Ionic

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Density Functional Study of Charge Transfer at the Graphene/Ionic Liquid Interface ́ ez-Gonzaĺ ez,† A. García-Fuente,‡ A. Vega,§ J. Carrete,∥ O. Cabeza,⊥ L. J. Gallego,† V. Gom and L. M. Varela*,†

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Grupo de Nanomateriais, Fotónica e Materia Branda, Departamento de Física de Partículas, Universidade de Santiago de Compostela, Campus Vida s/n, E-15782 Santiago de Compostela, Spain ‡ Departamento de Física, Universidad de Oviedo, E-33007 Oviedo, Spain § Departamento de Física Teórica, Atómica y Ó ptica, Universidad de Valladolid, E-47011 Valladolid, Spain ∥ Institute of Materials Chemistry, TU Wien, A-1060 Vienna, Austria ⊥ Grupo Mesturas, Departamento de Física e Ciencias da Terra, Facultade de Ciencias, Universidade de A Coruña, Campus A Zapateira s/n, E-15012 A Coruña, Spain ABSTRACT: We use density functional theory to analyze the charge transfer between lithium or magnesium cations and a graphene wall beyond the predictions of classical Marcus theory. To that end, metal atoms are placed in three different kinds of environments: (i) in a vacuum, (ii) among fluorine atoms to simulate a molten salt, and (iii) in an ionic liquid. We prove that a complete charge transfer to the electrodes takes place in all of the studied environments and that the charge transfer process starts at longer distances from the electrode in the ionic liquid. Vertical ionization potentials and vertical electron affinities are studied, and they confirm that the nanoconfined region close to the electrode is a favorable environment for electronic exchange. No significant difference between monovalent and divalent cations was found. Our results suggest a certain catalyzing effect of ionic liquids regarding metal-electrode charge transfer in these densely ionic environments. Moreover, they show that ionic liquids can actually enhance charge transfer to electrodes in electrochemical devices without significantly altering the nature of the process.

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aprotic ILs in the bulk or near an interface33−39 have been reported, as well as different DFT studies, both in bulk and at interfaces.35,40−42 From these studies, as well as from others involving molecular cosolvents and other solutes (see ref 43 for a recent review on solvation in ILs), a detailed picture of a peculiar way of solvating metals in these media has emerged: metal cations are swollen into the polar nanoregions of these densely ionic solvents, forming a solid-like pseudolattice of metal-anion solvates or solvation complexes (according to the nanostructural solvation paradigm43), limiting the electrical conductivity and the ability of metal cations to reach the electrochemical interface. The formation of these metal-anion carrying species, quite different from those found in traditional solutions of metal cations in molecular solvents, is expected to have also important consequences in electron transfer in this highly ionic environments. A correct microscopic description of electron transfer in ILs is crucial to their proper use in electrochemical applications.

INTRODUCTION Over the past 2 decades, the field of ionic liquids (ILs) has enormously expanded due to the current and expected applications of these green, amphiphilically nanostructured “designer” solvents,1,2 whose properties can be specifically “tuned” for each application choosing the appropriate building blocks from a large number of known cations and anions.3 One of the most outstanding applications of ILs is as electrolytes in electrochemical devices, specifically in batteries, fuel cells, and supercapacitors, as has been repeatedly reported in recent years.4−7 This usage relies on the very large electrochemical stability of these solvents, which results in unrivaled electrochemical windows. Notwithstanding, due to this same property, ILs must be doped with some electrochemically active additive, usually metal salts, in order to get practical electrolytes for batteries. In the past few years, different studies on this subject have been reported for mixtures of ILs with alkaline8−29 and alkaline earth30−32 metals, including classical molecular dynamics (MD) and density functional theory (DFT) to dissect the microscopic mechanisms behind solvation, structure, and transport in these media. In particular, several MD analyses of mixtures of monovalent and divalent salts with protic and © XXXX American Chemical Society

Received: March 23, 2018 Revised: June 8, 2018

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DOI: 10.1021/acs.jpcc.8b02795 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

paper. Their possible contributions are estimated to be well within the uncertainty of the model70 and significantly lower than, for instance, solvent effects. Therefore, the added computational cost would not be justified. The systems are placed in a box of X and Y dimensions matching the simulated graphene sheet (comprising 32 C atoms in simulations with IL and 72 C atoms in all others and assuming its planarity in order to focus in the charge transfer and avoid extra complexities) and Z dimension of 20 Å (25 Å in the case of the systems with IL), in order to have sufficient vacuum so as to avoid influence from periodic replicas. Monkhorst−Pack grids of 8 × 8 × 1, 2 × 2 × 1, and 6 × 6 × 1 were employed for the calculations involving boxes in vacuum, with fluorine, and with IL respectively. We base our initial configuration for each system on the results of MD simulations with large numbers of particles, which can capture the effect of medium- and long-range order: the initial simulation box for the system with IL was built from previously reported MD results of [BMIM][BF4] near a graphene wall,36 taking the average configuration of the IL pair when placed close to a neutral graphene sheet. We then place the salt ion at a predefined distance from the wall and run a self-consistent-field (SCF) DFT calculation to obtain converged wave functions for the Kohn−Sham electrons and the charge density. We sample at least 35 distances along the normal to the graphene surface (see Figure 1) for each studied configuration. The charges of all atoms were calculated from the charge density using the Bader criterion72−75 after each simulation. In the Bader method, space is partitioned in volumes divided by zero-flux surfaces, which guarantees that the sum of the Bader charges equals the total charge of the system. The geometries for each of the three different systems are shown in Figure 1. With respect to the configuration with only a graphene sheet plus a Li or Mg atom, the system with fluorine adds a F atom at a distance of 4 Å from the wall and at 1.77 Å from the line perpendicular to the wall along which the central atom is moved. Those at 1.77 Å result from an average of the distance between Li and F atoms in LiF and the sum of the ionic radii of Li+ and F−. When we simulate Mg instead of Li, we introduce an additional F atom in the system in order to preserve electroneutrality. The position of this new atom is symmetric with respect to the line where the magnesium atom is getting moved. Finally, to simulate the system with IL, a [BMIM]+ ion and a [BF4]− ion are placed at around 3.5 Å from the carbon sheet, qualitatively reproducing the structure of the IL near a carbon interface, which was calculated previously by means of classical MD simulations. The lateral distance between them also matches the value found in MD simulations, which is longer than the radii of the metal atoms.36,39 The orientation of the IL pair relative to the graphene surface is the average orientation/configuration extracted from MD simulations of [BMIM][BF4] near a graphene wall, given the low mobility of the species in the innermost layer of the electrical double layer in these systems. More details of the system with IL are shown in Figure 2.

Up to now, most of the theoretical efforts devoted to the description of this phenomenon have been done using MD simulations and in the framework of the classical Marcus theory,44 including some extensions to account for deviations from linear behavior,45,46 which focuses in the description of the influence of solvent fluctuations on the rate of electron transfer and whose validity in bulk ILs was originally proved by LyndenBell.47,48 The predictions of Marcus theory may show significant deviations if fluctuations around reactants and products are similar, as has been shown by MD studies based on DFT.46 These deviations associated with the existence of different solvation states for a redox species were further confirmed by Salanne and co-workers49 by means of classical MD simulations of the Fe2+/Fe3+ electron transfer reaction in ILs under nanoconfinement, in which the authors found two solvation states for Fe3+. Although classical simulations provide a valuable average picture of this phenomenon, a proper microscopic analysis requires a detailed description of the electronic densities of the reacting species throughout the process, so quantum chemical methods are needed. Several examples of studies on the subject of charge transfer using DFT can be found in the literature: variations of effective charge of a recoiling atom along crystallographic directions of a SiC interface,50 analysis of the net charge of Li and Si atoms in LixSi compounds,51 use of DFTcalculated charges to assess a theoretical transfer parameter,52 charge analysis in an electron donor−acceptor complex of PA and CA,53 and even a study of charge transfer between NO2 and graphene,54 among others. With respect to ILs in particular, the study of charge transfer using DFT has only been applied to a pure IL and a Li electrode by Yildirim et al.55 Other DFT studies of ILs concerning their interaction with Li metal have also been reported in the past decade, regarding their adsorption,56−58 electrochemical stabilities,59−61 and the chemical decomposition of the IL species.62−65 In this work we present, for the first time up to our knowledge, a DFT study of the electron transfer from a monovalent or a divalent salt cation (lithium and magnesium, respectively) to a graphene wall as a function of the distance of this atom to the interface. In order to mimic different environments, this analysis has been performed for three different situations: in vacuum, with added fluorine atoms to mimic a high-temperature molten salt, and in the presence of 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]), to study the transfer reaction in ILs. In all cases, highly electronegative fluorine and spherically symmetric fluorine-based anions (BF4−) have been chosen, since F will expectedly enhance the charge transfer. On the other hand, we use an imidazolium cation as a model IL, since this family is frequently chosen in electrochemical applications, and it has been widely studied and properly parametrized for its computational analysis. The structure of the paper is as follows. After this Introduction, the computational details are included, and in section 3, we report our results and discussion. Finally, in section 4, the conclusions of the paper are summarized.

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RESULTS AND DISCUSSION Our simulations aim at qualitatively understanding the trends of electronic redistribution depending on the chemical environment that the salt cation may encounter, as well as how this environment influences the net charge transferred to the graphene sheet. Although the system is not fully relaxed in our vertical treatment of the process (the environment is not relaxed upon the movement of the salt cation through the selected path), the fact that the atomic and chemical environment and

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COMPUTATIONAL METHOD For all DFT calculations in this paper, we have used the projector augmented wave (PAW) method under the Perdew− Burke−Ernzerhoff (PBE) form of the generalized gradient approximation (GGA) for exchange and correlation as implemented in the Vienna ab initio simulation package (VASP).66−69 Dispersion corrections are not used in this B


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focus to the electronic configuration only when it matters the most. The results of these calculations for the system containing fluorine are shown in Figure 3, and the ones for the IL system are represented in Figure 4. The first relevant result to analyze is what happens in vacuum (only graphene and salt cation; dashed lines in Figures 3 and 4). Obviously, in this case all electronic charge lost by the atom is gained by the wall. Both the Li and Mg atoms are essentially neutral far away from the graphene sheet, but they start to ionize as they approach its surface, specifically at ∼3−4 Å, until they reach the expected ionization charge. However, while the Mg atom does not start transferring its charge until a distance of ∼4 Å, the Li atom is not entirely neutral even at long distances. This effect correlates with the lower electronegativity of lithium with respect to magnesium (0.98 and 1.31 in the Pauling scale, respectively), which makes electron transfer easier for the former. Another remarkable feature is that the Mg atom loses its two valence electrons in two separate steps, as the plateau around 2 Å suggests. The presence of fluorine atoms in the system drastically alters the shape of the charge curve. The fluorine atom remains ionized almost independently of the salt cation position (an unsurprising effect in view of its high electronegativity: 3.98 in the Pauling scale). There seem to be two distinct zones in the system with Li with regard to charge transfer and three in the system with Mg. In the Li−F system, the Li atom starts out ionized (with around +0.3e) when it is far away from graphene, and increases its charge exponentially until it reaches almost complete ionization at 4 Å, where the fluorine atom is placed. This charge is mainly transferred to the graphene wall, although some ends in the fluorine atom. From this point on, the charges of all species in the simulated system remain almost constant, as they reach an equilibrium point where Li+ is bonded with F−. In the Mg−F2 system, the behavior is similar to that in the monovalent case: fluorine atoms maintain their ionized state throughout all distances, and the salt cation increases its charge when approaching graphene, mainly by electron transfer to the wall but also to the fluorine atoms to a lesser extent. The main difference seems to be that Mg is almost fully ionized at a longer distance from the wall than Li. This effect is probably related to the fact that in this situation two fluorine atoms were introduced instead of one, so the opportunities to shed electrons are increased. Again, at distances to the wall shorter than 4 Å, the salt atom seems to be bonded with the F−, so the charges of all three species in the system remain approximately constant. However, when the salt cation is very close to the wall (≲2 Å), charge is transferred from the fluorine atoms to graphene. The preponderance of kinetic energy in the regime of high charge densities could be favoring a more uniform distribution of charge between graphene and the fluorine atom. However, it is clearly shown that the high electronegativity of the fluorine atom does not allow the graphene to reach negative enough charges (only around −0.1e/−0.25e in the monovalent/ divalent system), so although the salt cation atom is able to start losing electrons at longer distances from the wall than in vacuum, the transfer efficiency to graphene is much lower. This efficiency is obviously very important with regard to electrochemical applications. In order to get some qualitative insight into the energy barriers our salt cation must overcome when getting close to the graphene wall, we show in Figure 5 the total energy of the systems with magnesium as a function of the magnesium distance to the graphene sheet, choosing as the origin of energy

Figure 1. Starting configurations for all simulated systems: (a) graphene + Li or Mg cation system, (b) system with fluorine, and (c) system with IL, including the periodic replicas. The dashed red line represents the normal to the graphene surface, along which Li or Mg atoms are moved in order to get the starting geometry of the simulation for each distance to the wall. This line goes through the center of a hexagon of the graphene sheet (hollow site), which is the energetically favored site for the adsorption of groups I−III metal adatoms on graphene (see ref 71). Atom colors are the following: C, cyan; Li/Mg, pink; F, blue; N, purple; H, white; B, green.

interatomic distances match the optimal configuration given by previous MD simulations,36 whose results were benchmarked against experimental data, means that those environments will not differ much from snapshots of the ones occurring during the dynamical process. Of course, ab initio MD simulations could provide a more quantitative description of the systems investigated, but their complex nature makes the multiscale workflow combining classical MD and DFT a trade-off between accuracy and feasibility. Moreover, it is unrealistic to try to use DFT to simulate large boxes of solute for a long enough time to achieve finite-temperature equilibrated configurations close to the graphene interface with the same quality that MD can afford. We hence harness the strengths of each method by shifting our C


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Figure 2. Simulated system of [BMIM][BF4] and Li/Mg and relevant distances between different species. Some replicas of the unit cell (which is shown in Figure 1c) are included for the sake of clarity. The blue arrow represents the direction along which the Li/Mg atom is being moved in order to get the starting geometry of the simulation for each distance to the graphene sheet.

Figure 3. Charges of the different species in the system with fluorine as a function of the (a) lithium or (b) magnesium distance to the graphene sheet. The dashed lines represent the charges of salt cation and graphene in the vacuum system. The red dotted line marks the position of the fluorine atom(s).

Figure 4. Charges of the different species in the system containing IL as a function of the (a) lithium or (b) magnesium distance to the graphene sheet. Dashed lines represent the charges of salt cation and graphene in the vacuum system. The positions of the other atoms of the system are represented in the background.

the configuration with the magnesium atom farthest from the graphene wall. The results are in good agreement with the

expected ones. In the system where only Mg and graphene are present, the energy of the system remains constant until the salt D


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2 Å. No qualitative differences between the monovalent and divalent salt cations are found in this regard. Furthermore, the efficiency of the charge transfer to the graphene wall is higher when IL is present than in vacuum or with fluorine atoms, without substantially altering the nature of its cations and anions (as the cation has the same charge at short and long distances of the salt cation to the wall and the anion maintains the same charge throughout the whole trajectory of the salt cation approaching the wall) in the whole process. Therefore, we could claim that ILs work as “catalyzers” of the charge transfer. We have also calculated the charges of all species in the system when the Mg atom is near (1.6 Å) and far away (8.0 Å) from the graphene sheet, when we add or remove an electron in the system. The results are shown in Figure 6. We can clearly see

Figure 5. Relative energies of the simulated systems with Mg, ΔE, as a function of the magnesium distance to the graphene sheet. Note that the origin of energy, ΔE = 0, has been chosen to be that of the configuration with the magnesium atom farthest from the graphene wall.

cation gets close to the wall. On the other hand, when we dope the system with two fluoride atoms, a minimum of energy is reached at 4 Å, where Mg forms bonded MgF2. However, when we have an IL added in the system, we recover the already known energy barriers that come from the anion and the cation, which were reported in previous works using classical MD simulations.39,76 These energy barriers are artificially high in these DFT calculations due to the lack of solvent relaxation. Finally, we analyze the electronic charge transfer in the IL system (shown in Figure 4). The main features of the behavior of the salt cation are qualitatively the same as in the previous fluorinated system, as there is a distance range far from the wall where the salt ion starts to ionize, and around 4.5 Å the charge stabilizes and remains approximately constant, mainly for Li. Again, the anion charge also remains constant independent of the position of the Li/Mg, as expected because of its nature as a heavily fluorinated compound. On the other hand, the IL cation is almost fully ionized when the salt atom is either very near or far away from the surface but displays a charge minimum when the Li/Mg atom is placed close to [BMIM]: the cation is half ionized when it is near the monovalent cation and almost fully neutral in the system with the divalent salt in the same position. This difference probably comes from the higher electronegativity of the divalent cation but also because electroneutrality has to be preserved, and the Mg atom can donate one more electron than the Li atom. If we had simulated this system with one extra anion, as we did in the system with fluorine, the cation charge curve should be approximately the same for both monovalent and divalent salt atoms. Moreover, it is clear that even when we approach bulk conditions (salt cation far away from the wall) the effect of the graphene wall over the IL anion is marked, as its charge is −0.98e while that of the IL cation is 0.87e, much more similar to the charge reported by Hollóczki et al. (approximately ±0.82) when the IL pair is completely isolated.35 In conclusion, clearly the main effect of the IL with respect to the vacuum system is to enhance the charge transfer from the corresponding salt cation: it starts at longer distances from the wall, reaching its fully ionized form at around 4.5 Å instead of at

Figure 6. Charges of the different species in the Mg + [BMIM][BF4] system as a function of the total charge of the system. The system with the Mg atom placed near the graphene sheet (1.6 Å) is represented with dots (a) while the system with this atom placed at 8 Å is represented with squares (b).

there is a difference in the behavior of the system’s components when the salt cation is near or far away from the wall, except for the anion: again, its charge remains practically immune to the addition or removal of one electron from the system, as it is fully ionized in all cases. An analogous behavior appears for the Mg atom when it is near the wall, as it is almost fully ionized and does not get influenced by a small variation of the number of electrons in the system, meaning that this geometric distribution forces the salt cation to give all its charge. At this point, it is natural to wonder where the excess/defect of charge in the system goes. It appears that both the IL cation and the wall distribute it among them, although not in the same proportion: carbon atoms in graphene seem to be more likely to lose some of their electrons when the total system charge is +1, while in the case of charge −1 the IL cation gets most of this electron excess. E



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On the other hand, when the salt cation remains far away from the graphene wall, the cation charge is almost constant, and only graphene and the salt cation change their charge in basically the same proportion. This is evidence that the IL pair is not affected by small charge variations in the system when it is in bulk phase (“isolated” from the salt cation), unlike in the situation where the salt cation is ionized near the IL pair, and hence the cation behaves as the predominant species that likes to lose/gain electrons. This was also observed in Figure 4, as in the distance range from ∼1.5 to 5 Å the IL cation can almost recover its electroneutrality because of the influence of the nearby salt cation. Finally, and in order to get some more insight into the ionic liquid system, we calculated the vertical electronic affinity (VEA) and the vertical ionization potential (VIP) of the system when the Mg atom is near and far away from the graphene sheet. These calculations are frequently done for clusters in DFT studies and are based on adding or removing an electron from the system without relaxing the structure.77,78 For clusters, these magnitudes are very similar to the corresponding ionization potentials and electronic affinities, so they tell us how difficult (energetically) it is to add or remove an electron from the system. In our system, we can qualitatively translate that to how difficult it is for an external potential (such as the one we should apply to a graphene electrode near our mixture of ionic liquid and salt) to be able to extract or supply electric energy (electrons) from or to the electrolyte. The results for the VIP and VEA for the system where the magnesium atom is close to the wall give values of 1.80 eV and −0.30 eV, respectively, and when this atom is placed far away from the graphene sheet, they change to 3.24 eV and −2.28 eV. This again shows that the system is more receptive to changes in its electronic environment when the metal ion is near the graphene wall, precisely what we want for the charge exchange to occur in a real battery.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

A. García-Fuente: 0000-0002-4570-8315 J. Carrete: 0000-0003-0971-1098 L. M. Varela: 0000-0002-0569-0042 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support of the Spanish Ministry of Economy and Competitiveness (Projects MAT2014-57943-C3-1-P, MAT2014-57943-C3-3-P, MAT2017-89239-C2-1-P, MAT2017-89239-C2-2-P, FIS2014-59279-P) is gratefully acknowledged. Moreover, this work was funded by the Xunta de Galicia (Grants AGRUP2015/11 and GRC ED431C 2016/ 001). All these research projects were partially supported by FEDER. V.G.-G. thanks the Spanish Ministry of Education for his FPU grant. Facilities provided by the Galician Supercomputing Centre (CESGA) are also acknowledged. Funding from the European Union (COST Actions CM1206 and MP1303) is also acknowledged.

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CONCLUSIONS We report the first, to our knowledge, DFT simulations of the process of electronic charge transfer between an alkaline (monovalent) and alkaline earth (divalent) salt cation (Li, Mg) to graphene electrodes in different environments (vacuum, a molten salt, and an IL). A complete charge transfer to the electrodes was found to take place in all the studied systems, but the IL seems to lead to a significant enhancement in the charge transfer process, which starts at longer distances than in the other environments, ultimately leading to the same degree of charge transfer to the electrode. Higher efficiency in the charge transfer process and higher vertical ionization potentials were found for the configuration with the metal closer to the electrode, and the opposite trend was found for the vertical electron affinities, confirming the favorable electronic exchange in the nanoconfined region close to the electrode. Finally, no relevant difference between monovalent and divalent cations was found. All our results suggest a certain catalyzing effect of ILs regarding metal/electrode charge transfer in these densely ionic environments. Our findings are promising for the future electrochemical applications of ILs: enhanced charge transfer to the electrode without an associated change in their behavior as solvents make them more attractive candidates for such purposes. It is, hence, of utmost importance to extend this research to more kinds of species and to larger systems that include more details about the equilibrium structure of the bulk phase in contact with the electrode. F


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