Article pubs.acs.org/est
Predicting Partition Coefficients of Polyfluorinated and Organosilicon Compounds using Polyparameter Linear Free Energy Relationships (PP-LFERs) Satoshi Endo*,† and Kai-Uwe Goss†,‡ †
Department of Analytical Environmental Chemistry, UFZ, Helmholtz Centre for Environmental Research, Permoserstrasse 15, D-04318 Leipzig, Germany ‡ Institute of Chemistry, University of Halle-Wittenberg, Kurt-Mothes-Strasse 2, D-06120 Halle, Germany S Supporting Information *
ABSTRACT: The environmental behavior, fate, and effects of polyfluorinated compounds (PFCs) and organosilicon compounds (OSCs) have received increasing attention in recent years. In this study, polyparameter linear free energy relationships (PP-LFERs) were evaluated for predicting partition coefficients of neutral PFCs and OSCs, using experimental data for fluorotelomer alcohols (FTOHs) and cyclic volatile methylsiloxanes (cVMS) reported in the literature and measured newly for this work. It was found that the recently proposed PP-LFER model that uses the McGowan characteristic volume (V), the logarithmic hexadecane−air partition coefficient (L), and three polar interaction descriptors can accurately describe partition coefficients of PFCs and OSCs. The prediction errors were 2 log units) occur when the EV and EL models are used to predict Kaw of cVMS. Moreover, trends are often not consistent; that is, the data points in Figure 2 are not aligned parallel to the 1:1 line. Often, deviations from experimental values increase with increasing size of FTOHs and cVMS. It is thus expected that prediction errors would be even larger for larger PFCs and OSCs. Significant inaccuracy in either the solute descriptors or system parameters used, or both, likely exists. Recalibrating Solute Descriptors of FTOHs and cVMS. To test whether the disagreement in values and trends between predicted and experimental partition coefficients observed above can be explained solely by possible inaccuracy in the solute descriptors used, we fitted the solute descriptors of 2779
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the calibration sets used in the literature,20,21,26,30,35−38 we found that the system parameters used above were calibrated with no Si-containing compounds and only a few highly fluorinated chemicals (i.e., F/C > 1.5). The highly fluorinated compounds included are, however, all small such as tetrafluoromethane and hexafluoropropan-2-ol. For Koilw slightly larger PFCs are included, but the largest PFC (nonafluorobutane, V = 1.01) is still smaller than 4:2 FTOH. To test whether insufficient calibration of the PP-LFER equations can explain the remaining inconsistency, we iteratively adjusted both the solute descriptors of FTOHs and cVMS and the system parameters. Thus, the procedure in the previous section was modified: (6′) For each system, PP-LFER system parameters were recalculated using all literature calibration data that had been used to derive the system parameters20,21,26,30,35−38 plus the data for FTOHs and cVMS, by multiple linear regression analysis. (7′) Solute descriptors of FTOHs and cVMS were iteratively adjusted (which simultaneously influenced the system parameters as well because FTOHs and cVMS were also used for calibration) to minimize the sum of the “overall RMSE values” for all partitioning systems using Excel Solver. The “overall RMSE” for a given system here refers to the RMSE between experimental and fitted data for “all compounds” (i.e., literature calibration compounds + FTOHs and cVMS). We note that the solute descriptors of literature calibration compounds were assumed accurate and were not modified during the procedure described above. We also note that the sum of the overall RMSE instead of the errors only for FTOHs and cVMS was minimized so that the finally optimized system parameters would give a good fit not only for FTOHs and cVMS but also for all compounds involved. Because the number of the literature calibration compounds is large (175− 390 for Kow, Kaw, Koa, and Koilw; 34−57 for GC retentions), the addition of FTOHs and cVMS to the calibration set should not dramatically change the system parameters. The system parameters will change only if there is a substantial improvement in the fit for FTOHs and cVMS without much of a deterioration in the fit for the literature calibration compounds. As above, two sets of calculations were performed; one with the EV and EL models (eqs 1, 2) and the other with the VL model (eq 3). The recalibrated solute descriptors are shown in Table 4, and the recalibrated system parameters in SI Table S1. The experimental and fitted partition coefficients are compared in Figure 3.
for FTOHs were assumed not to depend on the length of the perfluoroalkyl chain in this work. We opted to adjust B for cVMS because Atapattu and Poole23 did not include any aqueous system in the calibration set, which can lead to suboptimal B to be used to predict partition coefficients that involve water.40 All of S, A, and B for FTOHs were adjusted because the calibration set used in the literature was relatively limited.22 (4) The experimental data used for recalibration are Kow, Kaw, Koa, and Koilw in Table 1. Klipw and Koc were not used for descriptor optimization because of the complex mechanisms involved in the partitioning to liposomes and organic matter, which generally lowers the quality of fitting by PP-LFERs.30,35 (5) In addition to the partition coefficients mentioned above, GC retention data for FTOHs on three stationary phases reported in ref 22 were included. (6) System parameters reported in the literature (SI Table S1) were used to calculate partition coefficients. (7) The solute descriptors were adjusted by minimizing the sum of squared residuals for all data of cVMS and FTOHs using Excel Solver. Squared residuals for GC retention times were weighted by a factor of 2 because of generally good fitting of PP-LFERs to GC data. Two sets of calculations were performed. In the first case, the EV and EL models were used. Thus, EV was used for Kow, Kaw, and Koilw, and EL was used for Koa and GC retention times. In the second case, the VL model was used for all systems. The resulting descriptors are given in SI Table S2. In the first case (EV/EL), the agreement between PP-LFER calculated and experimental values improved only marginally (Table 3, SI Figure S3). The agreement for Kaw of cVMS was improved, but this was achieved at the cost of reduced agreement for Kow. RMSE values for the log of Kow, Kaw, and Koilw are still relatively high (>0.67) despite the fact that the descriptors were fitted to these partition coefficients. We have not experienced such a problem for other chemicals before. It follows that it is not only the accuracy of the solute descriptors that cause inconsistent predictions. In the second case (VL), a clear improvement was observed (Table 3, SI Figure S3). There is a high agreement between calculated and experimental Kow, Kaw, and Koilw with RMSE < 0.2 log units and a slope close to 1. This indicates that the VL equations reported for these systems in the literature appear to be accurate for both FTOHs and cVMS such that slight adjustment of the solute descriptors is sufficient to achieve overall consistency. RMSE for log Koa is only slightly higher (0.33). The fact that one set of descriptors for each chemical can well describe all partition coefficients further supports the accuracy of the experimental data used here. Klipw and Koc were predicted using the recalibrated descriptors. The resulting RMSE values were still relatively high (0.62−0.99 log units) in both EV/EL and VL approaches. Moreover, RMSE for Kaw predicted with the EL equation (a combination that was not used for descriptor optimization) was as high as 1.67 log units. These high RMSE cannot be explained by a poor accuracy of solute descriptors alone. Recalibrating Both Solute Descriptors and System Parameters. Inconsistent predictions can occur if the system parameters have not been calibrated with PFCs and OSCs, because PFCs and OSCs fall in a chemical domain that is not represented by hydrocarbon-based compounds. Looking into
Table 4. Final Adjusted PP-LFER Solute Descriptors of cVMS and FTOHsa EV/EL based optimization D4 D5 D6 4:2 FTOH 6:2 FTOH 8:2 FTOH a
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VL based optimization
S
A
B
S
A
B
-0.08 -0.10 -0.12 0.36 0.34 0.30
0.00 0.00 0.00 0.50 0.50 0.50
0.28 0.43 0.67 0.33 0.33 0.33
-0.08 -0.10 -0.12 0.18 0.17 0.14
0.00 0.00 0.00 0.62 0.62 0.62
0.32 0.50 0.74 0.31 0.31 0.31
Values in italics were fixed during adjustment. dx.doi.org/10.1021/es405091h | Environ. Sci. Technol. 2014, 48, 2776−2784
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Figure 3. Partition coefficients of FTOHs and cVMS calculated with adjusted solute descriptors and adjusted system parameters vs experimental data. Adjustment was performed individually for the EV/EL models and the VL model (see text). Solid lines show the 1:1 agreement. Dashed lines show a deviation of ±1 log unit.
inadequacy of the EL equation to model Kaw of diverse compounds. It is important to note that including FTOHs and cVMS in the calibration set has little influence on the fitting of the other (mostly hydrocarbon-based) compounds (SI Table S3). An increase of RMSE >0.01 was only found when the EV model was used. The LV model appears to be particularly robust in that it provides reasonable predictions for FTOHs and cVMS without having these in the calibration set, while it can be finetuned to further improve estimations for FTOHs and cVMS without lowering the quality of fit for hydrocarbon-based compounds. Statistical Consideration. As shown in Figure 1, V and L for hydrocarbon-based compounds broadly correlate with each other. Indeed, the literature calibration sets considered here have relatively high cross-correlations between V and L (R2 = 0.62−0.90 without FTOHs and cVMS). Because of the generally high cross-correlation, van Noort42 recently proposed to remove the V term from the VL equation (eq 3). He demonstrated that this simplified equation fits well to the data for hydrocarbon-based compounds with only a negligible or small increase in the standard deviation.42 We, however, stress that, if both hydrocarbon-based compounds and PFCs/OSCs are considered, it is necessary to include both V and L, because a high V−L correlation does not exist in this case (see Figure 1). In fact, when FTOHs and cVMS are included in the calibration set, the cross correlation between V and L is attenuated for all partitioning systems considered (R2 = 0.20− 0.75 with FTOHs and cVMS). This result also means that adding PFCs/OSCs to the calibration data set is effective to reduce the cross-correlation problem of the VL equation and thus helps obtain statistically stable values of system parameters. We also found that removing V from the VL model strongly deteriorates the fit if FTOHs and cVMS are included (SI Table S4). The only exception is the octanol−air
In nearly all cases, RMSE values for FTOHs and cVMS were further improved from the case where only the solute descriptors were adjusted (Table 3). RMSE particularly improved for the EV/EL models. However, the RMSE obtained with EV/EL is still relatively high (>0.4 log units). The errors are particularly large for Kow and Kaw of cVMS (Figure 3). This relatively poor fit is striking, as both descriptors and equations have been optimized using these experimental data in this last step. The result may be taken as an indication that the combination of “E and V” and “E and L” cannot accurately describe the nonspecific interaction properties when PFCs and OSCs are included. In contrast to the EV/EL approach, the VL model can fit all data to the accuracy of RMSE 0.1−0.2 log units. Optimization of the system parameters of the VL model has only a negligible or small influence on RMSE, indicating that the literature-reported system parameters are already reasonably accurate. Using the updated solute descriptors for FTOHs and cVMS, the system parameters for the two remaining partition coefficients (Klipw, Koc) were recalibrated. While RMSE largely improved regardless of the type of equation (Table 3), the slopes of FTOHs still deviate from 1 (Figure 3). The reason is unknown but may be related to the heterogeneity and anisotropy of phospholipid membranes and organic matter. Phospholipid membranes have a bilayer structure in which different chemicals have different preferred positions and orientations. Similarly, organic matter is a highly complex matrix encompassing different sorption sites that varyingly interact with chemicals. For such materials, the PP-LFER system parameters can only describe average sorption properties of different positions/sites. Regarding Koc, natural variability of organic matter may also contribute to the observed inconsistency. With the updated descriptors, the EL equation for Kaw was also recalibrated. The RMSE for FTOHs and cVMS remains large (1.15 log units), which points toward 2781
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predicted log Koc and log Kow for the considered OSCs (including cVMS), but the relationship found (log Koc = 0.65 log Kow − 0.25) differs substantially from that typically used for hydrophobic organic compounds (e.g, log Koc = 0.99 log Kow − 0.35).44 This result suggests that large differences between log Koc and log Kow exist not only for cVMS but also for many other OSCs. Note however that we do not infer here that there would be a single log Koc−log Kow correlation for OSCs in general, because the OSCs considered here represent only a subset of all possible molecular structures of Si-containing compounds. It should also be noted that the descriptors of the OCSs reported by Poole et al.8,23 were not calibrated with any aqueous system. The B descriptor can depend significantly on whether it is calibrated with or without aqueous systems (e.g., compare B for cVMS in Tables 2 and 4; also see ref 40). Thus, while the OSC descriptors in the literature may serve as first approximations, it is desirable that the descriptors be validated or optimized with additional experimental solvent−water and/ or air−water partition coefficients. This study demonstrated that PP-LFER approaches are useful to predict partition coefficients of PFCs and OSCs and understand their partitioning behavior. The solute descriptors for FTOHs and cVMS optimized in this study could be used to predict various other partition coefficients. Determination or optimization of the solute descriptors of other PFCs and OSCs may be helpful to promote our understanding of their partitioning behavior. Further optimization and validation of the system parameters for other environmental partitioning systems with regard to their accuracy for PFCs and OSCs is suggested.
partition coefficient, for which removing V does not significantly influence the overall fit. This may indicate that the nonspecific interactions (van der Waals interactions and cavity formation) in octanol are similar to those in hexadecane. A good fit, however, was not obtained for the water−air partition coefficient, and it is expected that other highly polar solvents such as methanol and ethylene glycol will also show a poorer fit because much higher cavity formation energy is needed in such polar solvents than in hexadecane. Therefore, as a general approach, both V and L should be included when PFCs, OSCs, and hydrocarbon-based compounds are all of interest. Implications for Predicting Partition Coefficients of PFCs and OSCs. The most important finding of this study is that the VL-type PP-LFER (eq 3) can predict partition coefficients for PFCs, OSCs and hydrocarbon-based compounds all together. In contrast, the EV/EL approaches can lead to substantial errors for PFCs and OSCs even if optimally calibrated solute and system descriptors are used. Both PPLFER approaches (EV/EL on the one hand and VL on the other hand) have been shown to work comparatively well if only hydrocarbon-based compounds are considered.20,43 PFCs and OSCs represent the first classes of chemical where the two approaches exhibit considerable differences in the quality of fit. The reason why the VL approach performs better than EV/EL cannot be clarified based on this study alone. We surmise that the consistent use of the L descriptor, which itself is an experimental partition coefficient, renders the VL model more robust for partition coefficient estimation than the EV/EL approach. The fact that the literature VL equations can accurately predict Kow, Kaw, Koa, and Koilw of FTOHs and cVMS without additional adjustment is interesting, because, statistically, the equations have to be extrapolated for FTOHs and cVMS. The system parameters were indeed not sensitive to the inclusion of FTOHs and cVMS into the calibration data set. It is expected, therefore, that other literature VL system parameters that were not used here may also provide reasonable predictions for PFCs and OSCs, provided that the parameters have been calibrated with as large a variety of compounds as the parameters for Kow, Kaw, Koa, and Koilw. However, validation and recalibration of system parameters with PFCs and/or OSCs appear to be inevitable for complex matrices as suggested by the results for liposomes and soil organic matter shown above. Other materials that may need further evaluation include dissolved organic matter, airborne particles, and proteins. For the six partition coefficients studied here (Kow, Kaw, Koa, Koilw, Klipw, Koc), the system parameters were recalibrated with FTOHs and cVMS in this work (SI Table S1) and thus should provide more accurate predictions for PFCs and OSCs. In combination with the VL equations recalibrated above, the solute descriptors for 61 additional OSCs reported by Poole and co-workers8,23 can be used to delineate the partitioning properties of OSCs. We predicted Kow, Koilw, and Klipw of the 61 OSCs using the respective PP-LFER equations (SI Figure S4). The predictions suggest that Koilw and Kow are within 0.5 log units on average (except for H-bond donor compounds and a few very large OSCs), whereas Klipw is consistently lower than Kow by around 1 log unit. Such systematic differences would be highly important for bioaccumulation and toxicity evaluation, because Klipw is usually assumed identical to Kow. Additionally, we predicted and compared Kow and Koc for the 61 OSCs (SI Figure S5). Interestingly, there is a correlation between
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ASSOCIATED CONTENT
S Supporting Information *
Additional tables for system parameters reported in the literature and adjusted in this work, adjusted solute descriptors, and RMSE for calibration compounds; additional figures for oil−water partition coefficients, dependence of partition coefficients on the number of CF2 and siloxane units, Partition coefficients of FTOHs and cVMS calculated with adjusted solute descriptors and literature system parameters, and comparison of Koilw, Klipw, Koc, and Kow for OSCs. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Phone: +49 341 235 1818; fax: +49 341 235 450822; e-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Andrea Pfennigsdorff for her assistance in the experimental work. REFERENCES
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