Thermodynamics of aqueous perfluorooctanoic acid (PFOA) and 4,8-dioxa-3H-perfluorononanoic acid (DONA) from DFT calculations: Insights into degradation initiation

Chemosphere 193 (2018) 1063e1070

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Thermodynamics of aqueous perfluorooctanoic acid (PFOA) and 4,8-dioxa-3H-perfluorononanoic acid (DONA) from DFT calculations: Insights into degradation initiation Alberto Baggioli a, b, *, Maurizio Sansotera a, b, Walter Navarrini a, b a b

Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Politecnico di Milano, Via L. Mancinelli 7, 20131 Milano, Italy Consorzio Interuniversitario Nazionale per la Scienza e Tecnologia dei Materiali (UdR-PoliMi), via G. Giusti, 9, 50121 Firenze, Italy

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


H-abstraction by OH$ is thermodynamically favored on hydroperfluosurfactants.
Conformational flexibility should be always considered for perfluoroether chains.
A standard reduction potential of 2.2 V was estimated for C7F15COO$ at DFT level.
The pKa of polyfluorocarboxylic acids is strongly influenced by substituents.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 July 2017 Received in revised form 18 November 2017 Accepted 21 November 2017 Available online 22 November 2017

Modern fluorosurfactants introduced during and after perfluoroalkyl carboxylates/sulfonates phase-out present chemical features designed to facilitate abatement, hence reducing persistence. However, the implications of such features on environmental partitioning and stability are yet to be fully appreciated, partly due to experimental difficulties inherent to the handling of their (diluted) aqueous solutions. In this work, rigorous quantum chemistry calculations were carried out in order to provide theoretical insights into the thermodynamics of hydroperfluorosurfactants in aqueous medium. Estimates of acid dissociation constant (pKa), standard reduction potential (E0), and bond dissociation enthalpy (BDE) and free energy (BDFE) were computed for perfluorooctanoic acid (PFOA), 4,8-dioxa-3H-perfluorononanoic acid (DONA) and their anionic forms via ensemble averaging at density functional theory level with implicit solvent models. A hpKai in the neighborhood of zero and a E0 of about 2.2 V were obtained for PFOA. Predictions for the acidic function of DONA compare well with PFOA's, with a pKa of 0.8e1.5 and a E0 of 2.07e2.15 V. Deprotonation thus represents the dominant phenomenon at environmental conditions. Calculations indicate that H-abstraction of the aliphatic proton of DONA by a hydroxyl radical is the thermodynamically favored reaction path in oxidative media, whereas hydrolysis is not a realistic scenario due to the high dissociation constant. Short intramolecular interactions available to the peculiar hydrophobic tail of DONA were also reviewed, and the relevance of the full conformational space of the fluorinated side chain discussed. © 2017 Elsevier Ltd. All rights reserved.

Handling editor: I. Cousins Keywords: Hydroperfluorcarboxylic acid Acid dissociation Reduction potential Bond dissociation PFOA DFT

* Corresponding author. Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Politecnico di Milano, Via L. Mancinelli 7, 20131 Milano, Italy. E-mail address: [email protected] (A. Baggioli). https://doi.org/10.1016/j.chemosphere.2017.11.115 0045-6535/© 2017 Elsevier Ltd. All rights reserved.

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1. Introduction Perfluorocarboxylic acids (PFCAs) fall in the chemical class of fully fluorinated carboxylic acids. Within this class, perfluorooctanoic acid (PFOA) was the compound with the largest number of applications in industry (Ameduri, 2009; Drobny, 2009; Grot, 2008; Moody and Field, 2000; Schultz et al., 2013). PFOA was in fact widely employed as surfactant in the synthesis of a variety of fluoropolymers, as hydrophobizing agent in outdoor clothing, etching agent on fused silica, as well as a component in fire-fighting foams. However, several studies demonstrated that PFOA and other perfluoroalkyl surfactants are bioaccumulative, carcinogenic, and toxic for liver, immune, and endocrine systems (Andersen et al., 2010; Lau et al., 2007; Post et al., 2012; Prevedouros et al., 2006; Sedlak, 2016; Ylinen et al., 1985). Thus, PFOA and perfluoroalkyl surfactants were listed as persistent organic pollutants under the Stockholm Convention, and their production was restricted and eventually discontinued in 2015. The decade preceding the phase out witnessed the introduction of several non-perfluoroalkyl PFOA alternatives (Wang et al., 2013; Zaggia and Ameduri, 2012). Furthermore, following the phase out decision, in order to address the recognized environmental threat posed by fluorosurfactants, a large number of approaches were considered and extensively tested to identify convenient techniques for their mineralization. In this context, PFOA was thoroughly adopted as the prototypical perfluoroalkyl emulsifier. Chemical, thermal, and photolytic stability of perfluorinated compounds are directly related to the high dissociation energy of CeF bonds (Amii and Uneyama, 2009; Avataneo et al., 2009; Lemal, 2004; Persico et al., 2013), which makes conventional degradation techniques rather inefficient. Advanced oxidation processes are thus required. These comprise Fenton and photo-Fenton treatments (Mitchell et al., 2014; Zepp et al., 1992), ozonization (Hoigne and Bader, 1983a, 1983b), photochemical treatments (Chen and Zhang, 2006; Hori et al., 2004; Li et al., 2017), photocatalytic techniques (Gatto et al., 2015; Sansotera et al., 2014), electrochemical oxidation (Niu et al., 2013, 2016), sonochemical degradation (Moriwaki et al., 2005), photolysis (Kochany and Bolton, 1992), and thermolysis (Krusic et al., 2005). Advanced reduction processes have also been proposed (Qu et al., 2014; Zhang et al., 2014; Vellanki et al., 2013; Song et al., 2013). Improvement of abatement techniques toward higher efficiency and higher throughput requires a comprehensive understanding of the underlying mechanisms of degradation of PFOA. However, decomposition routes reported in literature were mainly speculated due to experimental limitations in the detection of degradation intermediates (Vecitis et al., 2009). Quantum chemistry methods were also considered as alternative approaches for the prediction of reaction mechanisms, as they were successfully applied to the study of other organic pollutants. However, despite the variety of degradation pathways proposed so far for PFOA (Kutsuna and Hori, 2007; Niu et al., 2013, 2016; Park et al., 2009; Sansotera et al., 2015), the very first few steps of the mechanism are largely agreed upon: acid dissociation followed by the oxidation of the resulting carboxylate to carboxyl radical. The inherent difficulties associated with the study of such degradation processes are further aggravated by the absence of a general agreement on important chemical-physical properties of PFOA and of other perfluoroalkyl surfactants, such as their acid dissociation constant, pKa, and the standard reduction potential of the corresponding carboxyl radical to a carboxylate anion, E0. The appraisal of these quantities, via either computational prediction as attempted in this work, or experimental measurement, is valuable to the understanding of degradation mechanisms, to the identification of appropriate abatement processes, as well as to the design

of environmentally-friendly alternatives. Working with aqueous solution of fluorinated surfactants, however, is reported to be a
pez-Fonta
n et al., difficult task (Goss et al., 2006; Guo et al., 1991; Lo 2005; Kutsuna et al., 2012; Moroi et al., 2001) due to their scarce solubility in water, their tendency to aggregate in aqueous media even around picomolar concentrations, their habit to accumulate at air/water and glassware/water interfaces, and their preferential solvation by the alcoholic component of hydroalcoholic solvents. As such, a continued debate exists and several researchers reported markedly different results over a very short span of time. The value of the pKa rules the dissociation degree of the emulsifier, which is relevant in the context of transport processes between liquid and gas phases by directly influencing partition coefficients (Vierke et al., 2013). Spectroscopic measurements reported by Cheng et al. (2009) on micromolar aqueous perfluorooctanoate anion solutions, as well as computational analyses produced by Goss (2008) via popular thermochemistry codes SPARC and COSMO-RS, and by Rayne et al. (2009) and Rayne and Forest (2010a) via accurate solvation free energies at semiempirical and DFT level, all agreed on a pKa value for PFOA in the neighborhood of zero. In contrast, Burns et al. (2008) proposed a monomeric pKa value of 3.8 by means of alkalimetric titration measurements performed in a methanol-water mixed solvent, after extrapolation to zero methanol and PFOA concentration. Standard reduction/oxidation potentials represent a direct measure of the thermodynamic feasibility of an electrochemical half-reaction, and are consequently relevant to the oxidation step of the carboxylate species. As an example, the environmental persistence of halogenated aliphatic compounds has been found to correlate with their relative reduction potentials (Patterson et al.,
e and Unversucht, 2003). 2001; Totten and Roberts, 2001; van Pe Unfortunately, to the best of the author's knowledge, an estimate of reduction potential in aqueous media has yet to be reported for PFOA. In this regard, however, it is possible to devise reasonable upper and lower limits based on experimental oxidation procedures detailed in the literature (Vecitis et al., 2009; Merino et al., 2016). On one hand, the hydroxyl radical is reportedly highly inefficient in the oxidation of PFOA, with a one-electron reduction potential of 1.9 V (Buxton et al., 1988). On the other hand, the sulfate radical, SO4$, exploiting a one-electron reduction potential of 2.3 V (Wardman, 1989), has been successfully employed in the degradation of several perfluorinated carboxylates in water, including PFOA (Hori et al., 2005). Historically, almost all fluoropolymer manufacturers employed ammonium perfluorooctanoate (APFO) and other long-chain ammonium perfluorocarboxylates as emulsifiers. Following their phase out, most manufacturers developed their own alternatives. The large majority of these alternative surfactants is reportedly based on functionalized perfluoropolyethers (PFPEs), and, in some cases, by fluorotelomers and other partially hydrogenated species (Wang et al., 2013). However, due to relative novelty, little is currently known about the environmental fate and the potential toxicity of most of the APFO replacement compounds in production and in active usage across the globe. Among others, ammonium 2,2,3-trifluoro-3-(1,1,2,2,3,3-hexafluoro-3-(trifluorometoxy)propoxy)propanoate, commonly known as ammonium 4,8-dioxa-3Hperfluorononanoate (ADONA), from Dyneon3M, is an interesting example of a partially hydrogenated perfluorooligoether (Gordon, 2011; Hintzer et al., 2007, 2010; VonHooks, 2013). In the following sections, a number of computational predictions of acid dissociation constants and standard reduction potentials for PFOA and its conjugated base will be presented and critically validated based on literature. Subsequently, the results of similar calculations on acidic and aliphatic protons of 4,8-dioxa3H-perfluorononanoic acid (DONA) will be discussed in details. An

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appraisal of the homolytic bond dissociation energies relative to the acidic OeH bond in both PFOA and DONA, as well as to the aliphatic CeH bond in the latter, is also reported. Finally, a brief survey of the intramolecular interactions available to the aliphatic proton and to the ether function of DONA closest to the carboxyl group will be presented.

2. Methods 2.1. Acid dissociation calculations Monomeric aqueous pKa values for the acidic proton in PFOA and DONA, as well as for the hydrogen atom in b position in the latter, were obtained as pKa ¼ DGD;aq =RTln10. In this equation, DGD;aq ¼ DGX ;aq þ DGHþ ;aq  DGXH;aq represents the Gibbs free energy change associated with the acidic dissociation reaction. For each species, DG*i;aq is obtained from a straightforward thermodynamic cycle as the summation of a gas-phase Gibbs free energy, DG0i;g , a liquid phase Gibbs free energy of solvation, dDG*i;s , and an RT lnðvn Þ correction term to DG0i;g (Liptak and Shields, 2001) because of the reference state change from 1 atm in the gas to 1 M in the liquid (vn represents the molar volume of an ideal gas at standard conditions). For the hydrated free proton, a DG0Hþ ;g value of 26.28 kJ mol1 and a dDG*Hþ ;s value of 1112.8 kJ mol1 were used (Kelly et al., 2006; Topol et al., 1999).

2.2. Standard reduction potential calculations Monomeric aqueous E0 values for the conversion of carboxyl radicals in both PFOA and DONA, along with that of the radical resulting from the dissociation of the proton in b position in the latter, to the corresponding anionic species, were obtained as E0 ¼ DGRed;aq =nF  E0ðSHEÞ . In this case, DGRed;aq ¼ DGX ;aq  DGX$;aq represents the Gibbs free energy associated with the reduction of the radical in aqueous media. A value of 4.44 V for the standard hydrogen electrode (SHE) was used (Trasatti, 1986).

2.3. Bond dissociation calculations Monomeric aqueous bond dissociation enthalpies (BDE) and free energies (BDFE) for the acidic OeH bonds in both PFOA and DONA, as well as for the CeH bond in the latter, were computed as the total enthalpy and Gibbs free energy variations associated with the corresponding homolytic dissociation reaction in aqueous media. The hydrogen free radical was only considered in its gas phase as it is assumed to be sequestered by another abstracting radical. For BDE and BDFE calculations, unrestricted CCSD(T)/augcc-pV5Z (Bartlett and Purvis III, 1978; Dunning Jr., 1989; Pople 0 et al., 1978) values of DHH$;g and DG0H$;g of 0.497634 au and 0.510649 au respectively were computed and used throughout. While a BDE represents what is commonly referred to as bond dissociation energy, a BDFE represents the Gibbs free energy of a half-reaction of transfer, or H-abstraction in this case. It can be directly compared with the XH BDFE of another chemical species, so that the algebraic sum of the two BDFEs represents the total Gibbs free energy of the XHðaqÞ þ Y$ðaqÞ /X$ðaqÞ þ YHðaqÞ reaction. If water homolytic dissociation is considered, Y$ðaqÞ represents a hydrated hydroxyl radical and YHðaqÞ becomes liquid water. Based on literature estimates (see Buxton et al., 1988, and references therein), it is possible to estimate a BDFE for the OeH bond of liquid water (neglecting the solvation term for the hydrogen radical) in a range of 487e521 kJ mol1.

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2.4. Population averages Population-averaged values hpKai, hE0i, hBDEi, and hBDFEi, were calculated assuming a Boltzmann distribution weighted on the relative Gibbs free energies of the starting species. These are protonated species for pKa, BDE, and BDFE, and anionic species for E0. Although the relative abundance of isomers exploiting an intramolecular interaction might have been overestimated due to the lack of explicit solvent molecules in the calculations performed (see for example Cappelli and Mennucci, 2008; Oh et al., 2006), the presence of several fluorine atoms surrounding b and g positions of DONA is likely to reduce the accessibility of these regions to solvent molecules, so that implicit solvent models can be considered reliable in this case. 2.5. DFT calculations Calculations were carried out using the Gaussian 09 package (Frisch et al., 2016). Density functional theory (DFT) was used in conjunction with def2-TZVP triple-z basis set with polarization functions (Weigend, 2006; Weigend and Ahlrichs, 2005) and an unrestricted wave function to optimize the molecular structure of several conformational isomers of all species under infinite dilution conditions. Optimized structures were confirmed as actual minima by vibrational analysis. Free energy calculations used the harmonicoscillator, rigid-rotor approximation at the same level of theory. Implicit solvent models (Tomasi et al., 2005) were used in all calculations, so that deformation energy due to solute-solvent interaction was accounted for during the geometry optimization step. Cost-effective implicit solvent models have been proven in many occasions to perform remarkably well in the simulation of solvated species (Alongi and Sheilds, 2010; Cappelli et al., 2012; Cammi et al., 2000; Castiglione et al., 2012; Egidi et al., 2012), despite the lack of a proper description of discrete solute-solvent interactions. Overall, fourteen density functionals were tested to different degrees. These are Becke three-parameters hybrid functional B3LYP (Becke, 1993; Lee et al., 1988; Stephens et al., 1994; Vosko et al., 1980), the hybrid implementation of the Perdew-Burke-Ernzerhof functional (Perdew et al., 1996, 1997) by Adamo and Barone (1999), PBE0, along with their dispersion corrected variants using the third-generation model by Grimme et al. (2010, 2011) with and without Becke-Johnson damping, namely B3LYP-D3, B3LYP-D3BJ, PBE0-D3, and PBE0-D3BJ, Austin et al. (2012) hybrid functional with and without dispersion corrections, APFD and APF, t-based hybrids M06 and M06-2X by Zhao and Truhlar (2008), TPSSh by Tao et al. (2003), BMK by Boese and Martin (2004), and range-separated hybrids uB97X and uB97X-D by Chai and Head-Gordon (2008a, 2008b). Self-consistent reaction field approximations tested comprise the conductor-like polarizable continuum model (Barone and Cossi, 1998; Cossi et al., 2003), CPCM, and two implementations of the integral equation formalism model, PCM by Tomasi et al. (1999), and SMD by Marenich et al. (2009). Where applicable, UFF-based cavities were used. 2.6. NCI analysis The noncovalent interaction (NCI) index proposed by Johnson et al. (2010) was used to directly visualize weak interactions in real space. This technique is remarkably sensitive, and is based on the plot of low-isovalue surfaces of the reduced density gradient, s, within internuclear regions. The very appearance of a s-isosurface between two nuclei or molecular fragments indicates the presence of an interaction between the two entities. The character thereof, as in bonding or nonbonding (steric), is determined by color-mapping the isosurface based on the sign of the second eigenvalue of the

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Hessian matrix, l2. As such, l2 < 0 marks bonding (stabilizing) interactions while l2 > 0 marks steric (nonbonding) ones. The strength of the interaction has been shown to be qualitatively proportional to the value of the electron density at the point of minimum reduced gradient, r(smin) (Baggioli et al., 2016; Johnson et al., 2010) and quantitatively proportional to the integral of specific real space functions (e.g. electron density) inside the volume of the isosurface (Contreras-García et al., 2011). NCI calculations were performed on the Multiwfn 3.3.8 code (Lu and Chen, 2012) using B3LYP/6-311G(d,p)//PCM/B3LYP-D3BJ/def2-TZVP wave functions (Krishnan et al., 1980) on cubic grids with a density of 15,625 points per cubic Bohr, corresponding to a size step of 0.04 Bohr.

3. Results and discussion 3.1. Estimates for PFOA An exploratory study on PFOA was carried out by combining fourteen DFT methods with three continuum solvation models. The resulting population-averaged values of acid dissociation constant, hpKai, bond dissociation enthalpy, hBDEi, and bond dissociation free energy, hBDFEi, as well as the resulting values of standard reduction potentials, E0, are collected in Table 1. An ensemble of two conformational isomers differing by the position of the acidic proton (cis or trans to the carbonyl bond), was considered in this instance. It was in fact shown by Rayne and Forest (2010a, 2010b) that the helical conformation of the C7F15 tail (as well as other perfluoro-nalkyl chains) represents the only arrangement quantitatively contributing to room temperature populations. In this particular case, the relative abundance of the cis conformer across the 42 examined methods ranges from 0.9443 to 0.9973 (cis and trans monomeric values are reported in Tables S1 through S3 in the Supplementary Material). The acid dissociation constants obtained for PFOA are all within a range of 2.35 < hpKai < 1.57, which shrinks to 1.20 < hpKai < 1.02 if the two highest and two lowest estimates are removed from the sample, in overall good agreement with past computational estimates. Standard reduction potentials obtained for the conversion of the oxiradical of PFOA to the corresponding anion range from 1.95 V to 2.69 V. The reliability of these estimates, due to the current lack of unanimously accepted reference data, was assessed on the basis of a set of heuristic boundary conditions. As such, hpKai values were deemed creditable within a range of [0.50; 0.50], while E0 values were considered in line with the available literature

Fig. 1. Molecular structure of DONA and definition of torsion angles q1 and q2.

in the context of PFOA degradation whenever in the range of [1.90; 2.30] V, as discussed in the introductory paragraph. Across all tested approaches, five yielded both hpKai and E0 predictions within these boundaries, and will thus be exploited in following paragraphs. These are, namely, TPSSh/SMD and the four permutations of B3LYP-D3 and B3LYP-D3BJ with PCM and CPCM solvation models. Although BDFE estimates for PFOA are lower than those for HeOH bond dissociation in water (see Paragraph 2.3), which translates to a negative Gibbs free energy change for the Habstraction reaction by the hydroxyl radical on the acid function of PFOA, the high values of hpKai effectively negate this degradation initiation path (Vecitis et al., 2009). 3.2. Estimates for DONA 3.2.1. General considerations DONA, a Dyneon3M product, is one of the replacement compounds designed following the phase-out of long-chain perfluorocarboxylic and perfluorosulfonic acids. The two ether functions along its hydrophobic tail (see Fig. 1) lend a higher degree of flexibility compared to PFOA (Sianesi et al., 1994). Moreover, the CeH bond in b position is undoubtedly more polarized than an aliphatic CeH, with the surrounding fluorinated carbon atoms enhancing its otherwise mild electrophilicity. In addition, the oxygen atom in g position, although arguably deactivated by the surrounding CeF moieties, can act as an electron-donating group. These lead to a number of different intramolecular interactions with the acidic headgroup, providing further stabilization toward folded conformational isomers (refer to paragraph 3.2.5 for more details). Replacing a fluorine atom and a CF2 unit with H and O, respectively, also reduces the negative inductive (electron withdrawing) effect of the fluorinated tail on the carboxylic group. As such, a slightly lower polarization can be expected for the OeH bond of DONA compared to PFOA. Theoretical estimates for the

Table 1 Estimates of hpKai, E0 (V), hBDEi (kJ mol1), and hBDFEi (kJ mol1) computed for PFOA and its derivatives using different combinations of density functional and continuum solvation model. Method

B3LYP B3LYP-D3 B3LYP-D3BJ PBE0 PBE0-D3 PBE0-D3BJ APF APF-D BMK TPSSh M06 M06-2X uB97X uB97X-D a

E0

hpKai

hBDEi

hBDFEi

CPCM

PCM

SMD

CPCM

PCM

SMD

CPCM

PCM

SMD

CPCM

PCM

SMD

0.63 0.15a 0.22 0.58 0.77 0.90 0.65 0.93 0.94 0.98 0.94 1.06 0.29 1.57

0.60 0.17 0.17a 0.69 0.79 0.98 0.74 1.00 0.90 1.02 0.87 1.09 0.29 1.57

0.63 0.46 1.20 0.21 0.09 0.18 0.15 0.24 2.10 0.22a 0.86 2.35 0.58 0.11

2.22 2.22a 2.22 2.14 2.14 2.13 2.15 2.16 2.40 1.95 2.25 2.51 2.35 2.25

2.22 2.22 2.22a 2.13 2.14 2.13 2.15 2.16 2.41 1.95 2.25 2.51 2.35 2.25

2.41 2.37 2.42 2.33 2.33 2.33 2.34 2.37 2.57 2.16a 2.41 2.69 2.54 2.45

466.0 468.2 468.6 465.4 466.7 466.7 467.3 470.3 481.3 449.6 475.9 491.4 484.4 481.3

466.1 468.3 468.6 465.4 466.8 466.8 467.3 470.4 481.3 449.6 475.9 491.5 484.1 481.3

482.1 480.8 481.1 478.0 479.3 479.4 480.0 483.3 491.7 462.5 489.3 501.8 495.2 492.3

429.4 431.7 431.7 428.0 429.4 429.3 430.2 432.6 445.3 412.3 440.9 455.0 447.5 444.8

429.3 431.5 431.5 428.1 429.4 429.5 430.1 432.7 445.7 412.3 440.6 455.0 446.8 444.8

447.9 445.2 444.9 442.4 443.4 444.5 443.9 448.4 454.7 428.0 446.2 464.7 460.4 454.4

Estimates complying with both boundary conditions imposed ([0.50; 0.50] for hpKai, [1.90; 2.30] V for E0).

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former can thus be expected to be influenced accordingly. The computed values of hpKai, hE0i, hBDEi, and hBDFEi for both acidic and aliphatic protons of DONA are listed in Table 2. Three of the five solvation approaches that passed the literature validation test on PFOA were used in this case. Indeed, since the results of the four computational approaches featuring dispersion-corrected B3LYP are strikingly similar to each other (see Table 1), only two were selected to avoid excessive redundancy. As such, TPSSh/SMD (DFT1), B3LYP-D3/CPCM (DFT2), and B3LYP-D3BJ/PCM (DFT3), were chosen. Monomeric estimates (see Tables S4 through S8) have been averaged over two different populations of microstates, Pf and Pl. The former represents the full population of conformational isomers, comprising up to 22 unique couples of protonated/ anionic (pKa) and protonated/radical (BDE and BDFE) conformers, and up to 6 unique couples of anionic/radical conformers (E0). The latter represents a population empirically constrained to a set of conformations featuring a linear (helical) hydrophobic tail (q1 and q2 in trans position), thus using the conformational space of (CF2)6CF3 to approximate that of the CF2CHFO(CF2)3OCF3 side chain of DONA. 3.2.2. Conformational space Owing to the short range of inductive effects along nonconjugated chains, and due to the stiffness customarily expected from perfluoroalkyl residues (Rayne and Forest, 2010a, 2010b), the conformational space of DONA and all its derivatives was explored by probing a selection of internal degrees of freedom closest to the protons of interest (Baggioli et al., 2013, 2016; Baggioli and Famulari, 2014). Namely, the two dihedral angles directly involving the CHF unit in b position, q1 and q2 in Fig. 1, were investigated in their trans (t, qn z 180 ) and gauche± (g±, qn z ±60 ) arrangements. In addition to these, for all species with a protonated acid function, the orientation of the OeH bond (cis or trans to the carbonyl bond) and the dihedral angle 4 describing the orientation of the C(O)O group (which is not relevant for carboxylic anions and radicals due to resonance stabilization) were also scrutinized. Because of the planar arrangement of the carboxylic group, two conformers with 4 and 4’ z (180  4) V (220  4) angles would usually be obtained, all other parameters been even. The remaining internal degrees of freedom, most notably the dihedral angles associated with the terminal OCF2CF2CF2OCF3 group, were only considered in their relaxed helical arrangement. Different arrangements of this fragment are expected to increase the free energy of the system without however affecting the chemical surroundings of either XH moieties, thus leading to low relative abundance conformers of little interest in this context.

Table 2 Estimates of hpKai, hE0i (V), hBDEi (kJ mol1), and hBDFEi (kJ mol1) computed for acidic OeH and aliphatic CeH bonds of DONA.a Method

hpKai, Pf hpKai, Pl hE0i, Pf hE0i, Pl hBDEi, Pf hBDEi, Pl hBDFEi, Pf hBDFEi, Pl

OeH

CeH

DFT1

DFT2

DFT3

DFT1

DFT2

DFT3

0.82 0.86 2.07 2.06 459.1 459.7 421.8 422.6

1.05 0.58 2.15 2.15 466.0 466.8 429.7 429.6

1.48 0.80 2.15 2.17 466.6 467.3 430.3 432.5

33.9 32.7 0.17 0.22 421.8 421.9 388.4 389.9

32.1 32.5 0.00 0.03 427.4 428.6 389.5 390.2

32.4 34.4 0.02 0.07 425.5 426.5 391.9 389.1

a DFT1 refers to TPSSh/SMD calculations, DFT2 refers to B3LYP-D3/CPCM, DFT3 refers to B3LYP-D3BJ/PCM. Pf and Pl represent, respectively, the full population of conformational isomers, and a population only comprising conformers with a linear tail (q1 z q2 z 180 ).

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3.2.3. Acidic proton Comparison of DFT1, DFT2, and DFT3 estimates collected in Table 1 and in Table 2 for Pf reveals that the acid dissociation constant of the carboxylic function of DONA should be 0.6e1.7 pK units higher than that of PFOA. Similarly, all three computational approaches agree on a standard reduction potential of the carboxylate anion about 0.07e0.09 V lower for DONA compared to PFOA, which translates to population averaged \langle\langleDG*Ox;aq \rangle\rangle values 6e8 kJ mol1 lower for the former compared to the latter. Although implicit solvent models are reportedly able to reproduce standard reduction potentials in aqueous and non-aqueous media with mean unsigned errors of 0.05e0.2 V against experimental reference data (Baik and Friesner, 2002; Fu et al., 2005; Sviatenko et al., 2011), the decrease from PFOA to DONA is systematic and complies with qualitative predictions discussed in Paragraph 3.2.1. To no surprise, also BDE and BDFE estimates for the OeH bond of DONA are systematically lower (by 2e6 kJ mol1) than those obtained for PFOA at the same level of theory. In fact, these findings are in agreement with the inherently weaker electron-withdrawing effect of the partiallyhydrogenated oligoether side chain of DONA compared to the perfluoroalkyl one of PFOA. The same considerations noted for the carboxylic group of PFOA thus apply to DONA, whereas heterolytic dissociation of the OeH bond will be largely dominant in water despite the availability of a thermodynamically-favorable secondary path, homolytic dissociation via H-abstraction reaction from the hydroxyl radical. 3.2.4. Aliphatic proton Results obtained for the CeH bond of DONA expose a rather low tendency toward heterolytic dissociation, with hpKai estimates of 32e34, several pK units higher than the dissociation constant reported for CF3H (pKa ¼ 27, see Symons and Clermont, 1981). The population-averaged standard reduction potential of the corresponding radical is predicted to be very close to zero (see Table 2). Such values are in good agreement with those experimentally determined for several delocalized carbanions and, most notably, for aliphatic carbanions bound to electron-withdrawing groups (Bordwell et al., 1988, 1989). Population-averaged bond dissociation enthalpies and free energies obtained for this proton, on the other hand, are sensibly lower (by about 40 kJ mol1) than those discussed is Paragraphs 3.1 and 3.2.3 for acidic protons of PFOA and DONA. Such a high acid dissociation constant rules out any chance of realistically observing deprotonation of the CeH bond of DONA at environmental conditions. However, hBDFEi values obtained for the homolytic dissociation of this bond are low enough (by more than 100 kJ mol1) compared to the BDFE of a water molecule (see Paragraph 2.3) that the resulting H-abstraction reaction would be favored from a thermodynamical point of view. Such an isolated CeH group on an otherwise sturdy perfluorinated chain represents an easily exploitable weak-point for aggressive chemical species to initiate the degradation process. Indeed, CeH bonds in polyfluorinated compounds have been reported to serve as additional degradation sites by initiating a cascade decomposition via e.g. microbial fragmentation (Arakaki et al., 2010), nucleophilic substitution on the carbon atom by sulfate radical anions (Hori et al., 2010; Yang et al., 2014), and photocatalytic deprotonation (Hori et al., 2011). Further development of these as well as of other abatement processes specific to hydroperfluorinated surfactants is likely to receive increasing attention in the future. In fact, in recent years, several environmental studies on surface water and sediments near fluorosurfactant manufacturing facilities have produced evidence for the presence of polyfluorinated species along with their perfluorinated analogues. Although it is not clear

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Fig. 2. NCI 3D plot of the five interaction modes available to DONA, specifically involving the aliphatic proton and the ether closest to the acid function. Values of electron density at smin, and the s-isovalue of the surface depicted are also reported. Color-mapping is as follows: blue represents l2 < 0 (bonding regions), red represents l2 > 0 (nonbonding regions). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

whether such polyfluorinated compounds are actual products, intermediates, or byproducts, their presence in manufacturing wastewaters has been reported consistently over several years and across quite distant potential sources (see for example Baduel et al., 2017; Dauchy et al., 2017; Liu et al., 2015; Newton et al., 2017). 3.2.5. Intramolecular interactions The conformational isomer population obtained for DONA at room temperature was used to survey the spectrum of intramolecular interactions affordable by the aliphatic proton and by the ether function closest to the acidic function. Five groups of intramolecular interactions involving either the ether function or the aliphatic proton have been identified. These are, with reference to Fig. 2, two CeH/O interactions (A and B), two weaker O/O interactions (C and D), and a stronger OeH/O one (E). Interactions A through D, characterized by wide, bent s-isosurfaces with both bonding and nonbonding character, and by rather low values of r(smin), appear to be of mainly dispersive nature. Steric regions on such surfaces represent the crowding generated by the closure of HeCeCeCeO and OeCeCeCeO 5-membered rings, while the bonding regions along internuclear axes represent the stabilizing interaction itself. Interaction E features a flat disk-shaped isosurface, indicating a stabilizing hydrogen bond-like interaction with no evident steric crowding at the center of the resulting OeCe CeCeOeH 6-membered ring. However, due to the degree of deprotonation of the acidic function (see hpKai values in Table 2), interaction E will be less common compared to the others. It should be noted that such interactions are specific to, respectively, a CeH moiety in b position to the carboxylic group and an oxygen atom replacing a CF2 unit in g position. Different substitutions would lead to different potential intramolecular interactions. Furthermore, interactions C through E require a certain degree of deformation of the hydrophobic tail for the two interacting fragments to align properly, which may result in the mitigation (or even cancellation) of the energy stabilization. Neglecting these intramolecular interactions, thus approximating the full conformational space of DONA (Pf in Table 2) with that of a perfluoroalkyl carboxylic acid such as PFOA (Pl in Table 2), would have led to systematic prediction errors, particularly on hpKai estimates. Indeed, as shown in Tables S4 through S8 in terms of relative abundance, non-linear conformers of DONA can be as relevant as linear ones. 4. Conclusions The acid dissociation constant of PFOA and the standard reduction potential of the corresponding carboxyl radical in aqueous solution at infinite dilution conditions have been reviewed as obtained from a set of 42 DFT-based approaches using one of

three implicit solvent models. Comparison with available literature allowed the selection of three computational methods for further investigation. DONA, a polyfluorinated oligoether carboxylic acid, was chosen as a prototype of modern fluorosurfactants emerged during the phase-out of PFOA. The predicted acid dissociation constant, carboxylate oxidation potential, and XeH bond dissociation energies for DONA in standard conditions systematically comply with the weaker electron-withdrawing effect expected from its hydrophobic tail compared to a perfluoroalkyl one. With a macroscopic pKa of about 1, DONA is predicted to be only slightly less acidic than PFOA, while the computed E0 difference between the two is close to the minimum error attainable. The acidity of the aliphatic proton of DONA, on the other hand, is estimated to be lower than that of CF3H, negating acid dissociation. However, results indicate H-abstraction by hydroxyl radicals as a thermodynamically favorable reaction path. The reported values of BDFE for this proton can be useful in determining the reactivity of Hsequestering agents other than the hydroxyl radical itself. Finally, nature and relevance of intramolecular interactions involving aliphatic proton and ether functions of DONA were critically discussed in order to highlight the importance of a proper conformational space sampling in the investigation of such flexible chemical species. Acknowledgements We acknowledge the CINECA award under the ISCRA initiative, for the availability of high performance computing resources and support. Conflicts of interest: none. Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.chemosphere.2017.11.115. References Adamo, C., Barone, V., 1999. Toward reliable density functional methods without adjustable parameters: the PBE0 model. J. Chem. Phys. 110, 6158e6169. Alongi, K.S., Shields, G.C., 2010. Theoretical calculations of acid dissociation constants: a review article. Annu. Rep. Comput. Chem. 6, 113e138. Ameduri, B., 2009. From vinylidene fluoride (VDF) to the applications of VDFcontaining polymers and copolymers: recent developments and future trends. Chem. Rev. 109, 6632e6686. Amii, H., Uneyama, K., 2009. CF bond activation in organic synthesis. Chem. Rev. 109, 2119e2183. Andersen, C.S., Fei, C., Gamborg, M., Nohr, E.A., Sørensen, T.I., Olsen, J., 2010. Prenatal exposures to perfluorinated chemicals and anthropometric measures in Infancy. Am. J. Epidemiol. 172, 1230e1237. Austin, A., Petersson, G., Frisch, M.J., Dobek, F.J., Scalmani, G., Throssell, K., 2012. A density functional with spherical atom dispersion terms. J. Chem. Theory Comput. 8, 4989e5007. Arakaki, A., Ishii, Y., Tokuhisa, T., Murata, S., Sato, K., Sonoi, T., Tatsu, H.,

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