaussian, Inc.: Wallingford, CT, 2004. (52) Wang, S. Thermodynamic properties predictions using the COSMO-SAC solvation method. PhD Thesis, University of Delaware, Newark, DE, 2007. (53) Case, D. A., III; Simmerling, C. L.; Wang, J.; Duke, R. E.; Luo, R.; Merz, K. M.; Wang, B.; Pearlman, D. A.; et al. AMBER, version 8; University of California: San Francisco, 2004. (54) Cerius 2 Quantum Chemistry. Accelrys Software: San Diego, CA, December 1998. (55) Mullins, E.; Oldland, R.; Liu, Y. A.; Wang, S.; Sandler, S. I.; Chen, C. C.; Zwolak, M.; Seavey, K. C. Sigma-profile database for using COSMO-based thermodynamic methods. Ind. Eng. Chem. Res. 2006, 45 (12), 4389–4415. (56) Mackay, D.; Shiu, W. Y.; Ma, K. C., Illustrated Handbook of Physical-Chemical Properties and Environmental Fate for

8418

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 22, 2008

(57)

(58) (59)

(60)

(61) (62)

Organic Chemicals; Lewis Publishers: Chelsea, MI, 1992; Vol. 1. Goss, K. U.; Wania, F.; McLachlan, M. S.; Mackay, D.; Schwarzenbach, R. P. Comment on “Reevaluation of air-water exchange fluxes of PCBs in Green Bay and Southern Lake Michigan”. Environ. Sci. Technol. 2004, 38 (5), 1626–1628. McKinney, J. D.; Singh, P. Structure-activity relationships in halogenated biphenyls: unifying hypothesis for structural specificity. Chem. Biol. Interact. 1981, 33 (2-3), 271–283. Falconer, R. L.; Bidleman, T. F. Vapor pressures and predicted particle/gas distributions of polychlorinated biphenyl congeners as functions of temperature and ortho-chlorine substitution. Atmos. Environ. 1994, 28 (3), 547–554. Nakajoh, K.; Shibata, E.; Todoroki, T.; Ohara, A.; Nishizawa, K.; Nakamura, T. Measurement of temperature dependence for the vapor pressures of twenty-six polychlorinated biphenyl congeners in commercial Kanechlor mixtures by the Knudsen effusion method. Environ. Toxicol. Chem. 2006, 25 (2), 327– 336. Chamberlin, A. C.; Cramer, C. J.; Truhlar, D. G. Predicting aqueous free energies of solvation as functions of temperature. J. Phys. Chem. B 2006, 110 (11), 5665–5675. Baker, J. E.; Totten, L. A.; Gigliotti, C. L.; Offenberg, J. H.; Eisenreich, S. J.; Bamford, H. A.; Huie, R. E.; Poster, D. L. Response to Comment on “Reevaluation of air-water exchange fluxes of PCBs in Green Bay and Southern Lake Michigan”. Environ. Sci. Technol. 2004, 38 (5), 1629–1632.

ES800876W