Insights into the Structure and Transport of the Lithium, Sodium

Article Cite This: J. Phys. Chem. C 2018, 122, 20108−20121

pubs.acs.org/JPCC

Insights into the Structure and Transport of the Lithium, Sodium, Magnesium, and Zinc Bis(trifluoromethansulfonyl)imide Salts in Ionic Liquids Oleg Borodin,*,† Guinevere A. Giffin,‡,§,∇ Arianna Moretti,‡,§ Justin B. Haskins,∥ John W. Lawson,⊥ Wesley A. Henderson,# and Stefano Passerini‡,§

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†

Electrochemistry Branch, Sensor and Electron Devices Directorate, Power and Energy Division, U.S. Army Research Laboratory, Adelphi, Maryland 20783, United States ‡ Helmholtz Institute Ulm (HIU), Electrochemistry I, Helmholtzstrasse 11, 89081 Ulm, Germany § Karlsruhe Institute of Technology (KIT), P.O. Box 3640, 76021 Karlsruhe, Germany ∥ AMA, Inc., Thermal Protection Materials Branch and ⊥Thermal Protection Materials Branch, NASA Ames Research Center, Moffett Field, California 94035, United States # Army Research Office, P.O. Box 12211, Research Triangle Park, North Carolina 27709-2211, United States S Supporting Information *

ABSTRACT: Details of the lithium (Li+), sodium (Na+), magnesium (Mg2+), and zinc (Zn2+) cation coordination and electrolyte transport properties are examined using molecular dynamics (MD) simulations for the N-butyl-N-methylpyrrolidinium bis(trifluoromethansulfonyl)imide (pyr14TFSI) ionic liquid (IL) doped with LiTFSI, NaTFSI, Mg(TFSI)2, and Zn(TFSI)2 salts. MD simulations are performed as a function of temperature using a polarizable force field (APPLE&P) that yields the Li+, Na+, Mg2+, and Zn2+ cation binding energies to the TFSI− anions in excellent agreement with quantum chemistry results. At 333 K, 4.7−4.8 TFSI− oxygen atoms from approximately three TFSI− anions coordinate Li+ and Na+, while Zn2+ and Mg2+ cations are instead coordinated by approximately six TFSI− oxygen atoms. Significant Na+ coordination with the fluorine atoms of the TFSI− anions is observed, unlike for Li+, Mg2+ and Zn2+. The cation−TFSI− binding motifs and the propensity of the salts to form large aggregates are temperature dependent with opposite trends noted for the electrolytes containing the Li and Na salts vs Mg salts. The MD simulations accurately predicted electrolyte transport properties including ionic conductivity, viscosity, and self-diffusion coefficients. A connection between the metal cation coordination, transport properties, and transport mechanisms is established for the different cations. The much longer cation−anion residence times for the divalent Zn2+- and Mg2+-containing electrolytes, as compared to those with monovalent Na+ and Li+, indicate the significantly slower desolvation kinetics of the divalent salts and the dominance of the vehicular cation transport mechanism relative to the anion exchange mechanism.

1. INTRODUCTION Obtaining a fundamental understanding of the cation solvation/coordination and transport properties across a variety of salts is essential for improving electrolytes for batteries, hybrid capacitors, electrochromic windows, and other electrochemical applications. The structure of the metal cation cluster is intimately linked with the transport mechanisms and transference number,1 the cation desolvation process (as well as coordinated anion stripping) which contributes to interfacial impedance23 and electrochemical stability. For example, the extent of the cation−anion aggregate formation in Li salts of bis(fluorosulfonyl)amide (LiFSI) or bis(trifluoromethanesulfonyl)imide (LiTFSI) and the ability of the Li+ to approach the fluorine atoms of the anions controls © 2018 American Chemical Society

the electrolyte reduction stability and anion decomposition. Thus, controlling the propensity of the metal cation to approach the fluorine of the TFSI− anion provides additional avenues for adjusting the onset of the solid electrolyte interphase (SEI) formation, which is critical for protecting and stabilizing the electrode−electrolyte interfaces.4−7 In this work, we focus on obtaining a systematic understanding of the lithium (Li+), sodium (Na+), magnesium (Mg2+), and zinc (Zn2+) cation coordination by the TFSI− anions and ion transport properties in ionic liquid (IL)-based Received: June 11, 2018 Revised: August 7, 2018 Published: August 8, 2018 20108

DOI: 10.1021/acs.jpcc.8b05573 J. Phys. Chem. C 2018, 122, 20108−20121

Article

The Journal of Physical Chemistry C

increased from x = 0.05 to 0.20.39 In contrast to these results, the analysis of Raman and IR spectra from carbonate-based electrolytes doped with NaPF6 or LiPF6 yields a similar total number of anions and solvents coordinating the Li+ and Na+ cations, but the Na+ cation has more coordinating fluorines (from PF6−) than Li+.40 Numerous DSC, conductivity, cyclic voltammetry, and diffusivity experiments have focused on Na salt-containing ILs including the pyr14TFSI-NaTFSI electrolyte investigated in this work.41−47 MD simulation and quantum chemistry (QC) studies on similar Na+-containing ILs have provided some initial insight into the cation coordination and diffusion.48−50 Kubisiak and Eilmes reported MD simulations of the NaTFSI-doped emimTFSI electrolytes using a number of nonpolarizable and Drude-polarizable force fields with a focus on understanding the sensitivity of the transport properties and Na+ coordination on the model used.51 Another MD simulation study with Li and Na salts focused on understanding the dynamics of alkali metal cations in both high melting temperature organic ionic plastic crystal (OIPC) and low melting temperature IL materials, including one phosphonium-based salt, diethyl(methyl) (isobutyl)-(phosphonium hexafluorophosphate) (P1224PF6), and one pyrrolidinium-based salt, N-propyl-N-methylpyrrolidiniumFSI (C3mpyrFSI).48 As the salt concentration increased, numerous bulky anion−alkali complexes were observed in the MD simulations. These provide more opportunities for restructuring the ionic coordination environment through aggregate rearrangement and thus enhance the dynamics of the alkali metal ions in a cluster environment leading to a higher transference number.48 The lower solubility of the Na salts in ILs (relative to Li salts), however, limits the selection of Na salts that can be utilized in the salt-rich regime.50 A very recent study compared structural and dynamic properties of a number of ILs doped with LiTFSI, NaTFSI, and divalent metal salts at 0.5 M salt concentration, providing insight into the metal cation coordination and diffusion after validation of MD simulations done for the LiTFSI and NaTFSI-doped ILs.52 Mg salt-doped ILs were examined as potential alternatives to Mg organohaloaluminate complex solutions as electrolytes for Mg-based batteries. Mg, as an alternative anode, has a higher specific volumetric capacity than Li and is highly abundant in the earth’s crust.53−55 Mg2+ coordination in ILs was reported by numerous groups, with Mg2+ being coordinated by three TFSI− anions, on average, when salt mole fraction is between x = 0.25 and 0.55.39,56 Mg(TFSI)2 solvation in solvate ILs (SILs) was also investigated by Raman, conductivity, and density functional theory (DFT), indicating that Mg2+ is coordinated by 5−6 oxygens from the solvent molecules and anions.57,58 Application of nonvolatile ILs to Zn deposition has attracted recent attention due to the potential to mitigate the drawbacks of traditionally used concentrated KOH solutions that suffers from drying out, dendritic growth, self-discharge, and low Coulombic efficiencyif the cost and Zn2+ transport is improved.13−15,59−64 Zn deposition from ILs was shown to depend on the Zn2+−anion interactions with dense Zn deposits having nanowire- and hexagonal plate-like structures obtained from ILs with TFSI− and CF3SO 3− anions, respectively, indicating the importance of a fundamental understanding of ion coordination. 63 Electrolytes with pyr14TFSI containing Zn2+ have also been used for the electrodeposition of ZnO nanocrystalline thin films with innovative microstructural and optoelectronic properties,59 and DFT calculations and MD simulations have been reported

electrolytes. ILs have attracted significant attention for their potential applications in supercapacitors, actuators, batteries, material synthesis, dye-sensitized solar cells, and thermoelectrochemical cells applications due to their low volatility coupled with high electrochemical, thermal stability, and reasonable ionic conductivity.8−11 ILs doped with Li, Na, Mg, and Zn salts are of interest for battery and hybrid capacitor applications.9,12−15 Li salt-doped ILs have received the most attention over the past decade with their structural, transport, and electrochemical properties examined using Raman,16,17 impedance18 and NMR spectroscopies,16,18 neutron scattering, X-ray diffraction,19 and molecular dynamics (MD) simulations.19−30 ILs doped with the LiTFSI, LiFSI, and LiBF4 salts have been the most studied with a focus on the Li + coordination shell and transport mechanisms with, notably, the Li+ cation being the slowest diffusing component of the electrolytes.19−30 The Li+ coordination environment by TFSI− has been the subject of debate. The existence of Li+(TFSI−)2 clusters was suggested from Raman measurements.16,31 Force field-based and ab initio MD simulations, however, have revealed that both Li+(TFSI−)2 and Li+(TFSI−)3 clusters are present.26,32 Estimates of the vehicular and anion exchange contributions to the Li+ transport from MD simulations largely indicated the dominance of the vehicular contribution at low LiTFSI, LiFSI, and LiBF4 salt concentrations for smaller anions, while the importance of anion exchange for Li+ transport increases with increasing anion size and salt concentration.27,32 This is consistent with the experimentally observed decoupling of conductivity and viscosity in the highly concentrated regime.33−35 Challenges associated with modeling the Li salt-doped ILs were highlighted in a recent work by the Cisneros group which showed via MD simulations that the predicted ion self-diffusion coefficients and smaller densities are influenced by the treatment of the intramolecular polarization.30 A recent MD simulation study by the Maginn group examined numerous ILs with Li salts.29 Their results suggested the phosphonium triazolide-based ILs as favorable candidates for electrolyte applications due to their improved Li+ transference number and the small influence of Li+ concentration on the system dynamics, which usually slow down upon the addition of Li salts.29 Investigation of the Na salt-based electrolytes was initially motivated by the high Na abundance available worldwide and its low cost relative to Li.36 Na is the second smallest and lightest alkali metal next to Li. The Na+ cation is slightly larger than Li+, which can reduce its diffusion in the electrolyte if its coordination shell (of solvent molecules and/or anions) is bigger than that of the Li+ cation, provided that the cation diffusion is dominated by a vehicular mechanism. Recent Raman and IR studies were performed in order to identify the coordination shell differences between Li+ and Na+ cations. Raman spectroscopy was used to compare the Na+ solvation in N-butyl-N-methylpyrrolidinium FSI (pyr14FSI), 1-ethyl-3methylimidazolium TFSI (emimTFSI), and 1-butyl-3-methylimidazolium TFSI (bmimTFSI) ILs.37,38 It was found that Na+ is coordinated by three FSI− forming Na+(FSI−)3 in the FSI−based ILs,37 while in emimTFSI and bmimTFSI the Raman analysis suggested that Na+ is coordinated by three TFSI− anions on average for molar salt fraction x < 0.15, which is larger than the Li+ coordination by two TFSI− anions.38 Another Raman study yielded a decrease in the number of TFSI− anions coordinated (from 4 to 2) to the Na+ cations in a pyr14TFSI-based electrolyte as the NaTFSI mole fraction 20109


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solution. The doped ILs were placed in preheated conductivity cells inside the dry room. The measurement were conducted from 150 to 60 °C with a step decrease of 5 °C. The samples were equilibrated for 1 h at each temperature.

for acetonitrile−Zn(TFSI)2, acetonitrile−Zn(CF3SO3)2, and propylene carbonate−Zn(TFSI)2 electrolytes.65 In this contribution, we report progress toward establishing the metal cation coordination environment in ILs using the widely researched IL electrolyte pyr14TFSI doped with LiTFSI, NaTFSI, Mg(TFSI)2, and Zn(TFSI)2 salts, respectively. The coordination shell structure is related to the metal cation transport mechanism. This work is thus aimed at improving the microscopic understanding of ionic transport process fundamentals, which will facilitate the development of strategies to increase the ionic conductivity and manipulate the redox properties of electrolytes.5,66 While the gas-phase and explicit/implicit solvent hybrid modelswhere the first coordination shell is explicitly described in QC calculations have proven to be useful for the prediction of ion aggregation and coordination in dilute electrolytes,67−69 such models cannot be reliably applied to systems with a charged species such as the ions in ILs. Thus, we chose MD simulations using a quantum chemistry-based many-body polarizable force field that accurately describes the metal cation binding by TFSI− anions. The increasingly popular ab initio MD simulations that do not require force field parametrization are too computationally expensive and cannot routinely access the time scales (from 1 to 100 ns) which are necessary in order to equilibrate the cation solvation shell, even at elevated temperatures. Importantly, as we demonstrate below, the coordination shell undergoes significant changes as the temperature decreases, thus highlighting that the often reported high temperature predictions might not correspond to the low temperature characteristics of electrolytes. After a systematic comparison of the predicted conductivity, self-diffusion coefficients and viscosity obtained from the MD simulations with experimental data (where available), the metal cation coordination is compared for the different salts and discussed in the context of previously reported Raman data. This information is then used to establish the relationship between the transport mechanisms and metal cation coordination.

3. FORCE FIELD DEVELOPMENT AND QUANTUM CHEMISTRY CALCULATIONS The many-body polarizable APPLE&P force field was extended to include the nonbonded interactions for Na+, Mg2+, and Zn2+ and TFSI− in addition to the previously developed nonbonded terms for the Li+/TFSI− interactions.4 A detailed description of the APPLE&P is given elsewhere.71 Here we focus on the nonbonded energy UNB(r) which consists of the sum of the two-body repulsion and dispersion energy terms URD(r), the energy due to the interactions of the fixed charges Ucoul(r), and the polarization energy Upol(r) arising from the interactions between induced dipoles with fixed charges and other induced dipoles: U NB(r) = U RD(r) + U coul(r) + U pol(r)

ij 12 yz zz + Djjjj z j Bαβ rij zz k {

12

=

∑ Aαβ exp(−Bαβ rij) − Cαβrij

−6

i>j

qiqj

+

4πε0rij

−

1 2

∑ μι Ei0

(1)

i

where μi = αiEi is an induced dipole at force center i, αi is the isotropic atomic polarizability, Eitot is the total electrostatic field at the atomic site i due to the permanent charges qj and induced dipoles μj, ε0 is the dielectric permittivity of vacuum, Ei0 is the electric field due to fixed charges only, Aαβ and Bαβ are the repulsion parameters, and Cαβ is the dispersion parameter for the interaction between atoms i and j with atom types α and β. The term D = 5 × 10−5 kcal/mol is constant for all pair interactions. It is very small for most interactions, but becomes the dominant term at very small distances rij < 1 Å, thus ensuring that the nonbonded interactions are repulsive at very small distances. Intramolecular nonbonded interactions are included for atoms separated by three or more covalent bonds. Thole screening72 (aT = 0.4) smears the induced dipoles in order to prevent the so-called “polarization catastrophe” from occurring. Unlike the original version of the force field,71 the interactions between an induced dipole and a partial charge separated by three or less atom groups are omitted in order to improve the description of the electrostatic potential around the TFSI− anion. The groups were defined as follows: [CF3]-[SO2]-[N]-[SO2]-[CF3] for TFSI− and [CH3][CH2]-[CH2]-[CH3]-[N](CH3)-([CH2]-[CH2])2 for pyr14+. The TFSI− and pyr14+ partial charges were fit to reproduce the electrostatic potential on a grid of points calculated at the MP2/aug-cc-pvTz level. The modified Waldman-Hagler combining rules72 are given in eq 2. These were used for pyr14+/TFSI−, but not for the metal cation M = [Li+, Na+, Mg2+, Zn2+] interactions with TFSI− or pyr14+: tot

2. EXPERIMENTAL SECTION The IL pyr14TFSI was synthesized via a two-step synthesis procedure, i.e., the direct alkylation of N-methylpyrrolidine, followed by anion exchange with TFSI− in aqueous solution, as previously described.70 The IL was dried for 2 days using a turbomolecular pump (to below 10−7 mbar). The water content of the IL is below the detection limit of the Karl Fischer titration (i.e., less than 5 ppm). The LiTFSI (3M), NaTFSI (Solvionic), and Mg(TFSI)2 (Sigma-Aldrich) salts were dried for 2 days using a turbomolecular pump (to below 10−7 mbar) at room temperature. The doped pyr14TFSI mixtures (24 mol %) were prepared by mixing the appropriate amount of salt and IL. The mixtures were stirred at 90 °C until the salt completely dissolved. All sample preparation was performed in a dry room (dew point < −50 °C). The resulting solutions were further dried for 24 h using an oil pump and then additionally for 24 h using a turbomolecular pump. The water content of the solutions is below the detection limit of Karl Fischer titration (i.e., less than 5 ppm). The ionic conductivity was measured using an automated conductimeter (Materials Mates Italia) equipped with a frequency analyzer, a thermostatic chamber, and conductivity cells with Pt electrodes (Materials Mates Italia, HTCC-1 conductivity cells). Before the measurements, the conductivity cell constants were determined using a 0.01 M KCl standard

Aij =

Aii Ajj

yz ij 2 zz j ; Bij = jjj −6 z 3 3 6 − jj B + B zzz Bii Bjj jj { k ii Bij 6

1/6

; Cij =

CiiCjj (2)

The repulsion parameters A and B for the metal cation with TFSI− were fit to reproduce the binding energies on a grid of 20110


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Figure 1. Binding energy values of Na+ to TFSI− on the grid of points shown on the right from QC calculations using PBE/6-31+G(d,p) and force field (FF).

Table 1. Binding Energies (ΔE in kJ/mol) of the Metal−TFSI Complexes from QC Calculations and MM Optimization Using Developed Force Field (FF)a G4MP2

CBS-QB3

PBE/6-31+G(d,p)

complex

geom

TFSI conf

M···X (TFSI)

ΔE

ΔE

ΔE

BSSE

LiTFSI LiTFSI LiTFSI NaTFSI NaTFSI NaTFSI NaTFSI Mg2+TFSI− Mg2+TFSI− Mg2+TFSI− Mg2+TFSI− Mg2+TFSI− Zn2+TFSI− Zn2+TFSI− Zn2+TFSI− Zn2+TFSI− Zn2+(TFSI−)2 Zn2+ (TFSI−)3

a b c a b c d a b c d e a b c d e f

C2 C1 C2 C2 C1 C1 C2 C2 C1 C2 C1 C2 C2 C1 C2 C2 C2,C2 C2,C2,C1

O2 O2,F O,N,F O2,F O2,F O2 O,N,F O2,F O2,F O3 O2,N O2,N O2 O2,F O2 O3 O2,O2 O2,O2,O2

−567 −561 −522 −486 −483 −468d −461 −1382 −1380 −1375 −1360 −1353

−569 −565 −526 −466 −464 −451d −444 −1352 −1350 −1350 −1334 −1326 −1508 −1505 −1508 −1504

−577 −573 −543 −482 −480 −475 −467 −1393 −1394 −1403 −1398 −1390 −1619

4.8 4.8 6.8 7.6 7.5 8.8 7.6 7.6 8.0 7.5 9.6 9.2 16

−1621 −1601

16 16

b

c

M05-2X/6-311+G(2d,2p) ΔE

c

−1390 −1389 −1394 −1376 −1367 −1525 −1523 −1524 −1521 −2256 −2467

FF

BSSE

ΔE

6.6 6.4 6.1 6.3 6.1 5.8 6.4 5.5 6.0 16.1 34.5

−563 −561 −529 −482 −480 −466 −469 −1389 −1389 −1396 −1362 −1368 −1525 −1519 −1522 −1538 −2250 −2496

The TFSI conformations, the atoms from the TFSI− anions in contact with the metal cation M, are given in the M···X(TFSI) column. bTFSI anion conformations (C2-trans, C1-cis). cDFT binding energies are not corrected for BSSE. dConstrained the Na−N(TFSI) distance to that from the PBE/6-31+G(d,p) optimized geometry.

a

points, as shown in Figure 1 for Na+/TFSI− as an example. The Li+TFSI− and Zn2+TFSI− nonbonded parameters were taken from previous work,4,73 while other parameters were obtained in this work. Combining rules are used for all dispersion parameters. Because parametrization of the intermolecular force field terms requires accurate, yet practical, QC methods to obtain the cation−TFSI− binding energies calculated on a grid of points shown in Figure 1, two classes of QC methods were chosen for this purpose: (a) an accurate, but computationally expensive, G4MP2 composite methodology,74 less computationally expensive Complete Basis Set (CBS-QB3) methods (note that G4MP2 is not available for Zn, thus only CBS-QB3 composite calculations were performed for Zn2+TFSI−) and (b) a computationally expedient, but often less reliable, DFT utilizing the Perdew− Burke−Ernzerhof (PBE) exchange-correlation and M05-2X functionals.75,76 The G4MP2 method is more computationally expensive that CBS-QB3, but tends to have a lower standard deviation from the benchmark data, and thus G4MP2 is considered to be the most accurate estimate among the

methods used in this work.77 Binding energies were not corrected for basis set superposition error (BSSE); however, BSSE correction values are reported in Table 1 for binding energies obtained from the DFT calculations. The relatively inexpensive PBE/6-31+G(d,p) calculations were recently shown to yield more accurate predictions for Li+−solvent binding energies when compared to popular DFT functionals such as B3LYP, which overestimate the Li+−solvent binding energy.68,78,79 All cation−TFSI− repulsion parameters were fit to the binding energy calculated on the grid of points using PBE/6-31+G(d,p) for Li+/TFSI− and Na+/TFSI−, as shown in Figure 1, while M05-2X/6-311+G(2d,2p) calculations were used for Mg2+/TFSI− and Zn2+/TFSI−. The ability of the developed force field to predict the cation−TFSI− binding energy was examined by comparing the binding energy calculated at a higher QC levels using G4MP2 or CBS-QB3 for the Zn+-containing clusters, as shown in Figures 2−3 and Figures S1−S3 in the Supporting Information. Note that the Li+TFSI− G4MP2, CBS-QB3 and force field-based binding energies used in this work are in agreement with values from 20111


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Figure 2. Geometries of Na+TFSI− from the PBE/6-31+G(d,p) calculations with distances and energies from PBE/6-31+G(d,p) (first and in blue), G4MP2 (second, bold and italicized), CBS-QB3 (underlined) and molecular mechanics (MM) calculations using the developed force field (FF) shown in parentheses. The Li+−N(TFSI−) bond was constrained in the G4MP2 calculations for geometry-c to the value from the PBE/631+G(d,p) calculations. The TFSI− anion has a C2 (trans) conformer in (a, d) and a C1 (cis) conformer in (b, c). Energies before BSSE correction are shown; BSSE corrections are given in Table 1.

Figure 3. Geometries of Mg2+TFSI− from the G4MP2 calculations with distances (in Å) and energies (in kJ/mol) from PBE/6-31+G(d,p) calculations without BSSE correction (first, in blue), G4MP2 (second, bold, italicized), CBS-QB3 (third, underlined), and MM calculations using the developed force field shown in parentheses. Energies before BSSE correction are shown. Table 1 provides additional M05-2X/6-311+G(2d,2p) energies for these complexes and BSSE corrections.

stable clusters follow the order: Na+TFSI− (−486 kJ/mol, G4MP2; −466 kJ/mol from CBS-QB3) < Li+TFSI− (−567 kJ/ mol, G4MP2; −569 kJ/mol, CBS-QB3) ≪ Mg2+TFSI− (−1382 kJ/mol, G4MP2; −1352 kJ/mol CBS-QB3) < Zn2+TFSI− (−1508 kJ/mol, CBS-QB3), which is accurately reproduced by the developed force field as shown in Table 1. These trends are largely consistent with previously reported QC results.81−85 A comparison of the binding energies from G4MP2 and CBS-QB3 shown in Table 1 indicates that CBSQB3 slightly (by 2−4 kJ/mol) overestimates the Li+TFSI−

Møller−Plesset perturbation theory MP2 calculations with a complete basis set extrapolation, as shown in Figure S1 in Supporting Information.80 The other cation−TFSI− complexes with the TFSI− anion in the C2 conformer (ortho−ortho around the C−S−N−S dihedral angles or trans around the C−S···S−C angle) are slightly more stable than the complexes with the C1 conformer of TFSI−, as determined by both QC calculations and the developed force field. According to QC calculations reported in Table 1, the cation−TFSI− binding energies for the most 20112


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Figure 4. Radial distribution functions (RDFs) for metal cations with the oxygen (a), nitrogen (b), and fluorine (c) of the TFSI− anions at 333 K for Li+, Na+, and Mg2+ and at 393 K for Zn2+, respectively.

were gradually decreased to ∼60 Å (depending on the electrolyte composition) during a 2 ns initial simulation run at 500 K. NPT equilibration runs were then performed at 450 K, followed by NVT runs at the density corresponding to 1 atm, as indicated in Table S1. Figure S4 shows density predictions for all simulated electrolytes and experimental density values for pyr14TFSI and pyr14TFSI doped with the salt mole fraction x(LiTFSI) = 0.19. An excellent agreement between experiments and MD simulation predictions is observed. The Ewald summation method was used for the electrostatic interactions between permanent charges with either permanent charges or induced dipole moments with k = 73 vectors. Multiple time step integration was employed with an inner time step of 0.5 fs (bonded interactions), a central time step of 1.5 fs for all nonbonded interactions within a truncation distance of 7.0−8.0 Å, and an outer time step of 3.0 fs for all nonbonded interactions between 7.0 Å and the nonbonded truncation distance of 12−14 Å. The reciprocal part of Ewald was calculated every 3.0 fs. A Nose-Hoover thermostat and a barostat were used to control the temperature and pressure with the associated frequencies of 10−2 and 0.1 × 10−4 fs. The stress tensor was saved every 3 or 9 fs for calculating the stress, the tensor autocorrelation function, and the viscosity, while the atomic coordinates were saved every 2 ps for postanalysis.

binding energy relative to G4MP2, while underestimating the Na+TFSI− and Mg2+TFSI− binding energy by (16−19 kJ/mol) and (25−30 kJ/mol), respectively. Much less expensive PBE/ 6-31+G(d,p) calculations yield binding energies in good agreement with G4MP2 for the Li+TFSI− and Na+TFSI− complexes indicating that it is an acceptable level for exploration of larger clusters and calculating binding energies on the grid around the TFSI− anion, as shown in Figure 1, which required ∼1000 calculations. Application of the BSSE correction improves the agreement between the PBE/631+G(d,p) binding energies for Li+TFSI− and Mg2+TFSI−, but makes it slightly worse for the most stable Na+TFSI− complexes. For the Mg2+TFSI− complexes, PBE/6-31+G(d,p) yields a larger deviation from G4MP2 than is observed for the Li+TFSI− and Na+TFSI complexes; thus, we used the more computationally expensive M05-2X/6-311+G(2d,2p) calculations for the complexes containing divalent cation Mg2+ and Zn2+ which showed smaller deviations from the G4MP2 binding energies for Mg2+TFSI−. Increasing the basis set size from 6 to 31+G(d,p) to 6-311+G(2d,2f) in PBE calculations increases the Mg2+TFSI− binding energy, resulting in an even larger deviation of the PBE/6-311+G(2d,2f) energy from the G4MP2 energy than the PBE/6-31+G(d,p) energy, as shown in Table S2 in the Supporting Information; thus, PBE/6311+G(2d,2f) was not used as a basis for the binding energy calculations for parametrization of the repulsion parameters.

5. STRUCTURAL PROPERTIES We begin the analysis of the electrolyte structural properties by examining the cation−TFSI− radial distribution functions (RDF) with a focus on the oxygen, nitrogen and fluorine atoms of TFSI−, as shown in Figure 4. The positions of the first peak of the cation−O(TFSI−) RDF are similar for the Zn2+−O (1.95 Å), Mg2+−O and Li+−O (2.0−2.5 Å) RDFs, while the Na+−O(TFSI−) peak is located at a larger separation of 2.3 Å. This trend is in agreement with distances found by QC calculations for the corresponding complexes (in the gasphase) of metals with the TFSI− anion: Zn2+−O (1.86 Å from M05-2X/6-311+G(2d,2p) Li+−O (1.81 Å from PBE/6-31+G(d,p)), Mg2+−O (∼1.9 Å from PBE/6-31+G(d,p)), and Na+−

4. MOLECULAR DYNAMICS METHODOLOGY The MD simulation package, WMI-MD (including many-body polarization) was used for all of the MD simulations. The compositions of the simulated electrolytes are given in Table S1. Simulation cells comprised of 64 metal cations, 256 pyr14+ organic cations, 320 TFSI− anions for the IL doped with LiTFSI or NaTFSI, and 384 TFSI for the IL doped with Mg(TFSI)2 or Zn(TFSI)2. All simulated systems were created by replicating the (pyr14TFSI)4−(Li+ or Na+)TFSI− or (pyr14TFSI)4−(Mg2+ or Zn2+)(TFSI−)2 optimized clusters from the MM calculations 64 times resulting in large simulation cells of ∼95 Å. The simulation box dimensions 20113


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Figure 5. Running coordination numbers around the metal cations at 333 K for Li+, Na+, and Mg2+ and at 393 K for Zn2+, respectively.

approach was observed for Na+−F(TFSI−) followed by Li+− F(TFSI−), while no close approaches were observed for Mg2+ and Zn2+ to F(TFSI−). The easier Na+ approach to F(TFSI−), as compared to Li+−F(TFSI−), suggests that the reduction of NaTFSI to generate NaF is expected to be more facile than the corresponding reaction for LiTFSI to generate LiF. It is also consistent with the lower energy barrier for Na+ to be coordinated by the CF3 group of the CF3SO3− anion relative to that for Li+.93 Therefore, due to the substantially lower Li+− F(TFSI−) coordination number for short distances (closer than 2.4 Å), LiF formation as a result of LiTFSI reduction is expected to be slow. Interestingly, the most stable complexes of Na+TFSI−, Mg2+TFSI−, and Zn2+TFSI− in the gas-phase have metal cation coordinating F(TFSI−) in addition to O(TFSI−), while MD simulations predict that in the IL only Na+−F(TFSI−) contacts are frequent. We attribute the difference between the Na+ and Mg2+ behavior to their size and valence differences. The larger size of Na+ compared to Mg2+ (clearly seen in RDFs) makes it easier to incorporate F(TFSI−) in the first coordination shell of Na+. On the other hand, much tighter packing around Mg2+ due to its smaller size and much stronger interaction with the TFSI− oxygens does not leave enough space for fluorine from the CF3-group of TFSI− to coordinate the metal cation due to strong binding with six O(TFSI−). In order to support this argument, we performed DFT calculations on the Na+ and Mg2+ complexes with three TFSI− anions placed in two configurations. In the first configuration, both Na+ and Mg2+ are coordinated by six oxygens from three TFSI− anions and one fluorine with metal−fluorine bond constrained at 2.7 Å as shown in Figure S5a−b in Supporting Information. The second configuration does not impose any constraints and represents a local minimum, where the metal cation is coordinated by six oxygens from three TFSI− anions as shown in Figure S5c−d. DFT calculations show that bringing F(TFSI−) in contact with Mg2+ was energetically unfavorable by 38.3 kJ/mol, while bringing F(TFSI−) in contact with a much larger Na+ cation was energetically unfavorable by only 12.5 kJ/mol. The developed force field reproduced these trends well, as shown in Figure S5. These

O (2.2 Å form PBE/6-31+G(d,p)). The distances in the MD simulations are 0.1−0.2 Å longer than those in the gas-phase. The Li+−O(TFSI−) distances are similar to the Li+−O distances of 2.05−2.1 Å reported for PEO and oligoethers doped with LiTFSI from neutron diffraction with isotopic substitution experiments86,87 and from crystal structures containing LiTFSI, NaTFSI, and Mg(TFSI)2.88−90 The magnitudes of the first cation−O(TFSI−) peaks increase in the same order as the binding energies in cation−TFSI− gasphase clusters. An examination of the cation−N(TFSI−) RDF shown in Figure 4b similarly indicates that no close contacts are observed for the Li+, Mg2+, and Zn2+ cations, while the Na+−N(TFSI−) RDF has an additional small peak at the much shorter distance of 2.3 Å. Such a close approach is consistent with the gas-phase configurations shown in Figure 2c,d where Na+ closely approaches N(TFSI−), while in the NaTFSI salt crystal structure the Na+−N(TFSI−) coordination is observed at a slightly larger distance of 2.9 Å.91 In general, the cation− N(TFSI−) coordination (with Li+, Na+, and Mg2+) is rarely observed in crystals of the TFSI−-based salts.88,89,91 While the Mg2+TFSI− gas-phase complex Mg2+−N(TFSI−) binding, shown in Figure 3d, is only slightly less stable than the most stable complexes shown in Figure 3a−b, no close Mg2+− N(TFSI−) approaches were observed in the MD simulations of the Mg(TFSI)2-doped IL, nor were close Li+−N(TFSI−) approaches observed in the MD simulations for LiTFSI in the IL in accordance with the Li+−N(TFSI−) binding in the gas phase being less stable than the Li+−O(TFSI−) coordination by 38 kJ/mol. Understanding the metal cation approach to the fluorine of TFSI− is important for controlling the anion’s reduction potential. Concentrated electrolytes with LiTFSI, Zn(TFSI)2, LiFSI, and NaCF3SO3 salts were shown to undergo salt reduction and anion defluorination at much higher potentials than occurred in dilute solutions (with the metal cation− fluorine approach being central to this reaction).4,6,73,92,93 Such defluorination reactions enable inorganic-rich SEI formation at higher potentials due to anion decomposition prior to the solvent (if present) and/or organic cations and thus enables an additional avenue for tailoring SEI properties. The closest 20114


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Figure 6. Representative ion clusters from the small MD simulations (noted at the top) and the probability of the number of TFSI− nitrogen atoms found in the metal cation’s first coordination shell.

structure found in the condensed phase using DFT-MD.95 The Na+ cation coordination environments are more heterogeneous than those for the Li+ cation with coordination by two, three, and four N(TFSI−) being observed. Approximately twothirds of the Mg2+ are coordinated by three TFSI− and onethird by four TFSI− anions, while the Zn2+ is instead largely coordinated by three TFSI− anions. The metal cation coordination by TFSI− has been examined spectroscopically.96 For a metal cation mole fraction of 20%, Monti et al. reported Li+(TFSI−)2 and Na+(TFSI−)n complexes with n between 2 and 3.96 For NaTFSI mole fractions below 15%, however, the Na+(TFSI−)3 coordination was obtained from an analysis of the Raman bands.96 The coordination of Na+ by three TFSI− is similar to the reported coordination in a FSI−-based IL from FTIR studies.37 A similar conclusion was found for NaTFSI from a careful DFT and Raman spectroscopy analysis in alkylimidazolium TFSI−-based ILs.38 These results largely agree with Giffin et al.39 for this metal cation concentration range. Giffin et al.39 reported that Mg2+ is coordinated by three TFSI− anions at this metal cation mole fraction. Watkins and Buttry analyzed the Mg2+ coordination for the presently studied salt concentration and also reported slightly more than three TFSI− anions coordinating Mg2+.56 Zn2+ coordination in emimTFSI was investigated by Raman spectroscopy, but the coordination numbers were not determined.63 Overall, MD simulation predictions of the cation coordination environment are consistent with fits to spectroscopic datawith the largest deviation observed for the LiTFSI-doped IL, where MD simulations predict a slightly larger number of TFSI − coordinating Li+. This discrepancy, in part, could be attributed to the observed minimal or no shift of the TFSI− 743 cm−1 vibrational band in certain monodentate Li+TFSI− solvates as compared to the uncoordinated TFSI− anions, as was reported from DFT calculations.97 Thus, a Raman spectroscopic analysis of this band shift would underestimate the number TFSI− anions coordinating the Li+ cations. Interestingly, recent MD simulations by Vincent-Luna et al. showed even higher Li+ and Na+ coordination numbers of more than four TFSI− anions, albeit at a lower salt concentration of 0.5 M.52 As the Mg2+(TFSI−)2 and Zn2+(TFSI−)2 solvates are dominated by bidentate coordination configurations (as discussed below), such an underestimation is likely not an issue when analyzing these solvates. Figure 7 shows the calculated temperature dependence of the fraction of

calculations help to explain how packing effects for the much smaller Mg2+ with a much stronger interactions with O(TFSI − ) tend to exclude F(TFSI − ) from the Mg 2+ coordination shell in the IL, while TFSI− packing around a much larger Na+ leaves enough space to form Na+−F(TFSI−) contacts. Note that at the electroactive interfaces, an intermediate situation between the full coordination present in the bulk IL and incomplete coordination of the gas-phase is expected to occur. We also found that the addition of the salt does not significantly perturb the center of mass structuring of the pyr14+ cation with the other pyr14+ cations or TFSI− anions as shown in Figures S6 and S7, respectively, and therefore we focused on the metal cation−TFSI− anion coordination in the rest of the manuscript. The running coordination numbers for the metal cation coordination by the oxygen, nitrogen, and fluorine of TFSI− are shown in Figure 5. The Li+−O(TFSI−) and Na+− O(TFSI−) coordination numbers are similar (∼4.8), while the Zn2+−O(TFSI−) and Mg2+−O(TFSI−) coordination numbers are close to six. Six-fold oxygen−Mg2+ coordination was also observed in the coordinated MD simulation and X-ray scattering study of diglyme−Mg(TFSI)2 solutions.94 Despite the different cation−O(TFSI−) coordination numbers, the cation−N(TFSI−) values are close to each other, as seen in Figure 5b, indicating that all of the cations are coordinated by 3−3.5 TFSI− anions. Thus, different metal cations are coordinated by the TFSI− anions differently, as indicated by the different ratios of the cation−O(TFSI−) to cation− N(TFSI−) coordination numbers. Figure 6 shows representative metal cation coordination environments, along with the number of TFSI− nitrogen atoms found in the metal first coordination shell, for the most probable configurations. The Li+ cation is found to be solvated primarily by three (n = 3) TFSI− anions, though a small population of n = 2 solvation structures are present. Both the n = 2 and 3 coordinated structures observed here were found to be stable in the small simulation boxes examined in the DFTbased MD simulations of LiTFSI in pyr14TFSI, while a n = 4 coordinated structure was found to rapidly lose an anion to assume an n = 3 configuration.95 The frequently observed structure with four oxygens from three TFSI− anions coordinating a Li+ cation is shown in Figure 6. It was previously reported to be among the stable structures, from cluster DFT calculations, and was the preferred coordination 20115


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Mg(TFSI)2-doped IL because of the presence of Mg2+− TFSI−−Mg2+ bridges, as shown in Figure 6. A very similar influence of the LiTFSI and NaTFSI salts on IL viscosity was reported by Monti et al.96 in agreement with the MD simulation predictions. Diffusion coefficients (Figure 9) were extracted from the mean-square displacements using the Einstein relationship.

Figure 7. Fraction of monodentate binding of cations by TFSI− using a cutoff of 2.4 Å for (Li+, Mg2+, or Zn2+) with O(TFSI−) and 2.8 Å for Na+−O(TFSI−).

monodentate metal cation coordination by the TFSI− anions. For LiTFSI and NaTFSI, there is an opposite temperature dependence relative to that for the divalent cations. It is therefore expected that quite different coordination structures predominate at room temperature and at elevated temperature (e.g., 450 K)with the exception of the Zn(TFSI)2-doped IL, which shows little change for the limited temperature range evaluated. The fraction of the monodentate anion coordination to the cations serves as a marker for the TFSI− anion participation in extended cluster formation since the monodentate TFSI− often coordinate two metal cations (i.e., serve as bridges or cross-linkers), while bidentate TFSI− tends to coordinate only a single Li+ cation for the studied salt concentration. Thus, the LiTFSI- and NaTFSI-doped ILs become less aggregated with decreasing temperature, while the Mg(TFSI)2-doped IL becomes more aggregated with decreasing temperature and forms more extended Mg2+−TFSI−−Mg2+ bridges at lower temperature.

6. TRANSPORT The viscosity values were extracted from the integral of the stress-tensor autocorrelation function using the Einstein relation,71 and the data are summarized in Figure 8. The

Figure 9. (a−c) Self-diffusion coefficients of cations from the MD simulations of pyr14TFSI doped with TFSI− salts. The experimental data for pyr14+ and TFSI− for the Mg2+-doped IL is from Jeremias et al.99

Due to the finite size of the simulation cells, long-range hydrodynamic interactions restrict the diffusion and generally slow the ion diffusion by 10−20% for typical MD simulation cell sizes of 4−5 nm.71 The leading order finite size correction (FSC) to the self-diffusion coefficient is given by eq 3,

Figure 8. Viscosity of pyr14TFSI doped with the specified TFSI− salts.

ΔDFSC =

predicted viscosity for the pyr14TFSI IL deviates from the experimental value reported by Tokuda et al.98 by up to 40% with larger deviations observed at lower temperatures. The addition of salt increases the electrolyte viscosity in the order: NaTFSI < LiTFSI < Zn(TFSI)2 < Mg(TFSI)2. The stronger Li+−TFSI− binding, as compared to that for Na+−TFSI−, resulted in longer-lived Li+−TFSI−−Li+ aggregates, thereby yielding a slightly higher viscosity for the LiTFSI-based electrolyte. The more compact Zn2+(TFSI−)3 coordination (without Zn2+−TFSI−−Zn2+ coordination) results in a lower viscosity of the Zn(TFSI)2-doped IL, as compared to the

2.837kBT 6πηL

(3)

where kB is the Boltzmann constant, T is temperature, L is a linear dimension of the simulation periodic cell, and η is viscosity. As expected, pyr14+ has the highest self-diffusion coefficient values, while the metal cations have the lowest. Good agreement is observed with the published experimental data as shown in Figure 9. The salts with divalent cations slow down the ion diffusion coefficients more than what occurs for those with monovalent cations due to higher binding energies and the larger number of anion oxygens (i.e., O(TFSI−)) 20116


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observed for the different salts, the TFSI− exchange rate around the divalent cations is more than an order of magnitude slower than for Li+ and Na+. The extremely slow TFSI− exchange around Mg2+ and, especially, Zn2+ indicates that the negatively charged Zn2+(TFSI−)3 clusters are likely the predominant charge transport carriers in this IL-based electrolyte. In order to perform a more quantitative comparison of the vehicular vs anion exchange contribution to the metal cation transport, we calculated the average distance that the anion moves in one cation−N(TFSI−) residence time, as shown in Figure 11b. We observe that the first coordination shell of the Li+ and Na+ cations is renewed as they diffuse 13−15 Åwhich is roughly twice the size of the TFSI− anionalong the longest axis and slightly larger than the size of the full Li+(TFSI−)3 or Na+(TFSI−)3 coordination shells. This is consistent with the previous estimates that anion exchange contributes less than 40% to the Li+ diffusion coefficients and even less for smaller anions.27,32 The Zn2+(TFSI−)3 complex, in contrast, diffuses ∼70 Å before the Zn2+ coordination shell is renewed indicating that vehicular motion of the Zn2+(TFSI−)3 complex dominates the Zn2+ diffusion mechanism over TFSI− exchange. The metal cation− TFSI− residence times are also related to the anion stripping of the cation, which is important during the cation’s intercalation into the electrode or into the SEI formed at the electrode’s surface. Such an anion stripping process may therefore be orders of magnitude slower for the Zn2+ and Mg2+ cations, as compared to that for the monovalent Li+ and Na+ cations, indicating a significant disparity between the relatively minor differences of the bulk self-diffusion coefficients and anion exchange rates, although the interfacial electrostatic interactions may influence this.

complexing the Mg2+ and Zn2+ cations, as compared to Li+ and Na+. Ionic conductivity from the MD simulations was found to be in excellent agreement with experimental values, as shown in Figure 10. The ionic conductivity trends closely follow the self-

Figure 10. Conductivity from the MD simulations (symbols) and experimental data (lines) of pyr14TFSI doped with TFSI− salts.

diffusion coefficient trends because the degree of ion uncorrelated motion, or ionicity, is similar for all of the investigated systems (ranging from 0.5 to 0.6). The addition of the divalent cations not only slows the diffusion more than for the monovalent cations, but also changes the apparent activation energy, indicating that the reduction is expected to be more pronounced at lower temperatures. In order to obtain more insight into the metal cation transport mechanisms, we quantified how long the TFSI− anion stays in the vicinity of the metal cations. This allows us to probe the distance the metal cation moves before exchanging all of the TFSI− anions in its first coordination shell. The Li+−N(TFSI−) value was estimated by first calculating the residence time autocorrelation function (RTACF) given by eq 4: R(t ) = H(t )*H(0)

7. CONCLUSIONS A many-body polarizable quantum chemistry-based force field APPLE&P was extended to the Li+-, Na+-, Zn2+-, and Mg2+doped pyr14TFSI IL-based electrolytes. The metal cation coordination and transport properties are in good agreement with the available experimental data, thus validating the ability of the developed force field to adequately predict the electrolyte structural and dynamic properties. At 333 K, 4.7− 4.8 TFSI− anion oxygen atoms coordinate the Li+ and Na+ cations (on average), while approximately six TFSI− oxygen atoms coordinate the Mg2+ and Zn2+ cations. The calculated IL viscosity upon doping with the salts increased in the following order: NaTFSI-IL < LiTFSI-IL < Zn(TFSI)2-IL < Mg(TFSI)2IL. Despite the higher Zn2+−TFSI− binding energy (as compared to Mg2+−TFSI−), a slightly lower viscosity was

(4)

where H(t) = 1 if a Li −N bond is formed (r(cation− N(TFSI−)) < 5.0 Å) at time t and is zero otherwise and ⟨ ⟩ denotes the ensemble average over all of the Li+−N(TFSI−) pairs. RTACFs were fit using a stretched exponential a* exp(−(t/τ)β). The metal cation−TFSI− residence times were calculated from the integrals of the stretched exponential fits and are shown in Figure 11a. The order of the cation−TFSI− residence times follows the order of the metal cation−TFSI− binding energies with Zn2+ showing the lowest exchange rate and Na+ the fastest. Unlike the relatively small difference between the ionic conductivities and diffusion coefficients +

Figure 11. (a) Metal cation residence time near the TFSI− anion and (b) displacement of the metal cations during one residence time from the MD simulations of pyr14TFSI doped with TFSI− salts. 20117


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The Journal of Physical Chemistry C Present Address

predicted for the Zn(TFSI)2-IL electrolyte (than for the Mg(TFSI)2-IL electrolyte) due to the more compact Zn2+ coordination shell which has a significantly smaller number of TFSI− anions which bridge between different metal cations. The conductivity of LiTFSI- and NaTFSI-doped ILs was quite similar and higher than the conductivity of ILs doped with the salts with divalent cations due to the higher binding energy, slightly larger size of the first coordination shell, and slower exchange rate of TFSI− around the divalent cations. The TFSI− anion exchange rates around Mg2+ and Zn2+ were approximately 10 and 50 times slower, respectively, than for the anion exchange around Na+ and Li+in stark contrast with the much smaller difference between the ion diffusion coefficients for the electrolytes doped with the different salts which did not exceed a factor of 4. These results indicate much slower kinetics for the Mg2+ and, especially, the Zn2+ anion stripping relative to that for the Li+ and Na+ monovalent cations. Gas-phase QC calculations of the metal−TFSI complexes showed that the Na+, Mg2+, and Zn2+ cations prefer to be coordinated by either by two oxygens and one fluorine or three oxygens from TFSI−, while Li+ prefers to be coordinated by two oxygens from the same TFSI. Close contacts between the metal cation and fluorine of TFSI−, are needed for the salt defluorination reaction coupled with reduction that was shown to depend on the TFSI−, anion or solvent environment and ability to form metal fluorides.4−7 Packing restrictions for the TFSI− anions around the metal cations in the condensed phase further change the propensity of metal−fluoride close contacts making Zn2+−F(TFSI−) and Mg2+−F(TFSI)− contacts less probable in the bulk IL. The Na+−F(TFSI−) contacts remain the most prevalent in the IL among the four investigated metal cations and in the gas phase. At electrochemical interfaces, however, where the metal cations are partially uncoordinated, their propensity to have close contacts with F(TFSI−) is expected to be in between the bulk structure observed in MD simulations for ILs doped with salts representing a completely coordinated state and the gas-phase M(TFSI−) clusters representing incomplete coordination.

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∇

(G.A.G.) Fraunhofer Institute for Silicate Research ISC, Neunerplatz 2, 97082 Würzburg, Germany.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS G.G., A.M., and S.P. kindly acknowledge the basic support of the Helmholtz Association. O.B. acknowledges support from NASA via interagency agreement NND16AA29I with ARL.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b05573. The length of equilibration and production MD simulation runs. LiTFSI, (MgTFSI)+, (ZnTFSI)+, and ZnTFSI2 binding energies from quantum chemistry and molecular mechanics calculations using developed force field (PDF) All input files for the pyr14TFSI-LiTFSI together with MD simulation package (ZIP1, ZIP2) Description of the force field file for the Molecular Dynamics (MD) simulation package (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Oleg Borodin: 0000-0002-9428-5291 Arianna Moretti: 0000-0001-7936-8518 Justin B. Haskins: 0000-0003-4435-9018 Stefano Passerini: 0000-0002-6606-5304 20118


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