Vapor Pressures of the Fluorinated Telomer AlcoholsLimitations of

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Environ. Sci. Technol. 2004, 38, 1693-1699

Vapor Pressures of the Fluorinated Telomer AlcoholssLimitations of Estimation Methods NAOMI L. STOCK,† DAVID A. ELLIS,† LISA DELEEBEECK,† DEREK C. G. MUIR,‡ AND S C O T T A . M A B U R Y * ,† Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6 Canada, and National Water Institute, Environment Canada, Burlington, Ontario, L7R 4A6 Canada

The influence of the unique, physical properties of polyand perfluorinated chemicals on vapor pressure was investigated. Vapor pressures of a suite of fluorinated telomer alcohols (FTOHs) (CF3(CF2)nCH2CH2OH, where n ) 3, 5, 7, or 9) were measured using the boiling point method and ranged from 144 to 992 Pa. Comparison of experimental and literature values indicate that perfluorocarbons (CF3(CF2)nCF3 , where n ) 0-6) and fluorinated telomer alcohols have vapor pressures equal to or greater than that of their hydrogen analogues. These chemically counterintuitive results can be explained by the unique geometry of poly- and perfluorinated chemicalssin particular the stiff, helical perfluorinated chain and the significant intramolecular hydrogen bonding of the FTOHs. The majority of models investigated for the estimation of vapor pressure did not compensate for this unique geometry and consistently underpredicted the vapor pressures of the FTOHs. Calculation of partitioning constants using both experimental and estimated vapor pressures indicate that both the Antoine and Modified Grain models, and to a lesser degree the Mackay model, are insufficiently accurate for estimating the vapor pressures of the FTOHs, particularly the longer chain FTOHs. Future models should consider parameters such as geometry, strength, and location of intramolecular hydrogen bonds and other function groups in the molecule in order to improve vapor pressure estimation accuracy. It appears likely that the unique molecular geometry of the FTOHs influences not only their vapor pressure but also other physical properties and hence environmental fate and dissemination.

Introduction In April 2003, the United States Environmental Protection Agency (U.S. EPA) announced a Request for Comment on their intention to investigate the environmental fate and transport of several emerging environmental contaminants (1). The contaminants of particular interest to the U.S. EPA being perfluorooctanoate (CF3(CF2)6COO-)(PFOA), which has potential human health concerns, and the fluorinated telomer alcohols (CF3(CF2)nCH2CH2OH where typically n ) an odd * Corresponding author phone: (416)978-1780; fax: (416)978-3596; e-mail: [email protected]. † University of Toronto. ‡ National Water Institute, Environment Canada. 10.1021/es034773+ CCC: $27.50 Published on Web 02/05/2004

 2004 American Chemical Society

number)(FTOHs), that may metabolize or degrade to PFOA. This Request for Comment follows a preliminary risk assessment of PFOA completed by the U.S. EPA, in an attempt to resolve the substantial uncertainties associated with the initial risk assessment (1). The FTOHs and PFOA are examples of a large chemical class known as poly- and perfluorinated chemicalsswhere some or all hydrogens in the molecule are replaced with fluorine. Uses of poly- and perfluorinated chemicals are widespread with a multitude of applications ranging from agrochemicals to blood substitutes, cookware coatings to refrigerants, fire-fighting foams to lubricants, and many other industrial applications. In fact, it appears that fluorinecontaining organic chemicals are used on a daily basis by everyone in the developed world (2). Interest in these chemicals, from an environmental standpoint, has been steadily increasing as observed in the growing body of literature and the U.S. EPA’s decision for further evaluation (1, 3-6). The popularity of poly- and perfluorinated chemicals is primarily due to their unique propertiessthermal stability, resistance to chemical degradation, UV radiation and the weather, and in the case of poly- and perfluorinated surfactants, repellency to water and oils. Although these properties are beneficial from an industrial standpoint, the same properties can result in recalcitrant, accumulative, and persistent environmental contaminants (7). Many of the unique physical properties of poly- and perfluorinated chemicals, and those which govern its dissemination in the environment, are explained by the molecular structure and geometry of these compounds. Fluorine is the most electronegative element (8) and as such has a high ionization potential and very low polarizability (9, 10). The large difference in electronegativity between carbon and fluorine results in a strong polarization of the carbon-fluorine bond. The carbon-fluorine single bond is also the strongest observed in organic chemistry, ∼484 kJ/mol. This strength increases with increasing fluorination and has been reported as high as 531 kJ/mol in terminal CF3 groups (11). The unusual strength of the carbon-fluorine bond contributes to the thermal and chemical stability of poly- and perfluorinated chemicals (7). Although fluorine atoms are small, they are significantly larger than hydrogen atoms (van der Waal radii of 1.47 Å and 1.20 Å respectively). As a result, perfluorinated chains are stiffer, bulkier, and more infexible than their hydrogenated counterparts (12), and the electron cloud of the densely packed fluorine atoms forms a repellent sheath around the carbon backbone resulting in a rigid rodlike structure. To minimize steric hindrance, the geometry of perfluorinated compounds changes as chain length increases, particularly at chain lengths of 8-12 carbons (13). When the perfluorinated chain is eight or less carbons in length, the molecule assumes a zigzag conformation; however, the molecule is both zigzag and helical when the chain is 10 carbons in length and completely helical when the chain length increases to 12 or more carbon atoms (13-15). It would appear that the exact geometric nature of fluorinated chemicals is strongly dependent upon the physical state, either gas, liquid, or solid (14, 16). This unique geometry and molecular structure is unlike anything currently known in nature and also contributes to the stability and resistance of poly- and perfluorinated chemicals (7). It appears that fluorine substituents elicit different kinds of electronic effectsseither net stabilization or destabilization of the moleculeswhich depending on the situation may counterbalance or amplify each other. For example, some organofluorine compounds are nonpolar solvents while VOL. 38, NO. 6, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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others are extremely polar (10). Similarly, R-fluorination increases the bond strengths of carbon-fluorine and carbonoxygen bonds but does not alter the strength of carbonhydrogen bonds, while β-fluorination significantly decreases carbon-hydrogen bond strengths but has little effect on carbon-fluorine bonds (17). The unpredictability of the influence of fluorine is also evident when examining physical properties such as vapor pressure (as will be discussed in this investigation), acidity, and octanol-water partitioning (KOW). For example, the amino acids alanine and R-fluoroalanine have nearly identical pKa values, whereas trifluoroalanine is a fairly strong acid (18). Increasing fluorination of benzene from mono- to hexafluorobenzene appears to have little effect on the KOW values (19). An important parameter governing a chemicals tendency for transport and dissemination in the environment is its vapor pressure. For example, vapor pressure heavily influences whether a chemical will volatilize from soil or water and whether a chemical will occur as a free molecule in the atmosphere or will be associated with particulate matter. When vapor pressure measurements are not available, they are often predicted using a wide variety of estimation methods. Many vapor pressure estimation methods have been derived using adaptations of the Clausius-Clapeyron equation. These include such models as those by Lee and Kesler (20), Gomez-Nieto and Thodos (21), Mackay et al. (22), Grain (23), and Mydral and Yalkowsky (24). The differences between these estimation methods are a result of the assumptions made in their derivations. Methods derived from the Clausis-Clapeyron equation typically require the input of physical-chemical properties such as boiling, critical and/or melting points and molecular weight. As such, the prediction accuracy of these methods is dependent on the accuracy and availability of these required inputs. A second class of vapor pressure estimation methods is those that are structure-based and use fragment or group contribution calculations (such as universal functional group activity coefficients (UNIFAC)). These include such models as those by Jenson et al. (25), Joback and Reid (26), and Banerjee (27). More recently, Simmons developed a simple structure-based calculator for estimating vapor pressure (28), Staikova et al. (29) used a quantitative structure-property relationship (QSPR) to estimate vapor pressures of halogenated chemicals, and Asher et al. (30) compared the accuracy of vapor pressures estimated using UNIFAC calculations to those obtained using other vapor pressure estimation methods. An advantage of group contribution or structurebased models is that typically they do not require the input of boiling points and other physical-chemical properties of the compounds of interest (30). In light of the U.S. EPA’s interest in the environmental fate of several poly- and perfluorinated chemicals, the first goal of this investigation was to determine experimentally, the vapor pressures of the FTOHs. The second goal of this investigation was to compare these vapor pressures to those predicted using four common estimation models. Finally, using vapor pressure as an example, this investigation alerts future researchers to possible problems in modeling physical properties of the FTOHs.

Experimental Section Chemicals. The 4:2, 6:2, 8:2, and 10:2 FTOHs (all 97%) were both purchased from Oakwood Research Chemicals (West Columbia, SC) and donated by Dupont (Wilmington, DE). Cyclohexane (99.5%) was purchased from the Aldrich Chemical Co. (Milwaukee, WI). As it is well-known that fluorinated chemicals have high gas-dissolving capacities (31) all FTOHs were degassed via a freeze-thaw process, prior to obtaining vapor pressure measurements. 1694

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Vapor Pressure Measurements. Measurements of vapor pressures, at 25 °C, of the perfluorocarbons (CF3(CF2)nCF3, where n ) 0-6), hydrocarbons (CH3(CH2)nCH3, where n ) 0-6), and hydrogenated alcohols (CH3(CH2)nCH2CH2OH, where n ) 3, 5, 7, or 9) were obtained from the literature (32-34) and appear to be representative of the range of vapor pressures in the literature for these classes of compounds. Vapor pressures of the FTOHs (CF3(CF2)nCH2CH2OH where n ) 3, 5, 7, or 9) were measured using the boilingpoint method as previously outlined (35, 36), most recently in the U.S. EPA Test Guidelines for vapor pressure (37). Briefly, the analyte of interest was heated in a 2-headed Claissen flask, under vacuum, and equipped with a thermometer and reflux condenser. Pressure above the liquid was maintained with a large volume ballast bulb and measured using an electronic manometer (Pressure Transducer Type 122A, MKS Instruments, Andover, MA). The analyte was heated until steady boiling was observed at which point both temperature and pressure were recorded. To test the accuracy of the boiling point method, the vapor pressure of a reference standard, cyclohexane, was measured in triplicate (1.62 × 104 Pa ( 0.27 × 104 Pa), compared to the well-established literature value (1.29 × 104 Pa) (32, 33), and an acceptable percent difference (25.6%) was calculated. Ten pairs of temperature/ pressure readings were taken for all analytes, and experiments were repeated in triplicate. Recorded temperatures ranged from 50 to 125 °C (for the 4:2 FTOH) to 140 to 225 °C (for the 10:2 FTOH). Using linear regression, a value for the vapor pressure of each FTOH at 25 °C was calculated. The boiling point method has been recommended by the U.S. EPA for measuring the vapor pressures of both solids and liquids in the range of 10-105 Pa. (37). Vapor Pressure Prediction Models. Four models were used in this investigation to estimate the vapor pressures of the perfluorocarbons, the FTOHs, and their respective hydrogen analogues. These models were selected based on their ease of use. In addition, three of the four models (the Antoine, Modified Grain, and Mackay methods) are routinely used by environmental science professionals as they are available for download free of charge from the U.S. EPA Web site. Complete details of these models have previously been described (22, 23, 28, 38, 39) and are discussed briefly here. The Simmons Method (28) is a fragment-based approach that predicts the vapor pressure of a compound using structure and melting point in the following relationship

log P ) Σai / fi - 1.56(Tm - 25)/100 + 4.42

(1)

where P is the vapor pressure, ai is the regression coefficient for the ith fragment, fi is the number of times the ith fragment occurs, and Tm is the melting point (for the Simmons method Tm is assumed to be 25 °C if the chemical is a liquid at 25 °C). This method is appropriate for both liquid and solid species and was constructed using 1410 organic compounds described by 94 functional groups, including several fluorinated fragments X-F, X-CF3, and X-CF2R. The Simmons method also accounts for intramolecular H-bonding. Validation of this estimation method by Simmons (28) using a suite of 20 compounds, indicated variance between experimental and predicted values (r2) was 0.98 and mean error of prediction was 0.57 log P units. The Mackay Method (22, 38) uses the following adaptation of the Clausius-Clapeyron equation to predict vapor pressure

ln P ) -(4.4 + ln Tb)[1.803(Tb/T - 1) 0.803 ln (Tb/T)] - 6.8(Tm/T - 1) (2) where P and Tm have the same meaning as above, Tb is the boiling point, and T is the temperature at which the vapor pressure is estimated. The final term of the equation is ignored

TABLE 1. Vapor Pressures, at 25 °C, of the FTOHs Determined Using the Boiling-Point Method

FTOH

vapor pressure (Pa)

relative SD (%)

4:2 6:2

992 713

3.3 8.8

FTOH

vapor pressure (Pa)

relative SD (%)

8:2 10:2

254 144

6.3 7.6

for chemicals that are solids at room temperature. The Mackay method was originally derived using both aliphatic and aromatic hydrocarbons and halogenated compounds; however, it is “not unreasonable to think that [this model] might also work for other classes of chemicals” (38). Validation of the Mackay model using a 72-chemical test set of hydrocarbons and halocarbons indicated a mean error of 0.096 ln P units. The Antoine Method by Grain (23) predicts vapor pressures using the following modified version of the ClausiusClapeyron equation

FIGURE 1. Vapor pressures of perfluorocarbons and hydrocarbons versus carbon number.

ln P ) [(∆H(Tb - C2)2)/( ∆Z / R / Tb2)][1/(Tb - C2) 1/(T - C2)] (3) where P, Tb, and T have the same meaning as above, ∆Z is a compressibility factor and assumed to be 0.97, and R is the ideal gas constant. The constant C2 and the heat of vaporization ∆H are evaluated using eqs 4 and 5, respectively

C2 ) -18 + 0.19 Tb

(4)

∆H ) KF(8.75 + R ln Tb)

(5)

where KF is a Fishtine constant (40) and accounts for the dipole moment of the chemical of interest. Estimated Fishtine constants for the perfluorocarbons, FTOHs, and their hydrogen analogues are available in the Supporting Information, Table 1 (40). A comparison of experimental values versus vapor pressures predicted with the Antoine method found mean errors of 2.7 and 26% for vapor pressures in the ranges of 1-100 kPa and 10-3-1 kPa, respectively (39). Similar to the Mackay method, the Modified Grain Method (23, 38) also predicts vapor pressure using an adaptation of the Clausius-Clapeyron equation

ln P ) [(KF ln(RTb))/∆Z][1 - ((3-2Tp)m/Tp) 2m(3-2Tp)m-1 ln Tp] (6) where P, KF, R, Tb, and ∆Z have the same meaning as above and Tp ) T/Tb. The constant m is evaluated using eq 7 below:

m ) 0.4133 -0.2575 Tp

(7)

A comparison of experimental values versus vapor pressures predicted with the Modified Grain method found mean errors of 2.5, 38.7, and 46.9% for vapor pressures in the ranges of 1-100 kPa, 10-3-kPa, and 10-7-10-3 kPa, respectively (39). To ensure maximum accuracy in the vapor pressures predicted by all four models, experimental boiling points and melting points (for solid chemicals) (32-34) were used in all calculations. These values can be found in Table 1S of the Supporting Information. Estimated Fistine constants (KF) required for both the Antoine and Modified Grain method are also found in Table 1S of the Supporting Information. It is important to note, as discussed previously, that the accuracy of all vapor pressure estimates is dependent on the accuracy of these required input values. The Antoine, Modified Grain, and Mackay methods were downloaded free of charge from the U.S. EPA Web site in the program

FIGURE 2. Vapor pressures of the FTOHs, determined using the boiling-point method. MPBPWIN, version 1.40. All vapor pressure predictions were calculated at 25 °C and were evaluated by comparing to experimental vapor pressures. Variance between experimental and predicted values (r2) and mean error were calculated for each class of compound and model.

Results and Discussion Perfluorocarbons versus Hydrocarbons. Both perfluorocarbons and hydrocarbons are classes of volatile compounds. Vapor pressures (at 25 °C) range from 4.46 × 102 to 3.34 × 106 Pa for the perfluorocarbons and from 1.88 × 103 to 4.20 × 106 Pa for the hydrocarbons (Figure 1). For both classes of compounds, vapor pressure decreases with increasing carbon chain length and molecular weight. Vapor pressures of the perfluorocarbons and hydrocarbons are similar despite the large difference in molecular mass between two classes of compounds. This similarity in vapor pressure of perfluorocarbons and hydrocarbons is due to the fact that both classes of chemicals are nonpolar substances having essentially no permanent molecular dipole moment. As such the primary molecular attractive forces contributing to the vapor pressures of both perfluorocarbons and hydrocarbons are London dispersion forces (41). Polyfluorinated versus Hydrogenated Alcohols. Results obtained using the boiling-point method indicate that the FTOHs are volatile chemicals. Experimental pressure and temperature measurements are illustrated in Figure 2, and extrapolated vapor pressures, at 25 °C, range from 144 Pa (10:2 FTOH) to 992 Pa (4:2 FTOH) (Table 1). The vapor pressure measured is that of the liquids for the 4:2 and 6:2 FTOH and that of the subcooled liquid for the 8:2 and 10:2 FTOHs. These vapor pressures agree, with an average difference of 37%, to those obtained for the FTOHs by Lei et al. using the gas chromatography method (42). These vapor pressures also agree with the observation of the FTOHs being predominately in the gas phase in environmental tropospheric monitoring investigations (43, 44). The vapor pressure obtained in both this investigation and that of Lei et al. (42) for the 8:2 FTOH was approximately 100 times greater than that obtained by Berti (45) using the gas saturation method. The hydrogen analogues of the FTOHs are less volatile compounds, with vapor pressures ranging from 1.00 × 10-3 VOL. 38, NO. 6, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Vapor pressures of FTOHS and hydrogenated alcohols versus carbon number.

FIGURE 4. Structure of the 8:2 FTOH, indicating intramolecular hydrogen bonding. Pa (dodecanol, the hydrogen analogue of the 10:2 FTOH) to 1.24 × 102 Pa (hexanol, the hydrogen analogue of the 4:2 FTOH) (Figure 3). Similar to the trend observed with perfluorocarbons and hydrocarbons, the vapor pressures of the FTOHs and their hydrogen analogues decrease with increasing carbon chain length and molecular weight. It is important to note that the volatility of both the FTOHs and their hydrogen analogues is significantly less than that of the perfluorocarbons and hydrocarbons discussed above. This decrease in volatility is due to the addition of the polar -OH functional group that creates a dipole in the molecule and can participate in H-bonding. It is surprising to note that although the perfluorocarbons and hydrocarbons have very similar vapor pressures (Figure 1), the FTOHs have much larger vapor pressures than that of their hydrogen analogues (Figures 3). This apparent increase in vapor pressure of the FTOHs is chemically counterintuitive. One would expect the degree of hydrogen bonding between molecules to increase upon fluorination due to enhanced polarization of the -OH functional group, resulting in a relative decrease in vapor pressure. As this is not the case, it leads to the conclusion that the -OH functional group must be “masked” from other molecules and therefore the vapor pressure of the FTOHs increased. This increase in vapor pressure of the FTOHs also supports the hypothesis that there is electronic repulsion between molecules due to the negative sheath of fluorine atoms surrounding the carbon tail. The high vapor pressures of the FTOHs can be explained by the unique geometry of this class of compounds. Previous X-ray crystallography studies (13, 46) indicated that there is significant intramolecular hydrogen bonding that occurs in the FTOHs. In particular, it is believed that the hydrocarbon portion of the FTOH is back-bonded onto the perfluorocarbon portion of the molecule as illustrated in Figure 4. In addition, a 17O NMR study, conducted by Von Werner and Wrackmeyer (46), indicated that the electron density observed at the oxygen was increased through the oxygen shielding effect, strongly suggesting that the terminal ethanolic group is closely associated with the perfluorocarbon portion of the molecule. The intermolecular hydrogen bonding of FTOHs, observed in X-ray crystallography and NMR studies, was also confirmed using mass spectrometry. Studies (16, 47) investigating the fragmentation processes of several polyfluorinated chemicals, including the FTOHs, observed a loss of HF, indicating an H- - - -F bridging interaction and again drawing the conclusion that the hydrocarbon portion of the molecule folds back on top of the perfluorocarbon portion of the molecule and is held in position via hydrogen bonding. It is hypothesized that as the perfluorinated portion of the FTOH molecule increases in length, and hence becomes 1696

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FIGURE 5. Vapor pressure (at 25 °C), KOW, and Henry’s Law constants (at 11 °C) of the rigid PCB congeners (congeners with four and three ortho-chlorines) versus flexible PCB congeners (congeners with less than three ortho-chlorines). Error bars are standard deviation and account for the different electronic effects in each congener. (Henry’s Law constants at 11 °C for the rigid congeners of tetrachlorobiphenyl are unavailable in the literature.) more rigid, the strength of the hydrogen bonding also increases. This may explain why the difference in vapor pressure between the FTOHs and the hydrogenated alcohols increases with increasing carbon chain length and molecular weight. For example, the vapor pressure of the 4:2 FTOH is nearly 10 times greater than the vapor pressure of hexanol, while the vapor pressure of the 10:2 FTOH is more than 1000 times greater than that of dodecanol (Figure 3). Increases in vapor pressure, due to molecular rigidity, are not limited to polyfluorinated chemicals. For example, the molecular rigidity of the polychlorinated biphenyls (PCBs) increases with the number of ortho-chlorines present. Congeners with four ortho-chlorines have no free-rotation around the carbon-carbon bond and are held rigid, while congeners with no ortho-chlorines are flexible with complete free-rotation. Referred to as the “ortho-effect”, higher vapor pressures have been observed for those PCB congeners having greater numbers of ortho-chlorines (48) and, hence, greater molecular rigidity. As illustrated in Figure 5, the mean vapor pressures of the rigid congeners (congeners with four or three ortho-chlorines) is consistently greater than the mean vapor pressures of the flexible congeners (congeners with less than three ortho-chlorines). The ortho-effect is not limited to vapor pressuresmolecular rigidity also influences other physical properties of PCBs. As illustrated in Figure 5, the mean Henry’s Law constant of rigid congeners is consistently larger

TABLE 2. Mean Error (ln Pa) (Top) and Variance between Experimental and Predicted Vapor Pressure Values (r2) (Bottom) Calculated for the Perfluorocarbons, the Hydrocarbons, the FTOHs, and the Hydrogenated Alcohols Using the Antoine, Modified Grain, Mackay, and Simmons Vapor Pressure Prediction Methods Antoine method

Modified Grain method

Mackay method

Simmons method

perfluorocarbons (CF3(CF2)nCF3, where n ) 0-6)

0.8 0.9485

0.9 0.956

0.9 0.9643

2.3 0.772

hydrocarbons (CH3(CH2)nCH3, where n ) 0-6)

0.2 0.9992

0.1 0.9989

0.2 0.9994

2.9 0.9791

FTOHs (CF3(CF2)nCH2CH2OH, where n ) 3, 5, 7, or 9)

2.9 0.9739

3.1 0.9744

1.4 0.9745

1.0 0.8766

hydrogenated alcohols (CH3(CH2)nCH2CH2OH, where n ) 3, 5, 7, or 9)

0.3 0.9992

0.2 0.9985

1.8 0.9988

1.3 0.9792

than that of the flexible congeners (49, 50), and the log KOW of rigid congeners is consistently smaller than that of the flexible congeners (51). Vapor Pressure Estimation using Environmental Models. Variance between experimental and estimated vapor pressure values (r2) and mean error were calculated for the perfluorocarbons, the hydrocarbons, the FTOHs, and the hydrogenated alcohols using all four models and are tabulated in Table 2. The Modified Grain and Antoine methods were the most accurate for the estimation of the vapor pressures of the hydrocarbons and the hydrogenated alcohols. Mean errors using the Modified Grain method were only 0.1 and 0.2 log Pa units for the hydrocarbons and hydrogenated alcohols, respectively, while mean errors using the Antoine method were 0.2 and 0.3 log Pa units, respectively. There was little variance in these estimations, and experimental values as the r2 values were greater than 0.99. The Mackay method was also very accurate for the estimation of the vapor pressures of the hydrocarbons, and mean error and variance (r2) were 0.2 ln Pa units and 0.9994, respectively. The accuracy of the Mackay model decreased when used to estimate the vapor pressures of the hydrogenated alcohols as the mean error increased to 1.8 ln Pa units. This increase in the mean error for the estimation of the vapor pressures of the hydrogenated alcohols is most likely explained by the fact that the Mackay method was originally derived using only aliphatic and aromatic hydrocarbons and halogenated compounds, not polar compounds such as the hydrogenated alcohols. For the estimation of the vapor pressures of the hydrocarbons and hydrogenated alcohols, the Simmons method was the least accurate with mean errors of 2.9 and 1.3 log Pa units, respectively, and increased variance (r2 ) 0.97 and 0.98, respectively). Although the Modified Grain, Antoine, and Mackay methods were all accurate for the estimation of the vapor pressures of the hydrocarbons, this accuracy decreased when the three models were used to predict the vapor pressures of the perfluorocarbons. The mean error of the Antoine model for the estimation of the vapor pressure of the perfluorocarbons increased to 0.8 log Pa units, while the mean errors of both the Modified Grain and Mackay methods increased to 0.9 log Pa units. In addition, variance also increased for all three models (Table 2). As illustrated in Figure 6, the vapor pressures estimated by all three models were accurate for the perfluorocarbons of two to six carbon atoms in length. For perfluorocarbons of seven and eight carbon atoms in length, the vapor pressure was consistently overpredicted by the Antoine, Modified Grain, and Mackay methods. It is possible that this overprediction is due to a change in geometry of the perfluorinated chemical that is not accounted for in the vapor pressure prediction models. As discussed previously, perfluorinated compounds undergo a geometrical change from a rodlike structure to a zigzag conformation when the carbon chain reaches eight atoms in length. It

FIGURE 6. Experimental versus predicted vapor pressures of the perfluorocarbons. appears that this change in geometry reduces the vapor pressure of the perfluorocarbons to a greater degree than is compensated for by the Antoine, Modified Grain, and Mackay models. Estimation of the vapor pressures of the perfluorocarbons using the Simmons model was again less accurate than the other three models with a mean error of 2.3 log Pa units (Table 2). This mean error is decreased however from 2.9 log Pa units as obtained for the hydrogen analogues. The variance associated with these estimations was r2 ) 0.772. Similar to that observed for the Antoine, Modified Grain, and Mackay models, the Simmons model also overestimated the vapor pressure of the perfluorocarbon of eight carbon atoms in length, indicating a possible change in geometry that is not accounted for in the model. The Simmons model did not, however, overestimate the vapor pressure of the perfluorocarbon of six carbon atoms in length (Figure 6). The estimation of the vapor pressures of the FTOHs using both the Antoine and Modified Grain methods resulted in a dramatic decrease in accuracy with mean errors of 2.9 and 3.1 log Pa units, respectively (Table 2), and a consistent underestimation of vapor pressure (Figure 7). This underestimation of vapor pressure is most likely due to the fact these models do not account for the unique intramolecular hydrogen bonding and geometry of the FTOHs that results in higher than estimated vapor pressures. Furthermore, it is important to note that accuracy of the vapor pressures, estimated by both the Antoine and Modified Grain methods, decreases with increasing molecular size and carbon number. The estimation of the vapor pressures of the FTOHs using the Mackay and Simmons methods was more accurate than VOL. 38, NO. 6, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 3. Calculated Partition Constants (log Kp,i) and Associated Errors (both m3/µg) of the FTOHs Using Experimental and Estimated Vapor Pressures

4:2 FTOH 6:2 FTOH 8:2 FTOH 10:2 FTOH

log Kp,i (m3/ug) (expt) -9.0 -8.8 -8.4 -8.1

error

log Kp,i (m3/ug) (Antoine)

0.014 0.038 0.027 0.033

-8.6 -7.9 -7.0 -5.8

error

log Kp,i (m3/ug) (Modified Grain)

0.57 3.1 11 96

-8.5 -7.8 -6.9 -5.7

FIGURE 7. Experimental versus predicted vapor pressures of the FTOHs. that using the Antoine and Modified Grain methods, with mean errors of 1.0 and 1.4 log Pa units, respectively (Table 2). The increase in accuracy associated with the Simmons method may be explained by the fact that this model accounts for intramolecular hydrogen bonding. This may also explain why the Simmons method was the most accurate of the four models for the estimation of the vapor pressures of the FTOHs (Figure 7). The increase in accuracy associated with the Mackay model is unexplained, given as previously discussed the Mackay model was not derived using polar compounds. It also is important to note that similar to the Antoine and Modified Grain methods, although to a lesser degree, the Mackay method also underestimates the vapor pressures of the FTOHs (Figure 7). This indicates that the influence of the unique geometry of the FTOHs has not been fully incorporated into the Mackay vapor pressure estimation model. One of the questions that comes to mind is as follows: can the Antoine, Modified Grain, Mackay, and Simmons vapor pressure estimation models can be altered to increase their accuracy when predicting the vapor pressures of both poly- and perfluorinated chemicals. It would appear that the accuracy of vapor pressure estimation of poly- and perfluorinated chemicals using both the Mackay and Simmons could be improved with the inclusion of such chemicals into the data sets used to initially derive the models. Vapor pressure estimation may also be improved by adding correction factors to the Antoine, modified Grain, and Mackay methods that compensate for intramolecular hydrogen bonding and the associated geometric changes in the FTOHs. Implications of This Investigation. As discussed previously, vapor pressure is an important parameter governing a chemical’s dissemination in the environment. For example, in the model developed by Pankow (52, 53) vapor pressure is used to determine the partitioning of organic compounds between gas and particulate matter in the following relationship

log Kp,i ) -log p°L,i + log (fom 760RT/(MWom ζi106)) (8) 1698

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error

log Kp,i (m3/ug) (Mackay)

0.78 4.0 14 110

-9.1 -8.5 -7.7 -6.7

error

log Kp,i (m3/ug) (Simmons)

error

-0.11 0.41 1.6 11

-8.9 -8.2 -7.8 -7.6

0.11 1.4 1.2 1.1

where Kp,i is the partitioning constant of the ith compound (m3/µg), p°L,i is the vapor pressure of the compound i (mmHg), fom is the weight fraction in the absorbing organic matter phase, R is the gas constant, MWom is the mean molecular weight of the absorbing material, and ζi is the activity coefficient of the ith compound in the organic matter phase on the mole fraction scale. Pankow suggested (52, 53) that a typical range for the logarithm of the activity coefficient term is -8.9 to -7.3. Therefore, assuming a mean value of -8.1 for the logarithm of the activity coefficient term and using both the experimental and estimated vapor pressure values of the FTOHs, it was possible to calculate partitioning constants, log Kp,i, for this class of compounds using eq 8 (Table 3). As illustrated in Table 3, the partitioning constants of the FTOHs (calculated using the experimental vapor pressure values) range from -9.0 m3/µg for the 4:2 FTOH to -8.1 m3/µg for the 10:2 FTOH and increase with decreasing vapor pressure. Using standard propagation of error and assuming absolute accuracy for the mean value of -8.1 for the logarithm of the activity coefficient term, it was possible to calculate the level of error associated with the calculated partitioning constants, log Kp,i. These errors are a direct result of the error associated with the vapor pressure values, either experimental or estimated (Table 3). As illustrated in Table 3, the errors on the partitioning constants calculated using experimental vapor pressures were small, all errors were < 0.05 m3/µg. The errors on partition constants calculated using estimated vapor pressures were, at minimum, an order of magnitude larger. Partitioning constants calculated using vapor pressures estimated by the Simmons method had the smallest errors (mean error of 0.9 m3/µg) of all partitioning constants calculated using estimated vapor pressures. The errors associated with the partitioning constants calculated using vapor pressures estimated by either the Antoine, Modified Grain, or Mackay methods were reasonable for the 4:2 FTOH (0.57, 0.78, and -0.11 m3/µg, respectively); however, as illustrated in Table 3, these errors dramatically increased for the 6:2, 8:2, and 10:2 FTOHs. This error increase is consistent with the observation discussed earlier, namely that the accuracy of the vapor pressures estimated using the Antoine, Modified Grain, and Mackay models decreases with increasing molecular size and carbon number. For example, the error on the partitioning constant, of the 10:2 FTOH, was approximately 10 m3/µg using the vapor pressure estimated from the Mackay model and approximately 100 m3/µg using vapor pressures estimated from both the Antoine and Modified Grain models, respectively. These large errors indicate that both the Antoine and Modified Grain models, and to a lesser degree the Mackay model, are insufficiently accurate for estimating the vapor pressures of the FTOHs, particularly the longer chain FTOHs. The most accurate vapor pressure estimates for the FTOHs in this investigation were obtained using the Simmons model (Figure 7 and Tables 2 and 3). As discussed previously, the increased accuracy associated with the Simmons method may be explained by the fact that this model accounts for intramolecular hydrogen bonding, while the other three

models do not. This is an important observation as it indicates that perhaps group contribution methods are more appropriate for the estimation of the vapor pressures than models derived from the Clausis-Clapeyron equation. This observation also indicates that future models should consider parameters such as geometry, strength, and location of intramolecular hydrogen bonds and other function groups in the molecule in order to improve vapor pressure estimation accuracy. As predicted by Ellis and Mabury (16), the unique molecular geometry of poly- and perfluorinated chemicals will influence not only vapor pressure but also other physical properties that determine a chemical’s environmental fate and dissemination. As was the case for the PCBs, molecular rigidity influenced not only vapor pressure but also Henry’s Law constants and KOW (Figure 5). Drawing from this trend, it is reasonable to conclude that the influence of the unique geometry of the FTOHs on vapor pressure can be extended to other physical properties, such as water solubility, boiling point, KOW, Henry’s Law constant, and octanol-air partitioning (KOA).

Acknowledgments The authors would like to thank Dan Mathers of the ANALEST facility at the University of Toronto for his assistance with the vapor pressure measurements and Dupont for the donation of the FTOHs. Funding for this research was provided by the Natural Science and Engineering Research Council of Canada (NSERC) through a Strategic Grant.

Supporting Information Available Fishtine constants and boiling and melting points of the perfluorocarbons, the FTOHs, and their hydrogen analogues (Table 1); all experimental and predicted vapor pressures of the perfluorocarbons, FTOHs and their hydrogen analogues (Table 2S); the vapor pressures, Henry’s Law constants, and KOW values of 50 PCBs (Table 3S). This material is available free of charge via the Internet at http://pubs.acs.org.

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Received for review July 15, 2003. Revised manuscript received December 10, 2003. Accepted December 19, 2003. ES034773+ VOL. 38, NO. 6, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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