Prediction of Partitioning between Complex Organic Mixtures and

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Environ. Sci. Technol. 2006, 40, 536-545

Prediction of Partitioning between Complex Organic Mixtures and Water: Application of Polyparameter Linear Free Energy Relationships SATOSHI ENDO AND TORSTEN C. SCHMIDT* Center for Applied Geoscience (ZAG), Eberhard-Karls-University Tu ¨ bingen, Wilhelmstrasse 56, D-72074 Tu ¨ bingen, Germany

Equilibrium partitioning between nonaqueous phase liquids (NAPLs) and water is a governing process for contaminants leaching from NAPLs. Conventional prediction methods, such as Raoult’s law and single-parameter linear free energy relationship (SP-LFER), are inaccurate for compounds with polar functional groups. Therefore, this study introduces a polyparameter linear free energy relationship (PP-LFER) approach as a more general tool to predict NAPL-water partitioning coefficients. Our approach was evaluated using 441 experimental partitioning data from 30 references. Experimental fuel-water partitioning coefficients were generally well reproduced by existing PP-LFERs for pure solvents using either a volumefraction weighted sum of partitioning coefficients K (linear model, R2 ) 0.983, root-mean-squared error [rmse] ) 0.23) or a volume-fraction weighted sum of log K (log linear model, R2 ) 0.976, rmse ) 0.28). Using the linear model, estimations were, in most cases, within a factor of 2 from the experimental values, regardless of the type of compounds and the presence of a fuel additive. In contrast, the log linear model considerably underestimated partitioning coefficients in the presence of strong solutesolvent hydrogen bonding. For coal tar-water partitioning coefficients (Kcoal tar/w), new PP-LFER equations were calculated based on experimental log Kcoal tar/w values of 35 compounds. The resulting regression equation was log Kcoal tar/w ) 0.40((0.33) + 0.34((0.32)E + 0.61((0.57)S - 0.55((0.61)A - 5.07((0.61)B + 3.22((0.35)V with the rmse equal to 0.21, where E, S, A, B, and V are Abraham’s solute descriptors. Partitioning coefficients for phenol and alcohols, calculated by the above equation, were much closer to the experimental values than to those estimated by the SP-LFER approach with octanol-water partitioning coefficients. The values of the coefficients also provide insight into the properties of coal tar in terms of molecular interactions with solutes. Consequently, using the approaches presented in this study, complex organic mixture-water partitioning coefficients of a wide range of organic compounds with varying polarity can be reasonably estimated.

* Corresponding author phone: +49-7071-297 31 47/53; fax: +497071-29 51 39; e-mail: [email protected]. 536

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Introduction Groundwater contamination by fuels and other complex organic mixtures, such as coal tar and creosote, is a widespread problem. When an organic liquid enters into the subsurface, it moves downward to the aquifer and ends up on the top or bottom of the aquifer, depending on its density, often forming a pool of nonaqueous phase liquid (NAPL) (1). NAPL can stay there for a long time, releasing contaminants to the surrounding water, which may threaten downstream groundwater use. The extent to which a contaminant leaches out of the NAPL into the water depends on the equilibrium partitioning coefficient KNAPL/w between the NAPL and water phases (2-5). Thus, knowing the partitioning coefficient between NAPL and water is a prerequisite for estimating contaminant release in the subsurface. Partitioning coefficients between NAPL and water are determined experimentally, or estimated by theoretical or empirical approaches. Estimation is preferred, especially when a large number of samples and contaminants needs to be dealt with, and a time-consuming experiment should be avoided. The most frequently applied estimation method follows Raoult’s law, assuming that the activity coefficient of the solute in the NAPL is unity (i.e. the solute behaves in the NAPL exactly as it does in its pure liquid phase). The methods based on Raoult’s law have been reported to provide successful estimations for nonpolar compounds, e.g., alkylbenzenes and PAHs (3, 4, 6, 7), but considerably poorer results for compounds with polar functional groups, such as anilines and phenols (8), because the activity coefficient is considerably different from unity. Single-parameter linear free energy relationships (SP-LFERs), such as one using octanol-water partitioning coefficients (Kow) of the form log KNAPL/w ) β log Kow + R, are also used to describe partitioning behavior (2). The coefficients β and R are fitting parameters derived from an experimental data set and are supposed to explain different solute dissolution properties of n-octanol and the NAPL. SPLFERs have the advantage that the number of required input parameters is minimal. However, this is accompanied by a major drawback: prediction by SP-LFERs is, in principle, limited to the single compound class for which the equation has been derived, and a new equation is necessary for each individual class (5). While major components of fuels, coal tar, and creosote are hydrocarbons, these mixtures also contain different kinds of polar compounds. In fuels, there are various N-, S-, and O-containing compounds such as residuals from crude oil or additives for quality enhancement (8-10). Coal tar and creosote are more complex mixtures and are known to include a number of functionally substituted and heterocyclic aromatic compounds (11-13). Dissolution of these polar compounds from NAPL is, however, difficult to handle since experimental data on NAPL-water partitioning are very limited (8), and the estimation methods above are inaccurate for polar compounds. Polyparameter linear free energy relationship (PP-LFER) approaches have been increasingly introduced into environmental chemistry in recent years (8, 14-16). PP-LFERs explain partitioning by capturing all relevant molecular interactions in the respective phases. The advantage of PPLFERs is their general applicability to many organic compounds of varying polarity. With regard to fuels, Schmidt et al. (8) successfully reproduced the experimental gasolinewater partitioning coefficients for nonpolar and polar compounds, and later, Arey and Gschwend (17) demonstrated that synthetic fuels with a high content of alcohols or ethers can also be modeled by PP-LFERs. It is, therefore, expected 10.1021/es0515811 CCC: $33.50

 2006 American Chemical Society Published on Web 12/07/2005

TABLE 1. PP-LFER Parameters for Selected Solvent-Water Systems

a

solvent

c

e

s

a

b

v

ref

alkane toluene diethyl ether, weta isooctane cyclohexane n-hexadecane octan-1-ol, weta trichloromethane acetonitrile, dry dimethyl sulfoxide nitrobenzene

0.287 0.143 0.248 0.288 0.159 0.087 0.088 0.327 0.413 -0.221 -0.181

0.649 0.527 0.561 0.382 0.784 0.667 0.562 0.157 0.077 0.226 0.576

-1.657 -0.720 -1.016 -1.668 -1.678 -1.617 -1.054 -0.391 0.326 0.878 0.003

-3.516 -3.010 -0.226 -3.639 -3.740 -3.587 0.034 -3.191 -1.566 1.312 -2.356

-4.818 -4.824 -4.550 -5.000 -4.929 -4.869 -3.460 -3.437 -4.391 -4.604 -4.420

4.282 4.545 4.075 4.561 4.577 4.433 3.814 4.191 3.364 3.403 4.263

22 35 36 35 35 37 37 38 35 39 23

Solute B0 descriptors are required.

that PP-LFERs may be generally applied to any fuel-water system including partitioning of polar compounds. In contrast, the application of the PP-LFER approach to more complex mixtures, such as coal tar and creosote, has not been attempted yet. Since coal tar and creosote contain a huge number of nonpolar and polar contaminants (11, 12), PP-LFER approaches, which can handle a broad range of compounds, are likely to be useful. In the present study, we (i) compile the experimental partitioning coefficients existing in the literature for various compounds in complex organic mixture-water systems, (ii) evaluate the PP-LFER based approaches for the estimation of the partitioning coefficients in such systems, and (iii) discuss the NAPL-water partitioning behavior in terms of solute-mixture component molecular interactions. To this end, separate measures to handle fuels and coal tar were taken. Fuels such as gasoline, jet fuel, and diesel fuel are crude oil distillates composed primarily of aliphatic and mono-aromatic hydrocarbons. Since their compositions are relatively well-known, the partitioning coefficients in the pure liquid state of fuel constituents were calculated by PP-LFER, and they were combined to estimate the overall fuel-water partitioning coefficient. Two combination models, which were proposed previously (see the Theory section for detail), were used and compared. The advantage and disadvantage of the models are discussed based on the comparison with experimental data. In contrast to fuels, the composition of coal tar is too complex to perform the approach described above. Thus, new PP-LFER equations, specific to coal tar, were established based on the collected partitioning data.

Theory Abraham’s Polyparameter Linear Free Energy Relationships (PP-LFERs). Partitioning coefficients were estimated based on a PP-LFER approach. Abraham’s PP-LFER for solvent-water systems has the general form:

log Kj/w ) c + eE + sS + aA + bB + vV

(1)

where log Kj/w is the logarithm of the partitioning coefficient of a given solute between solvent j and water, and E, S, A, B, and V are the excess molar refraction, the dipolarity/ polarizability parameter, the overall hydrogen bond acidity, the overall hydrogen bond basicity, and McGowan’s characteristic volume, respectively, of the solute. The counterparts to these solute descriptors for solvent j are the coefficients e, s, a, b, and v, which characterize the solvent capabilities of different molecular interactions with solutes. The theoretical background of eq 1 and detailed explanation for each term were given by Abraham et al. (18-20). In brief, eq 1 describes partitioning by splitting the relevant solvation processes into terms. Each term of eE, sS, aA, and bB comprises one solute descriptor and one solvent parameter,

the product of which quantifies the contribution of that solute-solvent adhesive interaction to the overall partitioning coefficient. The vV term represents the difference between the energy required for cavity formation in the phases. The vV term also includes solute-solvent dispersive interaction since solute volume is correlated with polarizability. Solute descriptors are available in the literature for thousands of compounds (e.g., refs 21-23) and several estimation methods have been proposed for unknown descriptors (24, 25). Solvent parameters are normally derived as fitting coefficients which best reproduce several tens to hundreds of experimental partitioning constants. The limitation to the implementation of the PP-LFER is usually the narrow availability of solvent (or system) parameters. Thus, the main effort for introducing the PP-LFER approach into a new field of application is directed at determining system parameters of interest. Deviations of estimated log Kj/w by eq 1 from measured values are typically from 0.1 to 0.2 (see references in Table 1). Linear Model and Log Linear Model for Estimating Kfw. It is proposed that the partitioning coefficient of a solute between a fuel mixture and water (Kfw) is calculated by combining the individual partitioning coefficients of the solute between components j and water (Kj/w), using the volume fractions of components j (φj). For the combination of Kj/w, two different models have been suggested that result in eqs 2 and 3:

∑φ K ) ∑φ log K

Kfw ) log Kfw

(2)

j j/w

j

(3)

j/w

Equation 2 is the linear model proposed by Schmidt et al. for fuel mixtures (8), which says that the Kfw is calculated as the arithmetic mean of all the components’ partitioning coefficients weighted by the volume fractions. This model is conceptually equivalent to the hypothetical system where each mixture component is present separately, forming the pure liquid phase of the component within the mixture, and contributes to the solute partitioning, independently of the other mixture components. Equation 3 is the log linear model which was introduced into estimation of fuel-water partitioning by Arey and Gschwend (17). Equation 3 is formally equivalent to the geometric mean of the individual partitioning coefficients. Since log K is proportional to the free energy, eq 3 also means that the free energy of transfer varies linearly with the changing mixture composition. In this case, the change of partitioning coefficients is called ideal. The idea behind eq 3 becomes even clearer when eq 1 is inserted into eq 3. Now, the ideal change (eq 3) means that each parameter in eq 1 (e, s, a, etc.) of a given mixture is equal to the volume-weighted average of the corresponding parameters for pure components. In other words, each type of molecular interaction between a solute molecule and the VOL. 40, NO. 2, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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surrounding molecules of a mixture component occurs proportionally to the volume fraction of that component. In this regard, the linear model is in contrast to the log linear model; in the linear model, the solute is not necessarily homogeneously distributed over the various solvent compartments because of the different affinities of the solvents with the solute (recall that the linear model assumes the presence of separate pure solvent phases in the mixture). Thus, the solute interacts predominantly with the solvent component(s) that can take up more solute molecules than the others. For example, when a solute compound dissolves in a binary mixture containing 50 vol % of solvent 1 (K1/w ) 1) and 50 vol % of solvent 2 (K2/w ) 100), the log linear model assumes that solvent 1 and solvent 2 interact with the solute in the same proportion and calculates the mixture-water partitioning constant (K1+2/w) equal to 10. On the other hand, in the linear model, 99% of the solute molecules in the mixture are considered to be present in the compartment of solvent 2 (K2/1 ) K2/w/K1/w ) 100), and, thus, solvent 2 dominantly interacts with the solute. The calculated K1+2/w is 50.5, much higher than that of the log linear model and about half of K2/w. This shows that, in the linear model, solvent 1 is assumed to have little contribution to K1+2/w, which is contrary to the log linear model. It is known, for binary organic mixtures, that eq 2 applies well both to systems where hydrogen bond donor-acceptor complexation between solute and solvent molecules occurs and to those which cannot form hydrogen bonding complexes, but that eq 3 only applies to systems without strong hydrogen bond donor-acceptor interactions (26, 27). Noteworthy is that eqs 2 and 3 are nearly equivalent if the Kj/w values of concern are close to one another, with the resulting Kfw close to the Kj/w’s. This is the case if the mixture components all interact with the solute in a similar manner. Examples are a mixture consisting of only n-alkanes, which similarly interact with any solute, and n-alkane solutes in any organic mixture. Significant differences appear if Kj/w values differ considerably; that is, the solvation property is very different among the mixture components.

Methods Data Collection and Evaluation. Experimental partitioning coefficients from fuels, coal tar, or creosote to water were collected. The collection was restricted to the partitioning data obtained from static systems, i.e., partitioning coefficients calculated from column retention data were not included because of potential nonequilibrium conditions. References, sample types, compositions of the fuels, and experimental conditions from which the data were obtained are listed in Table S1, Supporting Information. During the evaluation process, the experimental temperature and coexisting substances in the aqueous phase were carefully examined. Because partitioning coefficients may vary at different temperatures (28), only data at 8-25 °C were considered. Temperature dependence of liquidliquid equilibrium partitioning is known to be minimal in such a narrow range (5, 8). Gasolines containing a large fraction of alcohol were not considered (e.g., gasohols in ref 29), considering that the cosolvent effect can be significant in the aqueous phase (5, 29). The data from Heermann and Powers (30) were included, although the gasoline they used contained up to a few vol % of ethanol, since this did not substantially affect partitioning coefficients of alkyl-substituted benzenes. Additionally, gasolines containing methyl tert-butyl ether (MTBE) were also considered; a potential influence of MTBE on partitioning was taken into account as explained below. Experiments with brine water were not considered since high salt concentrations can change partitioning coefficients (5). Data obtained under high 538

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pressures (up to 50 bar) were included in the list as pressure differences hardly affect liquid-liquid partitioning (28, 31). Data given as mole fraction or mass fraction were converted to the molar concentration, and the partitioning coefficients were always calculated as dimensionless. Several sets of experimental partitioning coefficients between synthetic coal tar and water were also collected for comparison. A synthetic (also called simulated) coal tar is a mixture of pure chemicals prepared in the laboratory. It is intended to model the natural counterpart but is made up of fewer and simpler compounds, and its composition is precisely known. Solute Descriptors for PP-LFERs. Solute descriptors were obtained from the literature. When one or several of the descriptors for the compound of interest were not available, those for a structurally similar compound were used (e.g. benzo[a]pyrene’s B descriptor was used for benzo[e]pyrene). If an appropriate alternative could not be found, the estimation method proposed by Platts et al. (24) was used (e.g. branched alcohols’ E and acenaphthylene’s B). According to Platts et al., this method gives accurate estimates for E, but may result in relatively erroneous numbers for S, A, and B. Therefore, the use of estimated descriptors may cause worse prediction of partitioning coefficients. All the solute descriptors used in this work are listed with their sources in Table S2, Supporting Information. For MTBE, a higher B value (0.55) than the literature value (0.45) (21) was used. The existing descriptors for branched ethers are known to give erroneous numbers to partitioning coefficients (8, 21, 32, 33). Due to the high environmental concern of this class of compounds, the descriptors were revised based on partitioning data so that a more accurate prediction of environmental behavior is possible. The detailed discussion is given elsewhere (33). Estimation of Fuel-Water Partitioning Coefficients Kfw and Solvent Parameters for PP-LFERs. To estimate Kfw, partitioning coefficients for fuel components (Kj/w) were calculated through eq 1, and either the linear model (eq 2) or the log linear model (eq 3) was used to combine the Kj/w values. Bulk compositions of fuels given in the respective references were used to simplify the fuel compositions. Saturated hydrocarbons were modeled by LFER parameters for “alkane” since it is known that there is little difference in values among individual alkanes (34). Olefins were assumed to be equivalent to alkanes, owing to the lack of solvent parameters for any olefin compounds. The aromatic fraction was represented by toluene. Aromatic compounds in the fuels of interest are predominantly monoaromatics and thus toluene may be a reasonable representative. Diethyl ether was chosen to represent MTBE. The solvent parameters used are listed in Table 1 together with other solvents for comparison. It should be noted that we used a wet diethyl ether parameter set for calculating MTBE-water partitioning coefficients. A wet solvent indicates that the solvent phase is saturated with water, and that the aqueous phase is saturated with solvent. By contrast, a dry solvent is a pure solvent without contact with water. Differentiation between wet and dry is necessary for alcohols and ethers which dissolve substantial amounts of water and slightly, but significantly, change their solvent properties from the pure phase (36, 40). By using wet parameters, the cosolvent effect in the aqueous phase and influence of dissolved water in the organic phase, if any, can be incorporated into the calculation in proportion to the content of MTBE. Variable solute basicity was taken into account to calculate MTBE-water partitioning coefficients. For some compounds (e.g. sulfoxides, alkylanilines, and alkylpyridines), hydrogen bond basicity (B) is not completely constant, but somewhat system-dependent (23). When dealing with partitioning of

TABLE 2. Summary of Data Compilation for Experimental Complex Organic Mixture-Water Partitioning Coefficients organic mixture

no. of data

no. of samples

no. of compounds

compounds considered

73

14

34

24 58 181 38 67

2 12 21 6 8

24 17 35 15 9

alkylbenzenes, naphthalene, ketones, MTBE, alcohols, phenols, anilines, heterocycles, radon alkylbenzenes, alcohols alkylbenzenes, PAHs, MTBE, alcohols, radon alkylbenzenes, PAHs, alcohols, phenol, benzofuran xylene, PAHs, phenol, heterocycles PAHs

gasoline jet fuel diesel fuel coal tar creosote synthetic coal tar

FIGURE 1. Comparison of experimental fuel-water partitioning coefficients with partitioning coefficients calculated by (A) the linear model (eq 2) and (B) the log linear model (eq 3). The solid line indicates calculated values equal to experimental values. The dashed lines denote deviations of a factor 2 from the measured Kfw. Fuels include gasoline with and without MTBE, jet fuel (JP-4), and diesel fuel. Data used and their sources are listed in Table S5, Supporting Information. The legends are common to (A) and (B). these compounds from water to a partially water miscible solvent (e.g. octanol or diethyl ether), B0 descriptors, instead of B, are suggested to be used (20, 23). In our case, B0 was applied when MTBE-water partitioning coefficients of anilines were calculated. When the composition of the fuel of interest was unknown, the following typical content was assumed: gasoline, 66% saturates and 34% aromatics (8); diesel fuel, 80% saturates and 20% aromatics (ref 41 and Table S3, Supporting Information). Estimation of Coal Tar-Water Partitioning Coefficients Kcoal tar/w. To estimate coal tar-water partitioning coefficients Kcoal tar/w, the estimation method discussed above is not useful because coal tar is a too complex mixture containing a large fraction of unidentified compounds. In addition, although the major components are known to be PAHs (ca. 30-50 wt %, ref 6, 11, 42, 43), they are solid at the standard state, and, accordingly, there exist no “solvent” parameters for these compounds. Therefore, a new equation for the coal tarwater system was established by the multiple regression analysis based on experimental data. The solute descriptors used are given in Table S2, Supporting Information. Regression analysis was done using an Excel add-in program, Analysis Toolpak. Additionally, the SP-LFER with log Kow was applied as comparison. The log Kow values used are listed in Table S4, Supporting Information.

Results and Discussion Data Compilation and Evaluation of Experimental FuelWater and Complex Organic Mixture-Water Partitioning

Coefficients. In total, 441 experimental partitioning coefficients for different complex organic mixtures were collected from 30 references. Tables 2 and 3 summarize the collected data, and the individual partitioning coefficients are given in Table S5, Supporting Information. The listed complex organic mixtures include MTBE-amended and nonamended gasoline, jet fuel, diesel fuel, coal tar, and creosote. The mean and standard deviations of the log partitioning coefficients were calculated for each compound in the respective systems. In general, the variation of experimental log K values was small for alkylbenzenes (sd 0) compounds in MTBE-amended gasoline. The log linear model largely underestimated the partitioning coefficients of the strong H-donors, i.e., phenols (A ) 0.37-0.60) and benzotriazole (0.61), in MTBE (H-acceptor)-containing gasoline, as previously pointed out by Arey and Gschwend (17). The deviation from the experimental values amounted to factors of 2-6 for phenols and 12 for benzotriazole. Figure 2 shows that at a hydrogen bond acidity of around 0.4, the 540

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1.15 0.97 1.64 1.34 2.08 1.72 0.49 1.08

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0.34 0.36

6.36 6.46 1.01 4.45 4.17

log linear model underpredicts Kfw by about a factor of 2 and, after this point, the deviation increases with the increasing A value. This threshold of A may vary, depending on the content of MTBE (8, 17). As stated in the Theory section, the log linear model assumes the ideal change of the partitioning coefficient during mixing, but the assumption appears not to hold for the system in which the solute strongly interacts with one of the mixing agents by hydrogen-bonding interaction. Note that the log linear model still worked for other polar compounds, anilines, MTBE, and thiophenes, which are weaker H-donors or non-H-donors (A ) 0.20-0.26, 0.00, and 0.00, respectively). Additionally, gasoline without oxygenates did not show a large error caused by the use of the log linear model for any investigated compound including

FIGURE 2. Plot of calculated log Kfw minus experimental log Kfw against Abraham’s hydrogen bond acidity (A) descriptor. Partitioning data are from refs 8 and 29; MTBE contents are 9% and 10% in the fuel phase, respectively.

TABLE 4. Regression Equations for Coal Tar-Water Partitioning Coefficients eq

n

R2

rmse

data set

8 9 10

log Kcoal tar/w ) 1.16 log Kow - 0.19 log Kcoal tar/w ) 1.22 log Kow - 0.50 log Kcoal tar/w ) 1.15 log Kow - 0.16

181 35 29

0.912 0.960 0.975

0.38 0.40 0.24

11

log Kcoal tar/w ) 0.56((0.26) + 0.24E((0.25) + 0.87S((0.44) 1.13A((0.71) - 4.47B((0.68) + 2.89V((0.29) log Kcoal tar/w ) 0.40((.33) + 0.34E((0.32) + 0.61S((0.57) 0.55A((0.61)- 5.07B((0.61) + 3.22V((0.35)

181

0.941

0.31

all data mean mean (only PAHs and benzenes) all data

35

0.989

0.21

mean

12

FIGURE 3. Partitioning coefficients of phenol between binary organic mixtures and water. Solid and dotted lines indicate estimations by the linear model and the log linear model, respectively, using experimental Korganic mixture/water values at volume fractions of 0 and 1. Experimental data are from ref 45. H-donating alcohols (A ) 0.37-0.43) (Figure S1B, Supporting Information). Interestingly, the linear model is still applicable for those systems possessing strong solute-solvent hydrogen bond interactions (Figure 1 and Figure S1A, Supporting Information). It has been reported that many nonideal changes of partitioning coefficients during mixing are well approximated by the linear model (26, 27, 44, 45). Figure 3 depicts some examples for organic mixture-water partitioning coefficients

of phenol across varying mixture compositions. The systems included here consist of one apolar (octane) or weakly monopolar (benzene) solvent and one monopolar or bipolar solvent. The latter is able to strongly interact with phenol by hydrogen bond donor-acceptor interaction. It is clearly seen in Figure 3 that the course of the change of partitioning coefficient considerably deviates from that of the ideal behavior and the log linear model is hardly able to reproduce it, while the linear model fits the experimental data surprisingly well. In the benzene/octanol binary mixture, measured partitioning coefficients were even higher than those predicted by the linear model. In this case too, the linear model is still superior to the log linear model in that it results in closer estimations. The advantage of the linear model is based on the fact that, whereas the log linear model does not take into account the effect of hydrogen bond complexation on the partitioning constant, the linear model does consider it in an approximated way (see refs 26 and 27) Arey and Gschwend (17) proposed that the linear model apparently overestimates the partitioning coefficients of phenols and anilines in isooctane/MTBE systems, but this is due to their use of less accurate solvent parameters for diethyl ether and omission of the variable basicity for anilines. Solvent parameters are sometimes revised based on additional partitioning data (e.g., compare refs 23 and 36), because the solvent parameters derived from a larger data set are more reliable than those from a smaller data set. The parameters for diethyl ether used in this study are based on 3 times more data than those used by Arey and Gschwend (239 compared to 84 data). The resulting difference in diethyl ether-water partitioning coefficients between the two parameter sets is about a factor of 1.6-1.8 for phenols, which leads to 1.4-1.8 times greater estimates of Kisooctane-MTBE/w by the old parameter set than by the updated one. Furthermore, the omission of the variable basicity increases anilines’ Kisooctane-MTBE/w by a factor of 1.5-3. By using appropriate parameters, the deviations they observed in the isooctane/ VOL. 40, NO. 2, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Experimental and calculated coal tar-water partitioning coefficients. Experimental data and equations used for calculation are (A) the mean values and eq 9 (SP-LFER), (B) all data and eq 8 (SP-LFER), (C) the mean values and eq 12 (PP-LFER), and (D) all data and eq 11 (PP-LFER), respectively. The solid line and the dashed lines are the same as in Figure 1. The equations are found in Table 4 and the individual experimental and calculated values in Table S5, Supporting Information. MTBE system would reduce, to within a factor of 2, from the experimental values. The linear model can be used generally for fuel-water partitioning, but the log linear model only for systems where the solute is not expected to strongly interact with fuel components by hydrogen bonding. Thus, in the presence of MTBE (or any other oxygenate) the linear model is recommended to be used for predicting partitioning coefficients of H-donors. In the context of our discussion, alcohol oxygenates in fuel would cause a nonideal behavior of partitioning coefficients for both H-donors and H-acceptors since alcohols are bipolar compounds, capable of interacting with both of them. However, this is unlikely to matter, considering that the dominantly used alcohol additive is ethanol, which readily partitions from fuel to water soon after contact with water. In this case, the cosolvent effects of alcohols in the aqueous phase may be more relevant, which should be treated by another method (e.g., refs 5, 17). Construction of PP-LFER Equations for Fuel-Water Systems. Despite the limited range of applicability mentioned above, the log linear model has merit in that it can produce a PP-LFER equation of each fuel from existing parameters for pure solvents. By combining eqs 1 and 3, each coefficient of the new equation for a mixture can be calculated as the volume-weighted average of the coefficients for the respective solvents:

coeffmixture )

∑φ coeff j

j

(4)

where coeff is the c, e, s, a, b, or v solute descriptor, φ is the volume fraction, and j is the solvents representing the fuel 542

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components. Using the typical compositions of the fuels given above, and alkanes and toluene as representative compounds for aliphatics and aromatics, respectively, we obtain:

log Kgasoline/w ) 0.238 + 0.608E - 1.338S - 3.344A 4.820B + 4.371V (5) log KJP-4/w ) 0.268 + 0.633E - 1.535S - 3.450A 4.819B + 4.316V (6) log Kdiesel fuel/w ) 0.258 + 0.625E - 1.470S - 3.415A 4.819B + 4.335V (7) The use of these equations is much simpler than the approaches discussed above and may be utilized for a priori estimations of partitioning coefficients. For instance, the log Kfw values of aniline and phenol in a nonamended gasolinewater system, which have not been experimentally examined yet, would be calculated as -0.58 and 0.25, respectively. If the fuel contains an oxygenate such as MTBE, the equations above should be modified so that the oxygenate is also taken into account as a fuel component. In this case, the modified equations should not be used for predicting strong Hdonating solute partitioning because the log linear model is not valid for these compounds as discussed above. Estimation of Coal Tar-Water Partitioning Coefficients Kcoal tar/w. Experimental coal tar-water partitioning coefficients of a compound often vary substantially among different studies. In addition to the experimental difficulty associated with low equilibrium aqueous concentrations of PAHs, the diversity of coal tar composition and the corresponding variable solvation property can be a reason for the

observed differences. The PP-LFER approach would reasonably explain the influence of variable coal tar compositions on partitioning based on molecular interactions if the large data sets, which include various kinds of solute compounds, were available for different coal tars. However, currently the limited number of existing partitioning data does not allow for such a comprehensive analysis. Therefore, in the following, we consider the various coal tars as a single material and perform the LFER analyses using all collected data or the mean values for each compound, bearing in mind that the resulting regression equations are best suited for coal tar having average solvation properties. Table 4 presents the resulting regression equations of the PP-LFER analysis along with those of the conventional SPLFERs using log Kow, and Figure 4 shows the plots of measured coal tar-water partitioning coefficients against those calculated from the regression equations. In the SP-LFER approach (eqs 8, 9), the majority of the data points fall within an error of a factor of 2 (0.3 log units) from the 1:1 line, which is comparable to the experimental variations (Table 3). However, up to 1.2 log units deviations between estimation and measurement were observed for alcohols and phenol. These deviations are considerably large compared to those for other compounds (Figure 4). As stated above, singleparameter methods are not applicable if different compound classes are included. The underlying dataset of eqs 8 and 9 consists primarily of PAHs and alkylbenzenes, so that the equations were adjusted to those aromatic compounds without polar moieties. Consequently, these equations are incapable of providing reasonable predictions for bipolar compounds such as alcohols and phenol. In contrast, the PP-LFER approach (eqs 11 and 12) provided accurate predictions for any compound, including alcohols and phenol. The predictions are also slightly better for nonpolar compounds. Statistics appear not to show a big difference in the performance between the SP- and PP-LFERs (Table 4), especially when all data are used to derive equations. This, however, is due to the fact that the data set consists predominantly of alkylbenzenes and PAHs. It may be worth noting that when focusing on alkylbenzenes and PAHs, the SP-LFER approach results in a much better estimation than when including polar compounds (compare eqs 9 and 10). Nevertheless, the improved result is only comparable to that of eq 12 (PP-LFER), as seen in correlation coefficients and rmse. Considering the applicability to a much wider range of compounds, the PP-LFER equation is concluded to be more useful. In addition to the accuracy and applicability, PP-LFER equations give us an insight into the properties of coal tar as a partitioning medium. Reflecting the variability of coal tar composition and the limited number of compound classes considered, the standard error for each coefficient is rather large, but interesting features of coal tar can be seen. Compared to other solvents (Table 1), the s parameter for coal tar was remarkably positive. The physical meaning of the coefficient s is thought to be a solvent’s capability of electrostatic interaction and solute polarization interaction (25). PAHs, which are major constituents of coal tar, can be involved in these interactions (see solute E and S descriptors for PAHs in Table S2, Supporting Information), and thus are likely to be responsible for the observed high s value. Since the s value is generally high for solvents with sulfur or nitrogen atoms (Table 1), S- or N-containing components in coal tar may partially contribute to the high s as well. The hydrogen bond basicity (a) of coal tar was higher than that of alkanes and toluene, but lower than that of diethyl ether and octanol. This is also attributable to highly conjugated aromatic and heteroatomic compounds. The hydrogen bond acidity (b) is not different from alkanes and toluene, indicating the absence of significant hydrogen bond donors in coal tar. The v value

FIGURE 5. (A) Creosote-water and (B) synthetic coal tar-water partitioning coefficients. The PP-LFER equation for coal tar-water (eq 12) was used to calculate log K. The solid line and the dashed lines are the same as in Figure 1. Data used are listed in Table S5, Supporting Information. of coal tar was relatively low compared to that of organic solvents (Table 1), indicating a high energy necessary for cavity formation in coal tar. This implies that the cohesive interactions between coal tar constituents are relatively strong. Eq 12 was applied to creosote and synthetic coal tar, which are complex mixtures similar to coal tar. Estimations by eq 12 agreed well with the measured partitioning coefficients in creosote and synthetic coal tar (Figure 5). This suggests that in all three mixtures, the dominating molecular interactions between solute and mixture components are similar (at least those interactions involved in PAHs’ partitioning [e, s, b, and v]). Creosote is a product formed from coal tar distillation, and the synthetic coal tars considered here are mixtures of 1- to 4-ring PAHs. They are not expected to contain the large, complex materials (asphalthenes) that coal tar contains. The observed successful estimations by eq 12 suggest that the influence of asphalthenes on partitioning in coal tar seems to be limited and that the dominant molecular interactions should be those which PAHs can undergo. Consequently, eqs 11 and 12 may also be used for estimation of creosote-water partitioning. Since the compounds used to derive eqs 11 and 12 include only five H-donors (i.e. A > 0), the predictive power might still be weak for hydrogen bond acidic compounds. Moreover, the data for each H-donor came from only one sample and thus eqs 11 and 12 are unlikely to represent the variable coal tar’s H-bond basicity. Further characterization of coal tar and creosote should be achieved by investigation of more VOL. 40, NO. 2, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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H-donor compounds. Additional data of coal tar-water partitioning coefficients will improve our understanding of coal tar solvation properties and the accuracy of prediction by PP-LFER approaches such as eqs 11 and 12.

Acknowledgments The authors thank Kai-Uwe Goss, Peter Grathwohl, Stefan Haderlein, Maik Jochmann, and Peter Heidenreich for their valuable comments on the manuscript, and Rowena Crockett of the Swiss Federal Laboratories for Materials Testing and Research for providing data on diesel fuel compositions. We gratefully acknowledge the financial support by the Deutsche Forschungsgemeinschaft.

Supporting Information Available Tables of detailed sample information, solute descriptors used, composition of diesel fuel, individual experimental partitioning coefficients with data sources, log Kow values used for regression analysis, and figures of comparison between experimental and calculated partitioning coefficients in individual fuels. This material is available free of charge via the Internet at http://pubs.acs.org.

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(17) Arey, J. S.; Gschwend, P. M. Estimating partition coefficients for fuel-water systems: Developing linear solvation energy relationships using linear solvent strength theory to handle mixtures. Environ. Sci. Technol. 2005, 39, 2702-2710. (18) Abraham, M. H.; Chadha, H. S. In Lipophilicity in drug action and toxicology; Pliska, V., Testa, B., van de Waterbeemd, H., Eds.; VCH Verlagsgesellschaft mbH: Weinheim, 1996; pp 311337. (19) Abraham, M. H. Scales of solute hydrogen-bonding: Their construction and application to physicochemical and biochemical processes. Chem. Soc. Rev. 1993, 22, 73-83. (20) Abraham, M. H.; Ibrahim, A.; Zissimos, A. M. Determination of sets of solute descriptors from chromatographic measurements. J. Chromatogr. A 2004, 1037, 29-47. (21) Abraham, M. H.; Andonian-Haftvan, J.; Whiting, G. S.; Leo, A.; Taft, R. S. Hydrogen bonding. Part 34. The factors that influence the solubility of gases and vapors in water at 298 K, and a new method for its determination. J. Chem. Soc., Perkin Trans. 2 1994, 1777-1791. (22) Abraham, M. H.; Chadha, H. S.; Whiting, G. S.; Mitchell, R. C. Hydrogen bonding. 32. An analysis of water-octanol and wateralkane partitioning and the DLOGP parameter of seiler. J. Pharm. Sci. 1994, 83, 1085-1100. (23) Abraham, M. H. Hydrogen-bonding. 31. Construction of a scale of solute effective or summation hydrogen-bond basicity. J. Phys. Org. Chem. 1993, 6, 660-684. (24) Platts, J. A.; Butina, D.; Abraham, M. H.; Hersey, A. Estimation of molecular linear free energy relation descriptors using a group contribution approach. J. Chem. Inf. Comput. Sci. 1999, 39, 835845. (25) Arey, J. S.; Green, W. H., Jr.; Gschwend, P. M. The electrostatic origin of Abraham’s solute polarity parameter. J. Phys. Chem. B 2005, 109, 7564-7573. (26) Purnell, J. H.; Vargas de Andrade, J. M. Solution and complexing studies. I. Gas-liquid chromatographic investigation of supposed complexing systems. J. Am. Chem. Soc. 1975, 97, 3585-3590. (27) Acree, W. E., Jr.; Bertrand, G. L. Thermochemical investigations of nearly ideal binary solvents. 4. Gas-liquid partition coefficients in complexing and noncomplexing systems. J. Phys. Chem. 1979, 83, 2355-2358. (28) Yang, Y.; Miller, D. J.; Hawthorne, S. B. Toluene solubility in water and organic partitioning from gasoline and diesel fuel into water at elevated temperatures and pressures. J. Chem. Eng. Data 1997, 42, 908-913. (29) Poulsen, M.; Lemon, L.; Barker, J. F. Dissolution of monoaromatic hydrocarbons into groundwater from gasoline-oxygenate mixtures. Environ. Sci. Technol. 1992, 26, 2483-2489. (30) Heermann, S. E.; Powers, S. E. Modeling the partitioning of BTEX in water-reformulated gasoline systems containing ethanol. J. Contam. Hydrol. 1998, 34, 315-341. (31) Bennett, B.; Larter, S. R. Partition behavior of alkylphenols in crude oil/brine systems under subsurface conditions. Geochim. Cosmochim. Acta 1997, 61, 4393-4402. (32) Arp, H. P. H.; Schmidt, T. C. Air-water transfer of MTBE, its degradation products, and alternative fuel oxygenates: The role of temperature. Environ. Sci. Technol. 2004, 38, 5405-5412. (33) Endo, S. Master Thesis, Eberhard-Karls-University Tu ¨ bingen, 2005. (34) Abraham, M. H.; Acree, W. E., Jr. Correlation and prediction of partition coefficients between the gas phase and water, and the solvents dodecane and undecane. New J. Chem. 2004, 28, 15381543. (35) Acree, W. E., Jr.; Abraham, M. H. Solubility predictions for crystalline polycyclic aromatic hydrocarbons (PAHs) dissolved in organic solvents based upon the Abraham general solvation model. Fluid Phase Equilib. 2002, 201, 245-258. (36) Abraham, M. H.; Zissimos, A. M.; Acree, W. E. Partition of solutes into wet and dry ethers; an LFER analysis. New J. Chem. 2003, 27, 1041-1044. (37) Abraham, M. M.; Chadha, H. S.; Dixon, J. P.; Leo, A. J. Hydrogen bonding. 39. The partition of solutes between water and various alcohols. J. Phys. Org. Chem. 1994, 7, 712-716. (38) Abraham, M. H.; Platts, J. A.; Hersey, A.; Leo, A. J.; Taft, R. W. Correlation and estimation of gas-chloroform and waterchloroform partition coefficients by a linear free energy relationship method. J. Pharm. Sci. 1999, 88, 670-679. (39) Abraham, M. H.; Zhao, Y. H. Determination of solvation descriptors for ionic species: Hydrogen bond acidity and basicity. J. Org. Chem. 2004, 69, 4677-4685.

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(44) Ashworth, A. J.; Hooker, D. M. Mixed solvents in gas-liquid chromatography. Activity coefficients for benzene, cyclohexane, pentane and heptane in squalane-dinonyphthalate mixtures at 303 degK. J. Chromatogr. 1979, 174, 307-313. (45) Medir, M.; Mackay, D. Extraction of phenol from water with mixed solvents. Can. J. Chem. Eng. 1975, 53, 274-277.

Received for review August 10, 2005. Revised manuscript received November 4, 2005. Accepted November 4, 2005. ES0515811

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