Experimental Determination of Air/Water Partition Coefficients for 21 Per- and Polyfluoroalkyl Substances Reveals Variable Performance of Property Prediction Models

Abstract

Per- and polyfluoroalkyl substances (PFAS) are a group of chemicals of high environmental concern. However, reliable data for the air/water partition coefficients (K_aw), which are required for fate, exposure, and risk analysis, are available for only a few PFAS. In this study, K_aw values at 25 °C were determined for 21 neutral PFAS by using the hexadecane/air/water thermodynamic cycle. Hexadecane/water partition coefficients (K_Hxd/w) were measured with batch partition, shared-headspace, and/or modified variable phase ratio headspace methods and were divided by hexadecane/air partition coefficients (K_Hxd/air) to obtain K_aw values over 7 orders of magnitude (10^–4.9 to 10^2.3). Comparison to predicted K_aw values by four models showed that the quantum chemically based COSMOtherm model stood out for accuracy with a root-mean-squared error (RMSE) of 0.42 log units, as compared to HenryWin, OPERA, and the linear solvation energy relationship with predicted descriptors (RMSE, 1.28–2.23). The results indicate the advantage of a theoretical model over empirical models for a data-poor class like PFAS and the importance of experimentally filling data gaps in the chemical domain of environmental interest. K_aw values for 222 neutral (or neutral species of) PFAS were predicted using COSMOtherm as current best estimates for practical and regulatory use.

Short abstract

New data for air/water partition coefficients for 21 PFAS demonstrated accurate prediction by quantum chemically based COSMOtherm and lower performance of empirical fit models.

1. Introduction

Per- and polyfluoroalkyl substances (PFAS) are a group of chemicals with high environmental concern because they are either resistant to degradation or transform into substances that are persistent in the environment and ecosystems. Some PFAS [e.g., perfluorooctane sulfonate (PFOS), perfluorooctanoic acid (PFOA)] have been proven to have significant health influences on some populations at the current levels of contamination.¹ Since accumulation of PFAS in humans and animals was reported in 2001,²⁻⁵ active research has been conducted on this class of chemicals worldwide. According to Bakhshoodeh and Santos,⁶ the annual number of scientific publications on PFAS exceeded 100 in 2007 and reached ∼900 in 2020. Despite the proliferation of literature on PFAS, experimental data for basic physicochemical properties, including air/water partition coefficients (K_aw), are scarce. K_aw largely dictates the contaminant transfer between air and water and has a tremendous influence on the fate of the chemical in the environment. In addition, K_aw has implications for analytical methods (e.g., sample collection, storage, extraction), remediation techniques (e.g., air stripping), and ecotoxicological test settings suitable for given chemicals.

There have been only a few scientific articles that reported direct measurements of K_aw for PFAS with a perfluorocarbon chain length of 4 or more. Three studies measured K_aw for 3 or 4 fluorotelomer alcohols (FTOHs).⁷⁻⁹ Some of the reported values, however, differ between the studies by up to a factor of 130 for a single compound. Two other studies took on the challenge of measuring K_aw of the neutral species of the strong acid PFOA and provided values that are an order of magnitude different.^10,11 To fill the huge data gap, various researchers derived K_aw from the saturated vapor pressure relative to the aqueous solubility (VP/S).^8,9,12,13 Even including such indirectly measured K_aw data, the authors of a recent review¹³ listed experimental data for only seven PFAS. A reason for the data limitation could be that PFAS of major concern are strong acids, which ionize and become strongly soluble in water, making K_aw of the neutral species less important for environmental fate analysis. Nevertheless, there exist many neutral or largely neutral PFAS, some of which are known precursors of the PFAS of high concern (i.e., PFOS, PFOA).¹⁴⁻¹⁶ Another reason may be measurement difficulty associated with the interfacial active nature of many PFAS. Direct measurement of K_aw often requires quantification of the gas phase PFAS concentrations^11,17 or relies on the mass balance in a closed air/water system,^7,8 neither of which could conveniently be achieved if the adsorption to a third phase such as a glass wall or air/water interface is significant. As K_aw data are largely missing, environmental transport models inevitably use model-based predictions.^18,19 However, no experimental data means no model calibration and validation; indeed, Arp et al.²⁰ reported prediction errors of several orders of magnitude in K_aw by some models.

The objectives of this study are to obtain new experimental data for K_aw at 25 °C for a series of neutral PFAS and to evaluate K_aw prediction models. New data for PFAS with various molecular structures can also improve our understanding on the structure–property relationship. To circumvent the difficulty associated with direct measurement of K_aw, we determined K_aw indirectly by measuring the hexadecane/water partition coefficient (K_Hxd/w) and applying the hexadecane/air/water thermodynamic cycle:

1

where K_Hxd/air is the hexadecane/air partition coefficient. K_Hxd/w can be measured more reliably than K_aw because gas phase quantification is not needed and hexadecane has a larger solubilization capacity than water, which minimizes the problem of third-phase sorption. Experimental K_Hxd/air values for 61 PFAS have already been reported in our previous study.²¹ A similar approach could be taken with the octanol/air/water cycle. However, octanol/air partition coefficients are unavailable for most PFAS. Additionally, there is some mutual solubility between octanol and water, and water-saturated octanol has been shown to have slightly different properties than pure octanol.²² In contrast, hexadecane has very little mutual solubility with water and is an ideal solvent to be used for the thermodynamic cycle approach.²³ The new K_aw data for 21 PFAS were compared to predictions by four models that are often used in environmental risk assessments. K_aw prediction models have been evaluated against experimental data in the literature but only for four FTOHs^20,24 and four additional PFAS¹³ so far because of the data limitation.

2. Materials and Methods

2.1. Chemicals

K_Hxd/w values were measured for 21 PFAS; their names, abbreviations, and CAS registry numbers are listed in Table 1. These compounds were selected according to their environmental relevance, structural variation, and measurement possibility. The providers and purity of the reagents are provided in Table S1, Supporting Information (SI). Hexadecane (anhydrous, ≥99%) was purchased from Sigma-Aldrich (Tokyo, Japan). Methanol, acetone, and n-hexane were of analytical grade and from Fujifilm Wako Chemicals (Osaka, Japan). Reverse osmosis-treated tap water was further purified with an Ultrapure Water System (RFU665DA, Advantec, Tokyo, Japan).

Table 1. List of PFAS Used in This Study^a.

name	abbreviation	CAS-RN
1H,1H-perfluorobutan-1-ol	3:1 FTOH	375-01-9
3-(perfluoropropyl)propan-1-ol	3:3 FTOH	679-02-7
1H,1H,2H,2H-perfluorohexan-1-ol	4:2 FTOH	2043-47-2
4-(perfluorobutyl)butan-1-ol	4:4 FTOH	3792-02-7
1H,1H,2H,2H-perfluorooctan-1-ol	6:2 FTOH	647-42-7
1H,1H-perfluorooctan-1-ol	7:1 FTOH	307-30-2
1H,1H,2H,2H-perfluorodecan-1-ol	8:2 FTOH	678-39-7
1H,1H,1H,2H-perfluoroheptan-2-ol	5:2s FTOH	914637-05-1
1H,1H,2H,2H-perfluorohexyl iodide	4:2 FTI	2043-55-2
1H,1H-perfluoroheptyl iodide	6:1 FTI	212563-43-4
1H,1H,7H-perfluoroheptyl iodide	6:1 FTI-7H	376-32-9
1H,1H,2H,2H-perfluorooctyl acrylate	6:2 FTAC	17527-29-6
1H,1H,2H,2H-perfluorohexyl methacrylate	4:2 FTMAC	1799-84-4
perfluorobutane sulfonamide	PFBSA	30334-69-1
perfluorohexane sulfonamide	PFHxSA	41997-13-1
perfluorooctane sulfonamide	PFOSA	754-91-6
N-methyl perfluorobutane sulfonamide	MeFBSA	68298-12-4
N-methyl perfluorohexane sulfonamide	MeFHxSA	68259-15-4
N-ethyl perfluorohexane sulfonamide	EtFHxSA	87988-56-5
N-methyl perfluorobutane sulfonamidoethanol	MeFBSE	34454-97-2
N-ethyl perfluorohexane sulfonamidoethanol	EtFHxSE	34455-03-3

^aSee Table S2 for the molecular structure represented by SMILES strings.

2.2. Experimental Determination of K_Hxd/w

K_Hxd/w values were determined by batch partition, shared-headspace, and/or modified variable phase ratio headspace (VPR-HS) methods. The experimental procedures for these methods are described in full in SI-1; here, brief explanations are provided.

2.2.1. Batch Partition Method

Hexadecane solution of PFAS (0.1–2000 mg/L) and water were put in 10-mL glass vials and gently shaken for 24 h (60 rpm, 25 °C). An aliquot of the water phase was analyzed by liquid chromatography/mass spectrometry (LC/MS; for all eight sulfonamides) or liquid–liquid-extracted with n-hexane and analyzed by gas chromatography (GC)/MS (for all others). The conditions for LC/MS and GC/MS analyses are described in SI-2. K_Hxd/w was calculated using the measured water phase concentration under the mass conservation assumption. The 95% confidence interval (CI) of the mean (x) was calculated with the formula, x ± 2.78 SD/√5, where SD is the standard deviation, based on the t-distribution and n = 5. The hexadecane phase was also analyzed with LC/MS or GC/MS, which confirmed 93–112% of the expected concentrations present in hexadecane. The PFAS concentration prepared in hexadecane and volumes of water and hexadecane, and recovery from the hexadecane phase for each compound are given in Table S3. The batch partition method was performed for 18 PFAS. It was not performed for 3:1 FTOH because its extraction from water and GC-separation from the solvent peak was difficult by the current method. Moreover, 7:1 and 8:2 FTOHs were not measured, as the shared-headspace method was expected to provide more accurate values of K_Hxd/w for these relatively hydrophobic chemicals (see the Results section).

For unsubstituted perfluoroalkane sulfonamides (PFASAs) and their N-alkyl derivatives, namely, PFBSA, PFHxSA, PFOSA, MeFBSA, MeFHxSA, and EtFHxSA, 1 mM HCl aqueous solution instead of pure water was used. Preliminary experiments with PFBSA and PFHxSA with pure water resulted in log K_Hxd/w values that were 0.5–0.9 log units lower than those determined with 1 mM HCl solution later. While measured pK_a values of these compounds are unavailable, an experimental pK_a value of 6.33 was reported for trifluoromethane sulfonamide (CF₃-SO₂NH₂).²⁵ COSMOtherm predicted pK_a values of 6.4 and 6.3 for PFBSA and PFHxSA, respectively, and 7.3 and 7.2 for MeFBSA and MeFHxSA, respectively. These results suggest that PFASAs and their N-alkyl compounds can be deprotonated in unbuffered water but remain largely neutral in 1 mM HCl.

2.2.2. Shared-Headspace Method

The method concept is based on the existing publications that used a shared-headspace system for salting-out experiments²⁶ and ecotoxicity tests.^27,28 Hexadecane solution of PFAS was placed in a 350 μL insert hosted by a 1.5 mL GC vial. This small vial was put in a 10 mL headspace vial that contained 1 mL of water. The 10 mL vial was closed with a PTFE-lined septum and gently shaken at 25 °C for 24 h. During this time, the compound dissolved in hexadecane was partially transferred to water via the headspace until a three-phase partition equilibrium was reached between hexadecane, air, and water. Water was then sampled and immediately extracted with n-hexane for GC/MS analysis. The hexadecane phase was also analyzed, which confirmed 85–100% mass conservation (Table S3). K_Hxd/w was obtained from the measured concentration in water, as in the batch partition method. The shared-headspace approach does not require a direct contact between water and hexadecane, avoiding the possible formation of emulsions or microdroplets in water. The shared-headspace method is useful for compounds with sufficient volatility (relatively high K_aw, low K_Hxd/air) and hydrophobicity (relatively high K_Hxd/w), as these properties ensure an efficient transfer from hexadecane to water via air and negligible concentration depletion in hexadecane. Therefore, nine PFAS that meet this requirement were measured by this method, while all eight sulfonamides and four short-chain FTOHs were not.

2.2.3. Modified VPR-HS Method

K_Hxd/w was also measured with a modified version of the VPR-HS method; 20 mL headspace vials were filled with water and hexadecane with different volume ratios. The total liquid volume was always 20 mL. All vials received the same amount of the target compound. After equilibration at 25 °C, the headspace was injected into the GC/MS. Based on the mass balance, the peak area (PA) should have the following relationship with K_Hxd/w:

2

where α is the GC/MS response factor, m is the mass of the compound added to the vial, V_tot is the total liquid volume, and V_Hxd is the volume of hexadecane solution. Here, response linearity as well as no significant mass of the compound in the headspace and any other interface (e.g., vial wall, hexadecane/water interface, septum) was assumed. As α, m, and V_tot (=20 mL) are constant for a given compound, K_Hxd/w can be fitted on the data of PA vs V_Hxd. Theoretically, K_Hxd/w could be determined with a minimum of two V_Hxd conditions (e.g., 0 and 20 mL), whereas at least four V_Hxd values were prepared in this work. Five FTOHs were measured with this method, which were measurable by headspace GC/MS and expected to have K_Hxd/w that is low enough for this method.

2.3. Direct Measurement of K_aw Using the VPR-HS Method

K_aw values for five PFAS were directly measured using a standard VPR-HS method, as in the literature.^7,8 The experimental procedure is similar to what has been described previously for K_Hxd/air(21) and is summarized in SI-3. This measurement was conducted for a comparison purpose because the VPR-HS measurement for K_aw could result in substantial errors if the mass balance assumption does not hold true, as was experimentally demonstrated before.⁸

2.4. Prediction Models for K_aw

In this work, four prediction models for K_aw were considered. All need only the molecular structure as an input parameter.

2.4.1. HenryWin

HenryWin (v3.21, April 2015) is a module of EPI-Suite (v4.11) provided by US EPA¹² and predicts the Henry’s law constants using two-dimensional structure-based quantitative structure/property relationships (QSPRs) calibrated on experimental data.²⁹ HenryWin offers the bond contribution method and the group contribution method, but the former was mainly considered here because the latter did not calculate a prediction for any of the eight sulfonamides used in this work. SMILES strings as shown in Table S2 were entered, and the output Henry’s law constants at 25 °C were converted to K_aw following the ideal gas law.

2.4.2. OPERA

OPERA (v 2.9, downloaded in January 2023) stands for OPEn structure–activity/property Relationship App and is provided by US EPA.³⁰ It predicts physicochemical properties based on a k-nearest neighbor method using PaDEL descriptors. For K_aw, the model is calibrated on the PhysProp experimental database. As for HenryWin, SMILES strings were the input, and predicted Henry’s law constants at 25 °C were converted to K_aw. For evaluation of the applicability domain (AD), the OPERA software provides a “global AD” based on the leverage calculation and a “local AD index” derived from the similarity to the five nearest neighbor chemicals.³⁰

2.4.3. LSER-IFSQSAR

The linear solvation energy relationship (LSER) is a polyparameter linear free energy relationship developed by Abraham and is a multiple linear regression model that describes logarithmic partition coefficients using five solute descriptors.^31,32 The iterative fragment selection quantitative structure–activity relationship (IFSQSAR)³³ predicts these solute descriptors. Combined with the published LSER equation for log K_aw,³⁴ IFSQSAR predicts log K_aw values based only on the molecular structure. An online toolbox, EAS-E Suite (Ver. 0.96-Beta, released November 2022, accessed in February 2023)³⁵ was used for the calculation. As an AD indicator, EAS-E Suite provides an “uncertainty level (UL)”, which indicates reliability of the predicted solute descriptors. In addition, EAS-E Suite calculates “estimated errors”, which are estimates of overall prediction errors resulting from uncertainty in both solute descriptors and the LSER equation.³³

2.4.4. COSMOtherm

COSMOtherm is a program that predicts activity-related properties including partition coefficients, following the COSMO-RS theory.³⁶ Turbomole, COSMOconfX, and COSMOthermX (COSMOlogic, Dassault Systèmes, version 2021) were used to perform COSMOtherm calculations, as described previously.²¹ Briefly, for each compound, an initial structure was entered to COSMOconfX, which generated and evaluated a number of possible conformers. Quantum chemical calculations were performed with Turbomole to obtain “COSMO files”, which contain the necessary information such as molecular surface polarity. COSMOthermX read the generated COSMO files, calculated pairwise interaction energy between molecules, and derived partition coefficients from statistical thermodynamics using the COSMOtherm algorithm. The parameterization applied was BP_TZVPD_FINE_21. Log K_Hxd/w and log K_aw at 25 °C were predicted with this method.

3. Results and Discussion

3.1. Measurement of K_Hxd/w

K_Hxd/w values measured in this study are summarized in Table 2.

Table 2. Log K_Hxd/w Values Measured in This Study and Log K_aw Derived from Eq 1.

	log KHxd/w						log Kaw
	batch partition methoda		shared-headspace methoda		modified VPR-HS method		eq 1	VPR-HS or VP/S
	mean	95% CI	mean	95% CI	mean	95% CI
3:1 FTOH	NA		NA		–0.35	[−0.37, −0.32]	–1.89	–2.03d
3:3 FTOH	0.52	[0.51, 0.54]	NA		0.32	[0.17, 0.47]	–2.17	–2.04d
4:2 FTOH	0.79	[0.77, 0.81]	NA		0.75	[0.70, 0.80]	–1.57	–1.56d, −1.30e, −1.63f, −1.21g, −1.52h
4:4 FTOH	1.60	[1.58, 1.62]	NA		1.43	[1.09, 1.71]	–1.97	–1.28d
6:2 FTOH	2.50	[2.42, 2.59]	2.51	[2.44, 2.58]	NA		–0.64	–1.47e, −0.56f, 0.37g, −0.44h
7:1 FTOH	NA		2.70	[2.56, 2.84]	NA		–0.26
8:2 FTOH	NA		3.75	[3.73, 3.78]	NA		0.11	–1.82e, 0.58f, 0.31g, 0.96h
5:2s FTOH	2.00	[1.93, 2.08]	2.04	[1.98, 2.11]	1.55	[1.18, 1.75]	–0.15
4:2 FTI	4.13b	[3.89, 4.36]	4.93	[4.86, 4.99]	NA		1.60
6:1 FTI	4.34b	[3.82, 4.86]	5.66	[5.36, 5.95]	NA		2.28
6:1 FTI-7H	4.06b	[3.72, 4.39]	4.62	[4.55, 4.70]	NA		0.70
6:2 FTAC	4.22b	[3.92, 4.51]	5.43	[5.40, 5.46]	NA		1.27
4:2 FTMAC	4.02b	[3.82, 4.21]	4.65	[4.58, 4.72]	NA		0.62	–0.14d
PFBSA	–1.15c	[−1.20, −1.10]	NA		NA		–4.89
PFHxSA	0.39c	[0.28, 0.51]	NA		NA		–3.94
PFOSA	1.80c	[1.72, 1.87]	NA		NA		–3.04
MeFBSA	0.82c	[0.80, 0.85]	NA		NA		–2.85
MeFHxSA	2.25c	[2.16, 2.34]	NA		NA		–2.01
EtFHxSA	2.95c	[2.85, 3.04]	NA		NA		–1.58
MeFBSE	0.49	[0.45, 0.52]	NA		NA		–4.35
EtFHxSE	2.76	[2.66, 2.87]	NA		NA		–3.02

^an = 5. T = 25 °C unless otherwise noted.

^bLikely inaccurate because of the presence of hexadecane in water.

^c1 mM HCl was used.

^dMeasured by the VPR-HS method in this study.

^eRef (7).

^fRef (8).

^gRef (9).

^hRef (12), 23 or 24 °C. CI, confidence interval. NA, not available. Underlined values were used for eq 1.

Log K_Hxd/w values measured by both batch and shared-headspace methods are available for seven compounds. The two methods resulted in practically identical values for 6:2 and 5:2s FTOHs. However, the log K_Hxd/w values measured by the batch method were significantly lower than those by the shared-headspace method for the remaining five compounds (i.e., 4:2 FTI, 6:1 FTI, 6:1 FTI-7H, 6:2 FTAC, 4:2 FTMAC), which are all relatively hydrophobic. The batch method-measured values for the five compounds were all ∼4 with wide 95% CIs. It is likely that the water phase equilibrated in the batch method contained invisible microdroplets of hexadecane, which increased the apparent concentration of the water phase and decreased the measured (apparent) K_Hxd/w. Indeed, if we assume that the water phase contained 0.006 vol % hexadecane droplets and that log K_Hxd/w determined by the shared-headspace method is accurate, we can reproduce the “apparent log K_Hxd/w” values measured by the batch method (see SI-4 for the calculation). The presence of 0.006 vol % hexadecane in water suggests that the current batch partition method is applicable to measure log K_Hxd/w values up to 3.6. For higher K_Hxd/w, an error of >0.1 log unit would occur. The method could be improved by making an additional effort to remove hexadecane from water, e.g., by centrifugation or filtration. In the shared-headspace method, the water phase is free of hexadecane. The shared-headspace method appears applicable for compounds with log K_Hxd/w values higher than 4, although the test compound should be sufficiently volatile and hydrophobic (see the Methods section). Thus, the batch partition and shared-headspace methods are largely complementary and, by combining these two methods, we were able to measure log K_Hxd/w from −1.15 to 5.66 for PFAS with different molecular structures.

The modified VPR-HS method resulted in log K_Hxd/w values comparable to those measured by the batch partition method (Table 2). However, the data plot did not always follow the relationship between PA and V_Hxd expected by eq 2 (Figure S1). As a result, the CIs were large, particularly for 4:4 and 5:2s FTOHs. The reason may be significant adsorption to, e.g., the glass wall, septum, air/water interface, and syringe used for GC injection, which violates the assumption of eq 2. Thus, although the method is by far the simplest, the use of this method may be limited to weakly sorptive compounds. In the following discussion, we consider only the data for 3:1 FTOH determined by the modified VPR-HS method because no other data are available for this compound.

3.2. Determination of K_aw

Using eq 1, we obtained log K_aw values (25 °C) from −4.89 to 2.28, thus over 7 log units (Table 2). Such a wide range would not be achievable by direct measurement methods alone, demonstrating an advantage of the thermodynamic cycle approach used here. Table 2 also shows log K_aw values determined by direct methods including the standard VPR-HS method in this study (Figure S2) and the literature as well as values derived from VP/S calculation in the literature. The values for 3:1, 3:3, and 4:2 FTOHs from different sources agree well with each other, mostly within 0.1–0.2 log units. However, larger difference was found for 4:4, 6:2, 8:2 FTOHs, and 4:2 FTMAC, which are less water-soluble and less volatile than the former three compounds and are likely more susceptible to experimental artifacts. As shown below, our values from eq 1 are internally consistent and should represent the most reliable set of experimental values available for PFAS. In the course of this work, a new paper appeared that reported K_aw values for 15 PFAS measured by the standard VPR-HS method.³⁷ These data, however, are inconsistent with the available knowledge for K_aw of PFAS (see SI-5 and Figures S5, S6 for more details) and thus are not further considered here.

3.3. PFAS Molecular Structure and Partition Coefficients

From the data obtained in this work, several important relationships between the structure of PFAS and the partition coefficients can be noted.

Fluorotelomer substances (i.e., FTIs, FTACs, FTMACs) favor air over water (log K_aw > 0), except for FTOHs. Even with a polar functional group such as acrylate or methacrylate, these chemicals readily partition from water to air. In contrast, unsubstituted PFASAs are water-soluble (log K_aw < −3), even if their ionization in water as discussed above is disregarded. N-methyl substitution of PFASAs increases K_aw by 2 log units, making them substantially less water favoring. Further N-hydroxyethyl substitution (e.g., from MeFBSA to MeFBSE) decreases K_aw back by 1.5 log units, because of the introduction of the polar −OH group.

We have K_aw data for two X:1 FTOHs, three X:2 FTOHs, three PFASAs, and two N-methyl FASAs, from which we can calculate the dependence of log K_aw on the CF₂ chain length (Figure 1B and Table S4). Log K_aw of these four groups increases consistently by 0.43 ± 0.02 log units per CF₂. This value is useful when the log K_aw for PFAS needs to be extrapolated from available data for shorter-chain homologues. The high consistency of the observed CF₂ dependence over four classes of PFASs supports accuracy of our data. Noteworthy is that log K_aw increases only by 0.14 ± 0.04 log units per CH₂. This small change in log K_aw with the addition of CH₂ can be explained by the fact that the increased van der Waals interaction energy with water molecules is nearly offset by the increased cavity formation energy cost. In the case of CF₂, the increase in cavity formation energy exceeds the increase in interaction energy, and thus, CF₂ has a substantially larger influence on log K_aw than CH₂. Interestingly, the CF₂ and CH₂ increments have similar influences on log K_Hxd/w (0.74 ± 0.02 and 0.64 ± 0.04, respectively; Figure 1A), as opposed to the differing influences on log K_aw.

Figure 1.

Dependence of (A) log K_Hxd/w and (B) log K_aw on the number of CF₂ or CH₂ units. Data for n-alkan-1-enes, n-alkylbenzenes, and n-alkan-1-ols are from Abraham et al.^41,42 The lines indicate the linear regression.

Another finding is that log K_Hxd/w of 6:1 FTI-7H is 1.0 log unit lower than that of 6:1 FTI and that log K_aw of the former is 1.6 log units lower than that of the latter. Both indicate that 6:1 FTI-7H has substantially higher water affinity than 6:1 FTI does. The only structural difference between 6:1 FTI-7H and 6:1 FTI is the F substitution pattern of the terminal methyl group (−CF₂H vs −CF₃, respectively). The H atom at the end of the perfluoroalkyl chain can serve as a relatively strong H-bond donor site because of the strong electron-withdrawing property of the F atoms, substantially strengthening the polar interactions with water molecules. It has been reported in the literature that H atoms of halogenated aliphatic compounds can serve as H-bond donor sites (e.g., chloroform,³⁸ hexachlorocyclohexanes,³⁹ and chlorinated paraffins)⁴⁰ and affect the partition properties of the compounds.

3.4. Evaluation of Prediction Models

Model predictions of log K_aw are presented in Table S5 and were compared to the experimental values obtained in this study (Figure 2; a larger version is provided in Figure S3). For each model, the root-mean-squared error (RMSE) was calculated from the difference between experimental and predicted values.

Figure 2.

Predicted vs experimental log K_aw for 21 PFAS. Solid lines indicate the 1:1 agreement and dashed lines 1 log unit difference. A larger version is available in the SI. RMSE, root-mean-squared error; ME, mean error, i.e., the mean of predicted minus experimental values.

HenryWin (bond contribution model) suffered from a high RMSE (2.2 log units) with strong biases to overprediction. Deviations from experimental values increased with increasing chain length. Particularly large errors were found for PFOSA (error, +4.9), PFHxSA (error, +4.4), PFBSA (error, +3.9), and 6:1 FTI-7H (error, +3.0), with the plus sign in the parentheses indicating overprediction. Predictions for FTOHs were better but still errors up to +2.1 were found. The group contribution model of HenryWin was not any better (RMSE 2.1 log units; n = 13; see Table S5). In 2006, Arp et al.²⁰ demonstrated similar overprediction for four FTOHs by a former version of HenryWin. There appears to be no major improvement in predicting log K_aw for PFAS.

OPERA also resulted in a high RMSE (1.8 log units). The OPERA prediction did not even follow the increasing trend of log K_aw with the chain length, but instead, it calculated a narrow range of log K_aw from −2.9 to −1.5 for 19 out of 21 compounds. More specifically, OPERA calculated ∼ −1.6 for 10 and ∼ −2.3 for 3 compounds. As shown in Table S6, all predictions were outside the global AD defined by the leverage calculation of OPERA. Moreover, the local AD indices generated by OPERA were low (<0.4) for all but 3:1 FTOH, meaning that the five nearest neighbors were not similar to the predicted compound. Thus, OPERA clearly indicated that its log K_aw predictions for the 21 PFAS were not trustworthy. Looking closer at the output file, we found that a few calibration chemicals (e.g., 6:2, 8:2 FTOHs) were frequently identified as neighboring compounds, which resulted in similar predictions for many of the tested PFAS. Lampic and Parnis¹³ proposed to compute K_ow and K_oa with OPERA and apply a thermodynamic cycle to calculate K_aw. This approach, however, did not result in major improvement in RMSE (1.7 log units, Table S5) even though all 21 compounds were considered within AD of both K_ow and K_oa prediction models.

LSER-IFSQSAR provided a better RMSE (1.3 log units) than the former two methods, and it captured the chain-length dependence of log K_aw. LSER-IFSQSAR consistently underestimated sulfonamides and their derivatives (errors, −2.7 to −1.0) and tended to overestimate the others including FTOHs (errors, −0.2 to +1.5), except 5:2s FTOH (error, −1.6). The ULs provided by EAS-E Suite did not have a relationship with the observed absolute errors (R², 0.01) but the estimated errors from EAS-E Suite did have a positive correlation with the observed absolute errors (R², 0.38) (Table S6).

COSMOtherm was by far the most accurate of the four models tested (RMSE, 0.4 log units). The accuracy of log K_aw prediction for neutral PFAS is comparable to that for nonfluorinated chemicals (∼0.3 log units).⁴³ Thus, COSMOtherm accurately modeled the influence of the perfluoroalkyl structure on log K_aw discussed in the previous section. There was slight overall underprediction with a mean error (ME) of −0.34 log units. This minor but consistent bias is similar to the prediction for log K_Hxd/air, reported in our previous paper.²¹ The ME of log K_Hxd/air predictions for the current 21 compounds is +0.48 (Figure S4). COSMOtherm appears to slightly overestimate the partitioning of PFAS from air to liquid phases. In contrast, log K_Hxd/w predictions by COSMOtherm have little bias (ME, +0.14; Figure S4), suggesting the liquid/liquid partitioning can be predicted more accurately. Note that, if we correct the COSMOtherm-predicted log K_aw values by adding 0.34, the RMSE would become 0.26 log units.

Overall, the evaluation of four models presented above suggests that fully empirical models (e.g., HenryWin, OPERA) do not seem to be useful for predicting K_aw of PFAS, at least for the moment. Errors by 4 or 5 orders of magnitude may be too high even for chemical screening purposes. The low performance might be no surprise, as there have not been sufficient calibration data for PFAS. Apparently, HenryWin lacks fragment values and correction factors required to describe the influence of F substitutions on log K_aw. OPERA needs far more K_aw data for PFAS that could serve as useful nearest neighbors. HenryWin and OPERA could be recalibrated with the experimental log K_aw data from this study, which should improve their prediction for PFAS that are similar to any of the test compounds of this study. However, large errors could still occur for the other PFAS. As the architecture of LSER-IFSQSAR is more complicated than that of HenryWin and OPERA, it is not straightforward to interpret the results. LSER-IFSQSAR has been built on the mechanically based LSER equation and calibrated not only on log K_aw but on many different partition data available, which could explain the better predictions. The high prediction performance of COSMOtherm indicates that this theoretically based model is suitable for predicting K_aw of PFAS. Arguably, for an extremely data-poor class of chemicals such as PFAS, a theoretical model that does not require substructure-specific calibration generates more accurate predictions than empirical models. An obstacle to using COSMOtherm for a broad range of PFAS is that it is not a free tool. For practical and regulatory use, we predicted log K_aw using COSMOtherm for 222 PFAS, including 107 neutral PFAS that Kissel et al. recently listed as candidate compounds as well as neutral species of PFAS acids of major concern such as PFOA and its alternatives (Table S7). The predicted log K_aw values were in the range of −10.0 to 9.7, and 200 (90%) of the 222 values were from −5 to 5, indicating a large variation of the partition properties. Further model validation would be desirable though, considering the diverse structures of existing PFAS. Nevertheless, as long as we do not have reliable experimental data, these predictions may be considered current best estimates and useful for various purposes, such as fate, exposure, and risk analysis.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.est.3c02545.

• Additional descriptions of experimental methods; evaluation of new literature data; lists of all PFAS used; SMILES strings for PFAS; experimental parameters; statistics of the regression lines; all predicted log K_aw values; figures for experimental methods and raw data; and COSMOtherm-predicted vs experimental values (PDF)

Author Contributions

Study design: S.E. Experiment: S.E., J.H., and S.M. Data evaluation: S.E., J.H., and S.M. Modeling: S.E. and J.H. Drafting of the manuscript: S.E. Revising of the manuscript: S.E., J.H., and S.M.

The authors declare no competing financial interest.