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A Combined Experimental and Computational Study of an Aluminum triflate/diglyme Electrolyte Luke D. Reed, Ana Arteaga, and Erik Jason Menke J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b08501 • Publication Date (Web): 10 Sep 2015 Downloaded from http://pubs.acs.org on September 17, 2015
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A Combined Experimental and Computational Study of an Aluminum triflate/diglyme Electrolyte Luke D. Reed, Ana Arteaga, Erik J. Menke* University of California, Merced Corresponding Author *Correspondence should be addressed to:
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Abstract. The physicochemical properties of aluminum trifluoromethanesulfonate in diglyme have been investigated. The spectroscopic and electrochemical properties have been examined to determine speciation, conductivity and electrochemical stability. Gaussian calculations provide optimized molecular geometries and offer insight into the electrochemical behavior of the solutions. The ions in solution appear to exhibit very straightforward behavior, with contact ion pairs forming at very low concentrations. In addition, the electrochemical window of the electrolyte initially decreases with increasing salt concentration to a minimum value of approximately 5.5 V around 1 M, and then steadily rises to a maximum value above 8 V.
KEYWORDS Electrochemistry, physicochemical properties, chelate. Introduction The development of new electrolytes for energy applications is of great interest from both a scientific and practical standpoint. As new cathode materials and new chemistries are explored for advanced battery applications new electrolytes will be required, in particular for magnesium and aluminum-based systems. Ionic liquids have been explored for many years as potential advanced electrolytes because of several well-known advantageous properties such as low volatility, high conductivity and wide electrochemical windows. However they have proven challenging to implement in commercial batteries due to various drawbacks, including high viscosity and increased cost. Recent research has shown that at sufficiently high concentrations binary mixtures of conventional metal salts and organic solvents can exhibit behavior very similar to ionic liquids. These mixtures have been termed ‘solvate ionic liquids’ and have shown promise as both lithium ion and sodium ion electrolytes.1-2 In general, early work done on highly concentrated
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electrolytes did not identify them by the term solvate ionic liquid; rather they were referred to and studied simply as concentrated electrolytes with a notable exception being an early work on equimolar mixes of lithium imide salts in glyme solvents.3 The intent of the bulk of the early research was to expand the understanding of electrolytes that deviated from the theoretical behavior governed by empirical laws such as Debye-Huckel theory and its extension by Onsager. While some limited success was obtained with efforts to add to the theories of concentrated electrolytes, the research could be largely considered as relatively specialized and of limited interest to a general audience. Resurgence in the field, including investigation of possible device applications as well as the origination of the term ‘solvate ionic liquid’, seems to have been brought about primarily by Watanabe’s detailed investigation of lithium electrolyte systems.2, 4-6 Further work by the same group expanded the range of the studies and was followed by papers investigating sodium trifluoromethanesulfonate in pentaglyme and ion size effects on solvate stability.1, 7 At some critical level of concentration, generally a 1:1 molar ratio of solvent:salt, all the systems studied exhibit a transition from attributes consistent with normal solvent/salt solutions to those more typically ascribed to ionic liquids.8 Extending this work to multivalent ions has the potential to lead to better electrolytes for next generation batteries, as similar systems are being explored for magnesium and aluminum rechargeable batteries.9-16 In this paper we report on the physicochemical properties of aluminum trifluoromethanesulfonate (aluminum triflate) in 2-methoxy-ethyl ether (diglyme), and compare these properties with properties calculated from DFT. The spectroscopic characteristics, investigated by FTIR, show evidence of free triflates in very dilute solutions and contact ion pairs in all but the most dilute solutions, rather than the complex ion pairing observed previously in lithium and sodium electrolytes. The electrochemical window and ionic conductivity were
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measured as a function of concentration. The electrochemical window initially decreases with increasing salt concentration to a minimum value around 1 M, and then steadily. Results from DFT calculations of optimized geometries, normal modes and absolute redox potentials help explain both the spectroscopic and electrochemical properties. Materials and methods. Experimental details. Aluminum triflate and diglyme were purchased from Sigma-Aldrich and were handled and stored in an argon-filled VAC glovebox with oxygen and water levels below 0.5ppm. The diglyme was purchased as ultra-dry and was further dried and stored over freshly activated molecular sieves. All solutions were made in the glovebox by addition of appropriate amounts of aluminum triflate to diglyme to control the ratio of solvent molecules to aluminum ions. The solutions were stirred overnight to ensure complete dissolution of the aluminum triflate. Cyclic voltammetry of the solutions were measured with a Gamry potentiostat in a standard three-electrode configuration, with an aluminum wire counter electrode, an aluminum wire reference electrode, and either an aluminum wire or platinum wire working electrode, at a scan rate of 1 mV/s. Ionic conductivity was measured via electrochemical impedance spectroscopy on a ParStat 2273 with a 10 mV AC signal and 0 V DC offset, over a frequency range of 10 kHz to 100 kHz, using an impedance cell prepared in the lab. The cell consisted of two platinum wires encased in flint glass tubing, with the exposed surface of the wires polished using 0.3 µm alumina, and was calibrated at 20 degrees C with a 0.1 M KCl standard solution. FTIR data was collected on a Thermo Nicolet 380 with 1 cm-1 resolution using 64 scans, KBr windows were used for the transmission cell. The more dilute solutions, 667 to 1 and 33 to 1, were gelled by addition of fumed silica at approximately 7wt% to increase the amount of material between the KBr windows. This technique has been previously utilized and has been
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shown to introduce no inference with the ion pairing of the electrolytes.17 The spectra were curve fit using Galatic Grams to a Voigt profile with a linear baseline. All fitted curves had r2 values greater than 0.98. Density functional calculations. All calculations were carried out with Gaussian 09.18 Geometry optimization calculations for the molecules and complexes studied were carried out with the B3PW91 method using a 6-311G(d) basis set. Solvation free energies were evaluated by the selfconsistent reaction field (SCRF) approach using the SMD model, implemented as the default SMD method in Gaussian.19 As diglyme has not been parameterized for SMD, tetrahydrofuran was used as the solvent for all SMD calculations given its similar physical properties to diglyme. Results and discussion.
Figure 1- Optimized geometry (hydrogens not shown) of A) the aluminum-diglyme complex, with the aluminum shown as pink, the oxygens as red, and the carbons as black, B) the aluminum-diglyme complex with one bound triflate, with the fluorines shown as blue and the
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sulfur as yellow, C) the aluminum-diglyme complex with two bound triflates, D) the aluminumdiglyme complex with three bound triflates. Calculated geometries. Figure 1A shows the optimized solvent-phase structure for an Al3+-bisdiglyme complex, while figures 1B-D show the optimized solvent-phase structure for the Al3+bis-diglyme complex with one, two, and three triflate anions, respectively. The calculated Gibbs energy for the reaction: Al3+ + 2 diglyme -> Al(dg)23+ is –1922 kJ mol-1, corresponding to an equilibrium constant of 10335. While the complexes in figures 1B-D are also very stable, given the additional coulombic attraction between the aluminum-diglyme complex and the triflate anion, there were no starting geometries that led to the triflate anion directly bound to the aluminum cation, either in the gas or solvent phase, suggesting that the diglyme molecule is a stronger Lewis base than the triflate anion. Based on these calculations we expect all of the aluminum ions to be chelated by two diglyme molecules, forming a stable Al(diglyme)2 complex, which interacts with the triflate anions primarily via coulombic attraction. FTIR Analysis. Spectral characterization of the solutions reveals a concentration sensitive region between 750 and 775 cm-1 corresponding to the CF3 symmetric deformation mode, δs(CF3), of the triflate anion.6, 17, 20 It has been shown for numerous electrolytes that peak centers and relative areas can be examined as a function of concentration to provide insight into the nature of ion pairing in the solution phase electrolyte. For example, previous work has shown the vibrational frequency of the δs(CF3) mode of triflate in monoglyme to be centered at 753 cm-1, increasing to 758 cm-1 upon forming contact ion pairs with solvated lithium ions, with a further
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increase to 769 cm-1 for a single triflate anion triply coordinated by lithium ions.21 The corresponding frequencies of the CF3 deformation in lithium triflate in diglyme are reported to be 752 cm-1 for free triflate, shifting to 757 cm-1 for contact ion pairs, 761 cm-1 for dimers or triple cations and 762 cm-1 for Li2Tf upon formation of the crystalline phase.17
Figure 2 – A) FTIR spectra of 2.5:1 (purple), 6.7:1 (green), 33:1 (blue), and 667:1 (red) diglyme:aluminum triflate solutions, showing the shift in peak position of the CF3 symmetric mode as a function of concentration. B) FTIR spectra of 667:1 (black) diglyme:aluminum triflate solution, showing fitted peak (purple). C) FTIR spectra of 33:1 (black) diglyme:aluminum triflate solution, showing fitted peaks (yellow, purple, green and blue). D) FTIR spectra of 6.7:1 (black) diglyme:aluminum triflate solution, showing fitted peaks (green and blue).
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Figure 2A shows the CF3 absorption region for four different concentrations of aluminum triflate in diglyme. The lowest frequency observed in the CF3 region occurs at 751 cm-1, similar to the peak position for free triflate in previous work, with an increase in frequency to a maximum of 766 cm-1 in the most concentrated solution. These frequencies are also consistent with DFT calculations on free triflate in THF, which has a CF3 vibrational frequency at 752 cm-1, and an Al(diglyme)2-triflate contact ion pair (figure 1B) in THF, which has a CF3 vibrational frequency at 762 cm-1. Increasing the number of triflates coordinated to the Al(diglyme)2 complex has little effect on the vibrational frequency of the CF3 deformation, as the Al(diglyme)2-bis(triflate) complex (figure 1C) has two CF3 vibrational frequencies at 761 cm-1, while the Al(diglyme)2tris(triflate) complex (figure 1D) has three CF3 vibrational frequencies between 758-761 cm-1. The shift observed in the Al3+ based electrolyte extends over a slightly larger range of frequencies than that observed in monovalent ion solvate ionic liquids, e.g., Li+ or Na+ in glyme solvents.1, 17 Monovalent systems typically span regions of 10 cm-1 for solution phase systems while the present Al3+ system spans 15 cm-1 from the most dilute to most concentrated solution. This extended range can likely be attributed to the higher charge density of the Al3+ relative to Li+ or Na+, as it has been shown that the shift in the δs(CF3) frequency depends on the degree of electron withdrawal from the triflate anion by the coordinating cation.22 Given the strong Lewis acidity of an aluminum ion it is natural to expect an increase in the δs(CF3) frequencies. Further, it is interesting to note that while monovalent systems generally show evidence of three or four spectroscopically measureable ion configurations at all concentrations17, 21 the Al(diglyme)2 data suggests somewhat simpler ion interactions. Curve fitting for the most dilute electrolyte, shown in figure 2B, reveals a single peak centered at 754 cm-1. Increasing the concentration to a 33:1 molar ratio (0.2 M) results in the appearance of 4 total peaks, shown in figure 2C, centered at
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751, 754, 761, and 766 cm-1. Finally, for the two most concentrated electrolytes only 2 peaks are observed, shown for the 6.7:1 molar ratio (1.1 M) electrolyte in figure 2D, centered at 766 and 761 cm-1. While the exact nature of the speciation present in these solutions is currently being investigated, in particular the shoulder peaks at 751 and 761 cm-1, it seems apparent that the triflate anions in these electrolytes can be viewed as either free triflates, with CF3 frequencies between 751 and 754 cm-1 and only occurring in dilute electrolytes, or bound triflates, with CF3 frequencies between 761 and 766 cm-1 and appearing in all but the most dilute electrolytes. Electrochemical characterization. Cursory analysis of the anodic region of the electrolyte cyclic voltammograms shows an increase of the oxidation edge as the concentration of aluminum triflate is increased, similar to previously published results on lithium and sodium triflate in diglyme.1-2 As seen in figure 3A the oxidation onset potential shifts by approximately 0.3 volts from 667:1 to 33:1, while smaller shifts of about 0.2 volts and 0.3 volts are evident between 33:1 and 6.7:1 and between 6.7:1 and 2.5:1, respectively. A larger shift of approximately 0.5 volts is observed in moving from 2.5:1 to 2:1 (not shown). This enhanced anodic stability has previously been attributed to the lowering of the HOMO level of the complex by the electron withdrawing effect of the solvated cations.1-2, 7, 23 Examining the cathodic edge, however, reveals more complex behavior. As seen in figure 3B the reduction onset potential initially shifts to more positive potentials as the aluminum triflate concentration increases, until the electrolyte reaches a molar ratio of approximately 7:1, at which point the reduction onset begins to shift to more negative potentials. The net result is that the overall electrochemical window, shown in figure 3C and which is a better measure of stability than either the anodic or cathodic onsets as it accounts for a shifting zero caused by the varying aluminum activity, exhibits more complex dependence on aluminum triflate concentration than expected.
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In contrast to the cyclic voltammograms measured on a platinum wire, the voltammograms on an aluminum working electrode, shown in figure 3D, show immediate electrochemical activity, which can be attributed to electrochemical accessibility of the Al/Al3+ redox reaction. Although the aluminum is electrochemically active in the electrolyte it is apparent upon repeated cycling that passivation takes place during the course of cycling the anode. The observed passivation is likely due to the formation of insulating aluminum-fluoride surface species over time, as this behavior is well known from investigations of aluminum current collector corrosion in the presence of fluorine containing anions in lithium ion batteries.23-27
Figure 3 – A) Anodic potentials showing a shift in oxidation potential as the aluminum triflate concentration increases for 2.5:1 (purple), 6.7:1 (green), 33:1 (blue), and 667:1 (red) diglyme:aluminum triflate solutions. B) Cathodic potentials showing the change in reduction potential as the aluminum triflate concentration increases. C) Overall cyclic voltammograms of diglyme:aluminum triflate solutions on a platinum electrode. D) 1st 4 cycles (dark to light blue)
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of cyclic voltammogram for the 6.7:1 solution on an aluminum working electrode, showing the passivation of the aluminum metal. Scheme 1.
To better understand the change in electrochemical window, the Gibbs free energy change associated with the solution-phase reduction of three redox couples (diglyme oxidation and reduction, triflate oxidation and reduction, and the Al(diglyme)2 complex oxidation and reduction) was calculated using the Born-Haber cycle shown in Scheme 1.28-29 This Gibbs free energy is then converted to an absolute reduction potential using Equation 1:
(1) where F is Faraday’s constant, n is the number of electrons involved in the reduction, and the solution-phase Gibbs free energy is:
(2) The results of these calculations are summarized in Table 1. Table 1. Gibbs free energies and absolute reduction potentials of solvent, anion and complexes.
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Reaction (hartree)
(hartree)
(hartree)
(volts)
Diglyme+ + e- → Diglyme
-0.307566
-0.007879
-0.076279
6.508
Diglyme + e- → Diglyme-
0.083992
-0.064593
-0.007879
-0.742
Triflate + e- → Triflate-
-0.177474
-0.071271
-0.005188
6.627
Triflate- + e- → Triflate2-
0.193534
-0.272905
-0.071271
0.220
Al(Dg)24+ + e- → Al(Dg)23+
-0.735813
-0.48723
-0.854533
10.027
Al(Dg)23+ + e- → Al(Dg)22+
-0.377725
-0.226205
-0.48723
3.176
From these calculations we predict that the electrochemical window for neat diglyme will be approximately 7.2 volts. As we increase the concentration of aluminum triflate, however, the oxidation edge will increase slightly as it becomes dominated by oxidation of the triflate anion, not the oxidation of the metal-diglyme complex as predicted by other work,2 while the reduction edge will increase significantly as it becomes dominated by reduction of the aluminum-diglyme complex, resulting in a expected electrochemical window of approximately 3.5 volts at high aluminum triflate concentrations. While the measured electrochemical window for these electrolytes is wider than 3.5 volts, much of that can be attributed to kinetic factors as we expect electron transfer to the Al(diglyme)2 complex to be slow, leading to a large overpotential, which is supported by the activity of the aluminum working electrode and inactivity of the platinum working electrode shown in figure 3D.
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Figure 4 - A) Electrochemical window of the solution as a function of aluminum triflate concentration. B) Ionic conductivity of the solution as a function of aluminum triflate concentration. To test for the effects ion transport on the electrochemical window, electrolyte conductivities were measured using electrochemical impedance spectroscopy with a two electrode platinum cell. The concentration dependence of the electrolyte’s electrochemical window is shown in figure 4A. The electrochemical window for the very dilute solutions starts around 6 V, and decreases to a minimum of 5.5 V as the concentration of the aluminum triflate increases to 1 M, consistent with the theoretical predictions. However, at a concentration around 1 M, the electrochemical window begins to increase, rising above 8 V for very high aluminum triflate concentrations, which is completely counter to the computational results above. Similar behavior is seen in the ionic conductivity of the electrolytes, shown in figure 4B. Initially the ionic conductivity of the electrolytes is low, at 4 mS cm-1 in the 0.04 M electrolyte, and increases with aluminum triflate concentration to maximum value of 25 mS cm-1 around 1 M. At this point the ionic conductivity begins to decrease due to the increased ion pairing and increasing viscosity of the electrolyte. Based on this, we believe that the increase in the electrochemical window observed above concentrations of 1 M are a result of poor ion transport rather than an enhancement in thermodynamic stability.
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Conclusions. The behavior of aluminum triflate in diglyme has been examined both experimentally and computationally. The concentration dependent trends in the physicochemical properties of the electrolytes offer insight into the solvation and ion pairing character of the solutions. In contrast to the 3-4 peaks present in FTIR spectra of monovalent solvate ionic liquids, independent of concentration, the FTIR spectra of the Al-diglyme electrolytes typically show 2 distinct peaks, 1 due to free triflate and 1 due to ion pairing, in the 752 to 766 cm-1 region indicating less complex ion pairing due to the increased charge density of the aluminum cation. Cyclic voltammetry shows an increase in electrochemical window of approximately 2.5 V between the most dilute and most concentrated electrolyte, with a local minimum observed at an intermediate concentration. DFT calculations show that the cathodic edge of the window is governed by the reductive stability of the Al(diglyme)2 complexes and the anodic edge is governed by the oxidative stability of the triflate. The predicted electrochemical window ranges from 7.2V for neat diglyme to 3.5V for highly concentrated electrolyte. The discrepancy between the calculated and measured window for the most concentrated electrolyte can be explained by a large increase in viscosity as well as slow electron transfer kinetics, leading to a large overpotential. AUTHOR INFORMATION Corresponding Author *Email:
[email protected] Notes The authors declare no competing financial interests. Acknowledgements
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The authors thank the American Chemical Society’s Petroleum Research Fund (52056-ND10) for providing financial support, as well as computing time on the Multi-Environment Computer for Exploration and Discovery (MERCED) cluster which is supported by National Science Foundation grant number ACI-1429783. In addition, the authors thank Hrant Hratchian and Jason Hein for valuable discussion. REFERENCES
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9. Abood, H. M. A.; Abbott, A. P.; Ballantyne, A. D.; Ryder, K. S., Do All Ionic Liquids Need Organic Cations? Characterisation of [AlCl2 center dot nAmide](+) AlCl4- and Comparison with Imidazolium Based Systems. Chem Commun 2011, 47 (12), 3523-3525. 10. Reed, L. D.; Ortiz, S. N.; Xiong, M.; Menke, E. J., A Rechargeable Aluminum-ion Battery Utilizing a Copper Hexacyanoferrate Cathode in an Organic Electrolyte. Chem Commun [Online early access]. DOI: 10.1039/C5CC06053B. Published online: Aug. 10, 2015. 11. Kitada, A.; Nakamura, K.; Fukami, K.; Murase, K., AlCl3-dissolved Diglyme as Electrolyte for Room-Temperature Aluminum Electrodeposition. Electrochemistry 2014, 82 (11), 946-948. 12. Canepa, P.; Gautam, G. S.; Malik, R.; Jayaraman, S.; Rong, Z. Q.; Zavadil, K. R.; Persson, K.; Ceder, G., Understanding the Initial Stages of Reversible Mg Deposition and Stripping in Inorganic Nonaqueous Electrolytes. Chem Mater 2015, 27 (9), 3317-3325. 13. Chang, J.; Haasch, R. T.; Kim, J.; Spila, T.; Braun, P. V.; Gewirth, A. A.; Nuzzo, R. G., Synergetic Role of Li+ during Mg Electrodeposition/Dissolution in Borohydride Diglyme Electrolyte Solution: Voltammetric Stripping Behaviors on a Pt Microelectrode Indicative of Mg-Li Alloying and Facilitated Dissolution. Acs Appl Mater Inter 2015, 7 (4), 2494-2502. 14. Mandai, T.; Johansson, P., Al Conductive Haloaluminate-free Non-aqueous Roomtemperature Electrolytes. J Mater Chem A 2015, 3 (23), 12230-12239. 15. Su, S. J.; Huang, Z. G.; Nuli, Y.; Tuerxun, F.; Yang, J.; Wang, J. L., A Novel Rechargeable Battery with a Magnesium Anode, a Titanium Dioxide Cathode, and a Magnesium Borohydride/tetraglyme Electrolyte. Chem Commun 2015, 51 (13), 2641-2644. 16. Tutusaus, O.; Mohtadi, R.; Arthur, T. S.; Mizuno, F.; Nelson, E. G.; Sevryugina, Y. V., An Efficient Halogen-Free Electrolyte for Use in Rechargeable Magnesium Batteries. Angew Chem Int Ed 2015, 54 (27), 7900-7904. 17. Petrowsky, M.; Frech, R.; Suarez, S. N.; Jayakody, J. R. P.; Greenbaum, S., Investigation of Fundamental Transport Properties and Thermodynamics in Diglyme-salt Solutions. J Phys Chem B 2006, 110 (46), 23012-23021. 18. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A., et al. Gaussian 09, Gaussian, Inc.: Wallingford, CT, USA, 2009. 19. Marenich, A. V.; Cramer, C. J.; Truhlar, D. G., Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J Phys Chem B 2009, 113 (18), 6378-6396.
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20. Petrowsky, M.; Frech, R., A Spectroscopic Investigation of the Mechanism of Gel Formation in Tetraglyme/fumed Silica Composites. Electrochim Acta 2003, 48 (14-16), 20932097. 21. Rhodes, C. P.; Frech, R., Local Structures in Crystalline and Amorphous Phases of Diglyme-LiCF3SO3 and Poly(ethylene oxide)-LiCF3SO3 Systems: Implications for the Mechanism of Ionic Transport. Macromolecules 2001, 34 (8), 2660-2666. 22. Huang, W. W.; Frech, R.; Wheeler, R. A., Molecular-Structures and Normal Vibrations of Cf3so3- and Its Lithium Ion-Pairs and Aggregates. J Phys Chem 1994, 98 (1), 100-110. 23. Zhang, C.; Yamazaki, A.; Murai, J.; Park, J. W.; Mandai, T.; Ueno, K.; Dokko, K.; Watanabe, M., Chelate Effects in Glyme/Lithium Bis(trifluoromethanesulfonyl)amide Solvate Ionic Liquids, Part 2: Importance of Solvate-Structure Stability for Electrolytes of Lithium Batteries. J Phys Chem C 2014, 118 (31), 17362-17373. 24. Brito, P. S. D.; Sequeira, C. A. C., Organic Inhibitors of the Anode Self-Corrosion in Aluminum-Air Batteries. J Fuel Cell Sci Tech 2014, 11 (1). 25. Hyams, T. C.; Go, J.; Devine, T. M., Corrosion of Aluminum Current Collectors in Highpower Lithium-ion Batteries for use in Hybrid Electric Vehicles. J Electrochem Soc 2007, 154 (8), C390-C396. 26. Zhang, X. Y.; Devine, T. M., Factors That Influence Formation of AlF3 Passive Film on Aluminum in Li-ion Battery Electrolytes with LiPF6. J Electrochem Soc 2006, 153 (9), B375B383. 27. Morita, M.; Shibata, T.; Yoshimoto, N.; Ishikawa, M., Anodic Behavior of Aluminum Current Collector in LiTFSI Solutions with Different Solvent Compositions. J Power Sources 2003, 119–121, 784-788. 28. Konezny, S. J.; Doherty, M. D.; Luca, O. R.; Crabtree, R. H.; Soloveichik, G. L.; Batista, V. S., Reduction of Systematic Uncertainty in DFT Redox Potentials of Transition-Metal Complexes. J Phys Chem C 2012, 116 (10), 6349-6356. 29. Roy, L. E.; Jakubikova, E.; Guthrie, M. G.; Batista, E. R., Calculation of One-Electron Redox Potentials Revisited. Is It Possible to Calculate Accurate Potentials with Density Functional Methods? J Phys Chem A 2009, 113 (24), 6745-6750.
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