Perfluoroalkyl-Fluorophosphate Anions for High ... - ACS Publications

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Perfluoroalkyl-Fluorophosphate Anions for High Voltage Electrolytes in Lithium Cells: DFT Study Marco Carboni,† Riccardo Spezia,‡ and Sergio Brutti*,§ †

Dipartimento di Chimica, Sapienza Università di Roma, P.le Aldo Moro 5, 00185 Roma, Italy CNRS, Laboratoire Analyse et Modélisation pour la Biologie et l’Environnement, UMR8587, Université d’Evry Val d’Essonne, 91025 Evry Cedex, France § Dipartimento di Scienze, Università della Basilicata, V.le Ateneo Lucano 10, 85100 Potenza, Italy ‡

S Supporting Information *

ABSTRACT: Lithium perfluoroalkyl-fluorophosphates (LiFAFP) are almost unexplored organic−inorganic hybrid salts suitable for application in innovative lithium-ion batteries. LiFAFPs are obtained from lithium hexafluorophosphate by replacing one or more fluorine atoms with fluorinated alkyl chains. Among them only lithium tris(pentafluoroethyl)trifluorophosphate (LiFAP) and lithium bis(trifluoromethyl)-tetrafluorophosphate [LiPF4(CF3)2] have been tested successfully in a lithium cell. In this paper, we present a detailed systematic study by electronic structure calculations of two subfamilies among LiFAFP: the pentafluoroethyl and the trifluoromethyl substituted FAFP [i.e., LiPF6−x(CF3)x with 0 ≤ x ≤ 6 and LiPF6−x(C2F5)x with 1 ≤ x ≤ 4]. In particular, the equilibrium structures, ion pair dissociation energies, and anion ionization potentials have been predicted for the considered chemical species by density functional theory (DFT), also including dispersion effects. Apparently all the evaluated LiFAFPs show a remarkable decrease of the dissociation energies upon perfluoroalklation without suffering any parallel drastic drop in the anion ionization energy. For all FAFP anions with 1−3 perfluoroalkyl substituents, the ionization potentials are predicted above 5 V versus Li+/Li0, a value suitable for application with 5 V cathode materials in lithium-ion cells. LiFAFPs affinity toward water has also been evaluated and the equilibrium constants for the hydrolysis reactions predicted. requires a careful balancing case-by-case to fit the peculiarities of the anode-electrolyte-cathode configuration. Currently, the standard formulation of an electrolyte for Liion cells is a blend of organic alkyl carbonates (e.g., dimethyl carbonate, ethylene carbonate, methyl ethyl carbonate, propylene carbonate, etc.) mixed with a lithium salt, typically LiPF6. Alkyl carbonates are used in the view of their acceptable anodic stability for the 3−4 V cathodes (e.g., LiCoO2, LiNi1−xCoO2, and LiFePO4) and the lithiated graphite, as well as their high polarity, the reasonable thermal range of the liquid phase, and the low toxicity. LiPF6 is, to some extent, a compromise in the view of the disadvantages of the other possible options available (e.g., LiClO4 is explosive, LiAsF6 is highly toxic, LiBF4 is problematic on the anode side, LiSO3CF3 solutions show low lithium conductivity, LiTFSI is problematic on the cathode side, etc.). However, LiPF6 spontaneously decomposes to LiF and PF5, and the latter readily hydrolyses to form HF and POF3.13 These two hydrolysis products are highly reactive and catalyze parasitic chemical and electrochemical processes both on the anode and cathode sides. Their unavoidable presence in LiPF6 organic carbonate solutions

1. INTRODUCTION Next generation Li-ion and post-Li-ion batteries include a number of electrochemical devices able to store and supply electric energy well beyond the capabilities of the current stateof-the-art technology: the cobaltite-graphite carbonate-based lithium-ion configuration. The most innovative technological options worldwide investigated are the so-called lithium−sulfur, lithium−air, and next-generation lithium-ion cells.1 Although the latter are considered similar to the state-of-the-art Li-ion cells, all innovations proposed and validated in private and public R&D laboratories worldwide involve a drastic alteration of the overall configuration by changing the anode2−4 and/or cathode5−7 active materials as well as the electrolyte.8−10 Such modifications are mainly aimed at improving the specific capacity and/or the operating voltage of the cell (from 3.6 to 5 V) and, therefore, the specific energy of the device, without jeopardizing costs, safety, and durability. Electrolytes are a peculiar playground for original improvements.11 Innovations may address both the alteration of the solvent blends and the substitution of the lithium salt. Moreover, electrolytes may also include various other chemical species (i.e., additives12) aimed at altering the surface chemistry at the anode/cathode sides (e.g., film forming agents, HF scavengers) as well as protecting the cell components from electric abuse (e.g., overcharge or shutdown protectors) or from ignition (e.g., flame retardants). The use of these additives © XXXX American Chemical Society

Received: June 6, 2014 Revised: September 26, 2014

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dx.doi.org/10.1021/jp505624h | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Chemical structures for the studied anions.

stability windows,29 being comparable with that of bis(trifluoromethylsulfonyl)imide-based ILs, and a smaller viscosity compared to the parent PF6− ILs;29 these properties make this class of ILs potentially suitable as solvents or cosolvents in electrolytes for high voltage Li-ion cells. In this paper, we present a detailed and systematic theoretical study of two subfamilies among the LiFAFP series: the pentafluoroethyl and the trifluoromethyl substituted FAFPs (i.e., LiPF6−x(CF3)x with 0 ≤ x ≤ 6 and LiPF6−x(C2F5)x with 1 ≤ x ≤ 4). In particular, the equilibrium structures, ion pair dissociation energies, and anion ionization potentials have been predicted for the considered chemical species at various levels of theory (different DFT functionals, Hartree−Fock, and MP2). The effect of dispersion has also been considered. Furthermore, the thermodynamics of the corresponding hydrolysis reactions have been evaluated and compared with LiPF6 in order to predict the reactivity of the various LiFAFPs toward H2O.

has a detrimental impact on the cell performances and its calendar life. In the last years, a quite large number of innovative salts has been studied computationally,14 synthesized in laboratory, and validated in lithium cells. Some examples are lithium bis(oxalato)borate (LiBOB),15 lithium bis(malonato)borate (LiBMB),16 lithium(malonato oxalato)borate (LiMOB),17 lithium pentafluoroethyl trifluoroborate (LiC2F5BF3),18 lithium tetrafluoro(oxalate)phosphate (LiPF4C2O4),19 or the more exotic pseudo delocalized anions proposed by Jónsson and co-workers.20 Among the possible replacements for LiPF6, lithium tris(pentafluoroethyl)trifluorophosphate (LiFAP) has also been proposed.21−24 This salt is part of a homologous series [i.e., lithium fluoroalkyl-fluorophosphates (LiFAFP)], obtained from the lithium hexafluorophosphate by replacing one or more fluorine atoms with fluorinated alkyl chains. Among them, in the open literature, only the so-called LiFAP and LiPF4(CF3)n25 (n = 1−3) have been synthesized and tested in lithium cells, showing good performances, reduced hydrolysis to HF, and high conductivity and thermal stability. Many FAFP− anions have also been implemented as negative counterparts in ionic liquids (ILs) combined with pyridinium, pyrrolidinium, alkylammonium, alkylphosphonium, guanidinium,26 uronium,27 thiouronium,28 as well as imidazolium cations.29 Many of these salts are liquids at room temperature and by definition they belong to the class of room temperature ionic liquids. On passing, it is interesting to mention that aprotic FAFP− based ILs show very large electrochemical

2. COMPUTATIONAL DETAILS In this study, several anions derived from PF6− have been considered by substituting the fluorine atoms with fluoroalkyl groups. The studied chemical species can be summarized in two different groups by the nature of the fluoroalkyl sustituents in the anion. (1) Trifluoromethyl substituents (−CF 3 ): PF6−x(CF3)x− with 0 ≤ x ≤ 6 and (2) pentafluoroethyl sustituents (−C2F5): PF6−x(C2F5)x− with 1 ≤ x ≤ 4. B



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All compounds showing two, three, or four fluoroalkyl substituents bonded to the central phosphorus lead to two nonequivalent possible structural conformations (i.e., axial or vicinal). As a consequence, 17 structures have been considered and investigated. A summary of the chemical structures of the studied anions is shown in Figure 1. In this study, isolated anions as well as ion pairs with Li+ cation have been here considered and studied. The PF6− anion and the corresponding LiPF6 ion pair have been considered for benchmarking. All equilibrium structures have been obtained by density functional theory (DFT): anion geometry optimizations have been carried out at B3LYP30−32 and B97D33 levels by adopting 6-311+G* basis sets.34−36 In order to evaluate the effect played by dispersion forces on the ground state structures, the functional B3LYP has also been improved by adding empirical dispersion by means of the Grimme D3 damping function (B3LYP/D3).37 Anions optimized at the B3LYP level of theory have been used as starting points to obtain the most stable configurations of ion-pairs formed with Li+. Owing to the ability of Li+ to coordinate one to four electronegative atoms (i.e., fluorine atoms in these case) and in order to evaluate the most stable coordination geometry for the Li+/FAFP pairs,20,38 a large number of alternative configurations have been considered for each structure as the starting guess. In total, 230 hypothetical starting structures have been tested, ranging from 5 to 32 for the various molecules depending on the chemical complexity of each ion pair. As an example, in order to describe LiPF5CF3, 5 different configurations have been considered, whereas for axial and vicinal LiPF2(C2F5)4, 17 and 32 configurations have been adopted, respectively. All ion pair structures have been relaxed at B3LYP, B3LYP/ D3, and B97D levels with 6-311+G* basis sets to identify the ground-state configuration for all the 17 different conformers. The basis set super position error (BSSE) has been evaluated for the ground states of all ion pair conformers by employing the counterpoise method.39 Natural bond orbital analysis40 (NBO) has been carried out on the optimized anion and ionpair structures. NBO analysis allows for the evaluation of the partial charges of the atoms in the anions and, also, the nature of the orbital mixing in the ion-pair. Possible computational inaccuracies have been evaluated by the standard deviations of the net values on identical nuclei in each molecule. Ion pair dissociation energies, ΔEd, have obtained from the self-consistent total energies by the simple equation:

and the dispersion corrected B97D) and three meta-GGA (VSXC, TPSS, and M06L) functionals. On passing, it is important to mention that although B3LYP and other hybrid methods may lack in providing accurate energies, as reported by Johansson,49 results on a variety of Li+ ion pairs show the same energy trends reported by more accurate MP2(full)/631G(d) and G3 calculations. On the other hand, these last computational methods are too computationally expensive to deal with large anions, such that B3LYP has been widely used for this purpose (e.g., by Jonsson et al.20) to study other Li+/ anion interaction strengths. All calculated ionization energies have been converted to the so-called ionization potentials versus Li+/Li0 accordingly to what suggested by Johansson and co-workers.50,51 In particular, in order to convert the ionization potential, in units of eV, to a relative potential in reference to the Li+/Li0 redox couple, a constant value is subtracted from the calculated absolute potential.52 It is known and widely accepted that the reference half reaction behind the SHE, the standard hydrogen electrode, has an experimental absolute oxidation potential close to 4.5 eV.53 Since the Li+/Li0 couple is at −3.04 V versus SHE,54 the calculated oxidation potential can be compared to the Li+/Li0 reference by relating it to a Li+/Li0 absolute value of 1.46 eV. Note that ionization potential calculations have been performed in vacuum without considering the effect of the solvent. Here our aim is to study the trend of the different ionization potentials as a function of −CF3 and −C2F5 substitutions. This trend is directly related to the gas phase ionization potential since all systems are chemically similar, and thus solvation should not largely vary upon substitution. In the available computational literature on similar systems (see as an example refs 20 or 38), ionization potentials are always computed in the gas phase. Although the inclusion of the solvent is expected to slightly alter these values, a simple continuum solvation method (like CPCM) may fail. In order to recover the expected trends easily obtained from gas phase calculations, semiempirical corrections have been considered in the literature (see, for example, ref 49). However, the prediction of ionization energy from isolated molecules is a reasonable compromise to estimate their intrinsic propensity toward ionization. In fact, the real ionization environment in an electrochemical device is of complex definition, since the electron transfer does not happen in the solvent bulk but at the electrolyte/electrode interface where an electric double layer occurs, thus leading to drastic local alteration of the dielectric constant. In this view, an exact definition of the ionization environment would be questionable unless simulation, taking explicitly into account solvent molecules and the electrode interface. However, such complex predictions are beyond the aim of the present work and also of the capability of the present approach. Besides ion pair dissociation energies and anion ionization potentials, we also studied the thermodynamics of simple equilibrium reactions commonly occurring in liquid nonaqueous electrolytes in lithium ion cells:55 (1) ion pair dissociation, (2) LiF self-release and, (3) hydrolysis with H2O. Reactions 2 and 3 are undesired chemical equilibria unavoidably occurring in lithium-ion cell electrolytes and are the onset a plethora of other detrimental processes. In order to derive a comprehensive comparison of the chemistry of these reactions for the computed lithium salts in the presence of water molecules, further DFT calculations have been carried out by the B3LYP functional with a 6-311+G* basis set for all

ΔEd = Etot(anion) + Etot(Li+) − Etot(ion pair)

Anion ionization energies (Eion) have been obtained from the energy of each anion and the corresponding neutral molecule (open shell, doublet spin state) with one missing electron. The Franck−Condon approximation has been assumed (vertical transitions), and thus the energies of the neutral radicals have been calculated from the nonrelaxed geometry of the corresponding anions. Besides B3LYP functional also other methods have been adopted to calculate ionization energies. In particular, we have used several DFT functionals, B3LYP, VSXC,41 HCTH,42 B97D, M06L,43 O3LYP,44 BLYP,45,30 TPSS,46 PBE,47,48 and two wave function based methods, Hartree−Fock (HF) and MP2. The 6-311+G* basis set is used. For each method, we have optimized the geometry of every anion structure. These functionals were selected among the huge list of available functionals in order to have three GGA (BLYP, PBE, and HCTC), three hybrid-GGA (B3LYP, O3LYP, C



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the perfluoroalkyl phosphate molecules (i.e., LiPF6−xRx, PF6−xRx−, PF5−xRx, POF3−xRx with x = 1−3 and R=CF3 and C 2 F 5 ) as well as for Li + , HF, LiF, and H 2 O. The thermodynamics of these reactions have been computed by calculating total energies for all chemical species in a simulated solvent by using self-consistent reaction field (SCRF) through a C-PCM algorithm.56,57 Dimethyl sulfoxide (DMSO) solvent has been adopted, owing to its dielectric constant (ε = 46.826 Fm−1) very close to the average of ethylene carbonate and dimethyl carbonate, the typical blend solvent used in Li-ion cells.58,59 All calculations have been carried out by the Gaussian09 code.60

3. RESULTS AND DISCUSSION 3.1. Anions and Ion Pairs Structures and Chemical Bonding. Coordinates of optimized structures of all anions and ion pairs, as obtained at the B3LYP/6-311+G* level, are reported in Table S1 of the Supporting Information. The evolution of the P−F and P−C bond length evolution at increasing perfluoroalkylation is reported in Table S2 of the Supporting Information together with the mean value of the deviation of the centrosimmetric X−P−X (X = F, CF3, and C2F5) bonds angles from a 180°, the latter being a measure of the degree of distortion of the octahedral coordination due to fluorine substitution.61 PF6− shows an octahedral coordination with a P−F bond length of 1.68 Å to be compared to the literature value of 1.65 Å.62 With the increase of the fluorine substitution with perfluoroalkyl groups, three parallel structural changes occur: (1) P−F and (2) P−C bonds elongate, and (3) the perfect octahedral geometry breaks down probably due to the steric repulsion between vicinal CF3 or C2F5 groups. NBO charges of fluorine and carbon atoms do not alter upon perfluoroalkylation for both the CF3 and the C2F5 substituent groups. The predicted values are −0.60 ± 0.01 and −0.37 ± 0.02 on F atoms bonded to P and C, respectively, as well as 0.80 ± 0.01 on C atoms bonded to P in CF3 substituents and 0.41 ± 0.01 and 1.01 ± 0.01 on C atoms bonded to P and C respectively, in C2F5 substituents. On the other hand, the NBO charge on P decreases monotonically upon perfluoroalkylation (see Figure 2) (charge errors in the case of the phosphorus cannot be evaluated as standard deviations among identical nuclei in each molecule and have been therefore omitted). This behavior is expected in the view of the different electronegativity of P, C, and F (2.19, 2.55, and 3.98, respectively63). This trend accounts also for the elongation of the P−F bonds upon substitution as the increase in the electron density on phosphorus is likely to reduce the Coulomb attraction between the atoms with opposite charges. The interpretation of the elongation of the P−C bond distance upon perfluoroalkylation is less obvious. Two major competitive phenomena may be considered: (1) the decrease of the Coulombic repulsion between the positively charged carbon and phosphorus atoms upon substitution due to the reduction of the net charge on P and (2) the increase of the steric and Coulombic repulsion between the perfluoroalkylic substituents bonded to the same central phosphorus. Apparently the balancing of these two opposite effects leads to a weakening of the P−C bond upon substitution, thus resulting in its elongation. Turning to ion pairs, lithium ions are coordinated in all cases by three fluorine atoms in all structures with the exception of

Figure 2. Partial charge on P atom on increasing perfluoroalkylations calculated at the B3LYP level. For 2, 3, and 4 substituents, the reported slightly shifted points correspond to axial and vicinal conformations, respectively (points have been shifted to help the reader).

LiPF4(C2F5)2 (axial conformer), where lithium interacts with four fluorine neighbors (two F-bonded with phosphorus and two F from different perfluoroalkyl branches). The 17 optimized ion pairs are shown in Figure S2 of the Supporting Information. Second-order (SO) perturbation theory analysis of the Fock matrix in the NBO basis is also reported in Table S3 of the Supporting Information in order to discuss the coordination chemistry of lithium. In particular, in Table S3 of the Supporting Information, the six strongest SO interactions between empty atomic orbitals of Li+ and lone pairs in anions are listed. The strongest interactions take place always between 2s2p-hybrid empty states of Li+ and 2s2p-hydrid full states of three different F atoms (lone pairs), except for LiPF4(C2F5)2 (axial conformer) where Li+ is tetracoordinated by F atoms. The orbital character of these interactions is only marginally altered by the substitution of the F atoms bonded to phosphorus. In fact, although the increase of the perfluoroalkylic groups leads to hindered anions larger in volumes compared to the hexafluorophosphate one (see Figure 3 where the increase of the net Li−P distance is shown upon perfluoroalkylation), Li+ ions are preferentially coordinated by fluorine atoms directly bonded to P. This evidence may be put in relation to the larger negative charge of the F atoms bonded to P in comparison to those bonded to carbons (see Table S4 of the Supporting Information). 3.2. Dissociation Energies. The calculated dissociation energies, ΔEd, are shown in Figure 4. Besides the B3LYP functional, also B97D and B3LYP/D3 functionals have been employed to estimate the dissociation energies of the ion pairs. Our results are in agreement with the work of Jonsson et al.20 on phosphorus-based anions. In fact, other simple F-rich anions have similar or larger dissociation energy than PF6− (e.g., 558, 602, and 774 kJ/mol for AsF6−, BF4−, and F−, respectively). Also other imidazole and benzimidazole fluorinated anions have dissociation energies in an analogue interval ranging between 300 and 570 kJ/mol, depending on the chemical nature of the anion and the Li+ binding site.38 The dissociation energies of both trifluoromethyl- or pentafluoroethyl-substituted FAFPs-lithium ion pairs decrease monotonically with the increase of the number of substituents D



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Figure 3. Li---P distance for the studied ion-pairs calculated at the B3LYP level. For 2, 3, and 4 substituents, the reported slightly shifted points correspond to axial and vicinal conformations, respectively (points have been shifted to help the reader).

for all three computational methods; for all molecules, dissociation energies are smaller than the benchmark LiPF6. The decreasing trend calculated by the B97D functional shows a much steeper slope in comparison with both the B3LYP ones, thus leading to a large destabilization of the ion pair with increasing perfluoroalkylation. On the contrary, predictions made by the B3LYP and the B3LYP/D3 functionals show similar mitigated trends and dissociation energy values. The addition of dispersion corrections to the B3LYP functional increases the dissociation energy with respect to pure B3LYP values, while B97D shows values smaller than B3LYP. In particular, the energetic weakening of the ion-pair interaction predicted by the B3LYP and the B3LYP/D3 functionals are 19 ± 6.7 kJ mol−1 for each (−CF3) substituent and 25 ± 9.8 kJ mol−1 for each (−C2F5) group. Thus, in the case of the B3LYP functional, the net effect of dispersion forces is to stabilize the ion pair. On the other hand, B97D results provide a larger destabilization of the ion pair, especially for the highly substituted ones. However, differences between B97D and B3LYP results are likely related to the differences in the functional rather than to the inclusion of the dispersion. Here we adopt B3LYP/D3 dissociation energies as final assessed predictions for the studied ion pairs: they are reported in Table 1. For the sake of completeness, the B3LYP and B97D values are listed in Table S5 of the Supporting Information. Errors on the assessed values in Table 1 have been evaluated from the standard deviations between the B3LYP and the B3LYP/D3 values. In conclusion, it is interesting to underline that the decrease of the dissociation energy of the perfluoroalkyl phosphate salts compared to the benchmark LiPF6 may be indirectly confirmed for the LiFAP [LiPF3(C2F5)3] molecule by the increase of the experimental dissociation degree in a liquid ethylene− carbonate dimethyl carbonate blend compared to LiPF6, obtained by NMR self-diffusion measurements.64 3.3. Ionization Energies. In order to evaluate the ionization potential of the anions (Eion), the energy of the following general reaction has been computed for all systems in vacuum:

Figure 4. Dissociation energies at increasing perfluoroalkylations for (a) −(CF3) and (b) −(C2F5) groups. Li---P, as obtained by three different DFT-based calculations. For 2, 3, and 4 substituents, the reported slightly shifted points correspond to axial and vicinal conformations, respectively (points have been shifted to help the reader).

Results are summarized in Table S6 of the Supporting Information. MP2 calculations have been omitted for threeand four-substituted chemical systems due to the very high computational cost. First, PF6− anion has been used as a benchmark in order to evaluate the performances of different computational methods. In this view, we would like to stress that ionization energies are defined as gas phase properties but unfortunately such determination is missing in the case of the PF6− anion. Turning to the hexafluorophosphate electrochemical oxidation in solution, in the available experimental and computational literature, there is a general consensus20,25,50,51 to set the Eion for the hexafluorophosphate anion in the range of 5.6−6.5 V versus Li. This wide range results from the large impact of the experimental (e.g., nature of thee electrode and the solvents) and computational (e.g., level of theory, functionals, and basis sets) conditions for the evaluation of this property.50,51,65−67 As shown in Table S6 of the Supporting Information, DFT performs better than wave function methods, since both HF and MP2 largely overestimate Eion. Interestingly, B3LYP and PBE are not the best DFT, while VSXC has very good

X − → X + e− E



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standard deviation at 99% of confidence. The final assessed predictions of the ionization potentials of the perfluoroalkyl phosphates are reported in Table 1. The oxidation stability decreases as the number of perfluoroalkyl substituents bonded to the central phosphorus increases. Each replacement of a fluorine atom with a CF3, or C2F5, group leads to a reduction of the ionization potential of about 0.25 V versus Li. This effect can be related to the main alteration occurring in the electrons distribution upon perfluoroalkylation: the decrease of the net positive charge of phosphorus. The increase of the electron density around phosphorus is likely due to the substitution of fluorine with less electronegative carbon atoms; this helps the removal of an electron from the HOMO of the anions. As an example in Figure 5, the representation of the three highest in energy (HOMO) molecular orbitals have been plotted for the PF6− and the PF3(CF3)3− anions. For PF6−, the highest three occupied orbitals are degenerate, and similarly in PF3(CF3)3−, these three orbitals are very close in energy. Anyhow, the shape of these orbitals is very different in the two cases. PF6− orbitals are highly localized nonbonding orbitals filled with lone pairs around fluorine atoms. In the case of the PF3(CF3)3− anion, the HOMO has also a partial bonding character delocalized across the P−C bonds. Summarizing, the removal of one electron (ionization) upon perfluoroalkylation is favored in comparison with the PF6− anions by the more delocalized character of the HOMO orbital. A useful synthetic description of the above-discussed molecular properties, commonly used in the relevant literature,20 is shown in Figure 6, where the assessed ionization potentials are plotted as a function of the dissociation energies. This plot is suitable to discuss the potential use of these chemical systems in Li-ion cells. In fact, small ΔEd and large Eion imply anions electrochemically stable upon oxidation and ion pairs easily ionized in polar solvents, thus fitting the typical requirements of lithium salts for lithium and Li-ion cell applications.

Table 1. Final Assessed Values for the Dissociation Energy and Ionization Potentials for the Studied Molecules and Anionsa anion −

PF6 PF5CF3− PF4(CF3)2− axial PF4(CF3)2− vicinal PF3(CF3)3− axial PF3(CF3)3− vicinal PF2(CF3)4− axial PF2(CF3)4− vicinal PF(CF3)5− P(CF3)6− PF5C2F5− PF4(C2F5)2− axial PF4(C2F5)2− vicinal PF3(C2F5)3− axial (FAP) PF3(C2F5)3− vicinal (FAP) PF2(C2F5)4− axial PF2(C2F5)4− vicinal

ΔEd (kJ mol−1) 555 536 513 509 479 481 464 466 463 410 511 482 476 422 431 390 374

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2 6 7 6 8 7 12 12 12 16 6 9 6 12 16 21 16

Eion (V vs Li+/Li0) 5.8 5.6 5.5 5.1 4.9 5.2 4.4 4.8 4.4 4.4 5.4 5.4 4.9 4.9 5.1 4.5 4.9

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3

a

Dissociation energies of all ion pairs have been calculated at the B3LYP/D3 level; errors have been derived from the standard deviation between B3LYP and B3LYP/D3 calculations. Eion values have been averaged among all the DFT predictions for all studied anions; inaccuracies have been estimated by the corresponding standard deviations.

performances as pointed out in different systems by Johansson.51 Other functionals are also able to provide values in good agreement. The ionization potential for PF6− obtained by us as average among the DFT result is 5.8 ± 0.4 V, in very good agreement with the computational literature as well as the experiments. Owing to this, the final assessed predictions of the ionization potentials for the substituted anions have been obtained as average of all the DFT estimates and the associated error as the

Figure 5. HOMO for the PF6− and the PF3(CF3)3− anions. Relative energy in respect to the HOMO orbital are reported below the pictorial representations. F



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predicted by Kita and by us using the Koopman’s theorem (i.e., assuming that IP = −EHOMO) are not in agreement with our assessed values shown in Table 1 and calculated by the Franck−Condon approximation. However, Koopman’s theorem does not consider wave function relaxation upon ionization, thus leading to a useful but crude approximation that may lead to not fully consistent results. Turning to the experimental investigation of the PF5CF3− and PF4(CF3)2− ionization potentials, the two values reported by Kita and co-workers (6.2 vs Li+/Li for both species) are of about 10−17% higher compared to our estimates. However, it is important to underline that electrochemical experimental oxidation potentials may be strongly dependent on the nature of solvents and electrodes. In fact, the thermodynamic stability of the solvents as well as the oxidation kinetics driven by the chemical nature of the electrode (e.g., platinum, aluminum, glassy graphite, real multicomponent cathode films, etc.) may have a large impact in the practical value of the oxidation potential of the anions. For this reason a large amount of experimental literature exists for PF6−, reporting oxidation potentials ranging between 5.5 and 6.5 V versus Li+/Li.65−67 In summary, the perfluoroalkylation of PF6− anions is apparently beneficial in the cases of CF3 and C2F5, up to 3 fluorine substitutions. The two competitive phenomena, one detrimental (i.e., reduction of the anion ionization potential) and one beneficial (i.e., decrease of the Li+ ion pair dissociation energy) result in an overall positive balancing. In fact, the remarkable weakening of the ionic bond between the Li+ cation and the perfluorophosphate anion, that is expected to enhance the salt dissociation in solvents, occurs without drastic drops of the stabilities toward oxidation that are well above 5 V versus Li for all the mono-, bi-, and trisubstituted perfluorophosphates. Furthermore, by directly comparing the two different types of alkylation and considering an equal number of substituents, C2F5 groups show the most promising features compared to CF3 both in terms of potentials and dissociation energies. 3.4. Ion Pairs Self-Dissociation and Hydrolysis. In Liion cells lithium hexafluorophosphate, besides the simple ionpair dissociation, undergoes an autocatalytic reaction sequence activated by the decomposition of the ion pair to give LiF and the electron-poor PF5 molecule.70 This chemical reaction is followed by the spontaneous hydrolysis of PF5 with water traces unavoidably present in electrolytes with the consequent release of HF and F3PO molecules. The general stoichiometry of the above-mentioned reactions for LiPF6 as well as for the lithium perfluorialkylphosphates salts is the following:

Figure 6. Ionization potentials plotted versus dissociation energies for (a) −(CF3) and (b) −(C2F5) substituents. X is the number of substituents on LiPF6.

Apparently, the substitution of 1 to 3 fluorine atoms with both CF3 or C2F5, groups leads to a moderate decrease in the ionization potentials that are predicted to be in all cases above 5 V versus Li, with a parallel beneficial drop of the dissociation energy of the ion pair with Li+. In the case of the CF3 group, this trend is kept also for 4−6 substitutions, but in parallel, the ionization potential falls below 4.5 V versus Li, a value unsuitable for modern high-energy cathode materials.68,69 Our predictions for the PF6−, PF5CF3−, and PF4(CF3)2− anions can be compared to the available experimental and theoretical values. Kita et al.25 have studied FAFPs with −CF3 substituents: they calculated HOMO energies of the anions and Li+/anion binding energies. Moreover Kita measured experimentally the oxidation potentials of PF6−, PF5CF3−, and PF4(CF3)2− anions in lithium electrochemical cells using propylene carbonate as the solvent. Our trend of the dissociation energies is in agreement with the findings by Kita et al., similarly to the trend of the HOMO energies (PF4(CF3)2− < LiPF6− < PF5(CF3)− < PF3(CF3)3−), as shown in Table S7 of the Supporting Information. The numerical differences between our absolute HOMO energy values and Kita et al. predictions may be derived by the different computational approaches (method, basis set, and functionals). On the other hand, the trend of the ionization potentials

LiPF6 − x R x ⇆ Li+ + PF6 − x R x −

(1)

LiPF6 − x R x ⇆ LiF + PF5 − x R x

(2)

PF5 − x R x + H 2O ⇆ 2HF + POF3 − x R x

(3)

The latter chemical species (i.e., the electron-rich POF3−xRx molecule), further reacts with the solvent [i.e., organic carbonates (RO)2CO], thus giving RF, CO2, and newly POF3−xRx70,71 that is therefore able to self-feed this reaction sequence. Besides this autocatalytic reaction scheme, in the case of the lithium hexafluorophosphate salt, the electron-poor PF5 and the electron-rich POF3 molecules have been observed to undergo to a plethora of other possible reactions in the electrolyte of lithium cells, both spontaneously or upon electrochemical discharge/charge. This complex mechanism can lead to the G



Article

of remarkable importance for practical application in lithiumion cell electrolytes, since reaction 3 is the onset key-step of the autocatalytic reaction sequence (see above) that drives the detrimental release of free HF.

precipitation of a complex and stable solid-electrolyte interphase (SEI) on the surfaces of the electrodes.72,73 Among them, the electroactive reactions are responsible for the accumulation of irreversible capacity. On the other hand, all these parasitic processes lead to the formation of soluble/ insoluble byproducts that, in the mid-to-long-term, contribute to the death of the cell. In this view, it is important to evaluate the equilibrium chemistry of the three above-reported reactions in the case of the perfluoroalkyl phosphate lithium salts. The thermodynamic equilibrium constants (Log Keq) for the three reactions are summarized in Table 2.

4. CONCLUSIONS In this study, we have reported the electronic and molecular structure, the thermodynamics, and the equilibrium chemistry of FAFPs lithium salts derived from LiPF6 by substituting fluorine atoms with perfluoroalkyl groups (−CF3 and −CF2CF3). Conclusions can be summarized as follows. (1) FAFPs anions ionization energies decrease upon perfluoroalkylation. The substitution of 1 to 3 fluorine atoms with CF3 or C2F5 groups leads to a moderate decrease of the ionization potentials still remaining above 5 V versus Li, a value suitable for application with high-energy 5 V cathode materials in lithium cells. In the case of the CF3 group, a larger number of substituents (4−6) leads to a fall of the ionization potential below 4.5 V versus Li. (2) FAFPs-lithium ion pair dissociation energies drop upon perfluoroalkylation. This beneficial effect is due to the remarkable weakening of the ionic bond between the Li+ cation and the perfluorophosphate anion and is expected to highly enhance the salt dissociation in solvents and possibly the Li+ ion conductivity and transport number. (3) Although LiFAFPs molecules are thermodynamically more dissociated in model solvents to give both PF6−xRx− anions or electron-poor PF5−xRx in comparison to LiPF6, their reactivity toward water molecules fades upon perfluoroalklation. This effect is likely to improve the performances in lithium cells; in fact, PF5−xRx hydrolysis is a key step in the detrimental formation of free HF. Subsituted LiFAFPs are apparently less reactive with water and then the release of HF is expected to be mitigated in comparison to LiPF6. In summary, mono- to tri- perfluoroalkylated LiFAFPs salts are competitive alternatives to LiPF6 in nonaqueous electrolytes for Li-ion cells as they positively balance a slight decrease of the ionization potential (still above 5 V vs Li), the drop of the dissociation energy of the ion pair together with a mitigated reactivity toward water, in particular for three-substituted molecules. These advantages are particularly relevant for the hydrolysis reactions, responsible for the reduced lifetimes of the batteries, which appear to be largely mitigated by the substitution of fluorine with perfluoroalkyl groups. On passing, it is interesting to observe that fluoro-ethylene substituents are apparently predicted to have larger beneficial effects on all the computed properties compared to fluoro-methylene ones. On the other hand, the increase in the length and substitution of the perfluoroalkyl chains around phosphorus may lead to an increase in the viscosity of the solution and ion conductivity. In order to address this point (that depends on the Li+ diffusion mechanism), besides experiments, further computational efforts are needed going beyond the electronic structure calculations approach, thus moving to dynamics.

Table 2. Thermodynamic Equilibrium Constants (Log Keq) for the Ion Pair Dissociation (Reaction 1), Self-Dissociation (Reaction 2) and PF5−xRx Hydrolysis (Reaction 3), Calculated at the B3LYP Level with C-PCM (DMSO) reaction 1 +

LiPF6−xRx = Li + PF6−xRx−

reaction 2

reaction 3

LiPF6−xRx = LiF + PF5−xRx

PF5−xRx + H2O = 2HF + POF3−xRx

X

R = CF3

R = C2F5

R = CF3

R = C2F5

R = CF3

R = C2F5

0 1 2 3

1.4 3.6 5.4 3.7

3.0 3.8 3.7

−22.2 −19.6 −16.4 −10.8

−19.9 −20.6 −11.1

8.2 7.5 4.4 −0.2

7.2 4.9 −2.8

For the di- and three-substituted perfluoroalkylphosphates, where two different isomers exist, equilibrium constants have been calculated, considering the Boltzmann averages of the energetic stabilities of the so-called vicinal and axial conformers. As already mentioned in the methods section, the thermodynamics of these three reactions have been computed by calculating total energies for all chemical species in a simulated solvent going beyond the isolated molecule approximation. As expected from the data of the dissociation energies of the ion pairs in vacuum (see previous sections), in DMSO-like solvents, LiFAFPs are more easily dissociated to solvated ions (reaction 1) in comparison to lithium hexafluorophosphate. Furthermore, their ability to easily delocalize charges across the structure leads also to a stabilization of the electron-poor PF5−xRx molecules obtained by simple release of the solvated LiF ion pair upon perfluoroalkylation (reaction 2). This effect leads to a remarkable increase of the values of the equilibrium constants of reactions 2 for LiFAFPs in comparison to LiPF6. As a consequence, the equilibrium PF5−xRx activities in solution are expected a growth of about 1.5, 2.5, and 5 orders of magnitude for the mono, di-, and tri-substituted LiFAFPs in comparison to the standard LiPF6 electrolytes. On the other hand, the thermodynamic driving force of PF5−xRx to react with water molecules apparently drops with the increase of the perfluoroalkylation on phosphorus (reaction 3). In fact, the values of the equilibrium constants of reaction 3 decrease more than 10 orders of magnitude upon perfluoroalkylation, in particular in the cases of the three-substituted phosphates. This effect may be qualitatively interpreted by considering the enhanced delocalization of charges in PF5−xRx molecules upon perfluoroalkylation. This effect likely corresponds to a decrease of the hard character of these Lewis acids and to the parallel fading of the strong interaction with H2O, a hard Lewis base. In summary, LiFAFPs salts in carbonate electrolyte-like solvents are more easily dissociated to both PF6−xRx− anions or electron-poor PF5−xRx in comparison to LiPF6, whereas their strong reactivity toward water molecules fades. This last effect is

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ASSOCIATED CONTENT

* Supporting Information S

Geometries of optimized structures, P−F and P−C distances, angular deviation from octahedral symmetry, NBO results details, dissociation energies at the B3LYP and B97D levels of theory, ionization potentials (in V vs Li+/Li) as obtained with all the methods employed, and HOMO energies. This material is available free of charge via the Internet at http://pubs.acs.org. H



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (+39) 0971 205455. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

S.B. would like to thank the University of Basilicata for the support through the RIL 2012 funding scheme and the PONREC 2007-2013 Italian Authority for the support through the SMARTBASILICATA project. M.C. would like to thank the Université d’Evry Val d’Essonne for the hospitality during a research stay.

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