Article pubs.acs.org/JPCB

A Combined Theoretical and Experimental Study of the Influence of Different Anion Ratios on Lithium Ion Dynamics in Ionic Liquids Volker Lesch,*,† Sebastian Jeremias,† Arianna Moretti,† Stefano Passerini,*,‡ Andreas Heuer,*,† and Oleg Borodin§ †

Institute of Physical Chemistry, Westfälische Wilhelms-Universität Münster, Corrensstrasse 28/30, 48149 Muenster, Germany Helmholtz Institute Ulm, Karlsruhe Institute of Technology, Albert Einstein Allee 11, 89081 Ulm, Germany § U. S. Army Research Laboratory, Electrochemistry Branch, Sensors & Electron Devices Directorate, 2800 Powder Mill Road, Adelphi, Maryland 20783, United States ‡

S Supporting Information *

ABSTRACT: In this paper, we investigate via experimental and simulation techniques the transport properties, in terms of total ionic conductivity and ion diffusion coefficients, of ionic liquids doped with lithium salts. They are composed of two anions, bis(fluorosulfonyl)imide (FSI) and bis(trifluoromethanesulfonyl)imide (TFSI), and two cations, N-ethyl-N-methylimidazolium (emim) and lithium ions. The comparison of the experimental results with the simulations shows very good agreement over a wide temperature range and a broad range of compositions. The addition of TFSI gives rise to the formation of lithium dimers (Li+−TFSI−−Li+). A closer analysis of such dimers shows that involved lithium ions move nearly as fast as single lithium ions, although they have a different coordination and much slower TFSI exchange rates.

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INTRODUCTION Within the last decades, the use of ionic liquids (ILs) in different fields has been established. Because of their unique properties, ionic liquids are promising materials for different applications, e.g., as solvent in synthesis, as catalyst, and in electrochemical applications.1−3 The bulky, organic cation can be easily tailored by selecting different side chains to specific demands.2,3 Especially for their application in electrochemical devices, ILs offer promising physical properties like high thermal stability, low vapor pressure, and wide electrochemical stability window.4,5 However, due to the low ambient conductivity of IL/lithium salt mixtures compared to conventional electrolytes, improvements related to this property are of main interest.5 Several attempts have already been made with respect to this issue. For example, Kühnel et al. added organic electrolytes to IL/LiTFSI mixtures, enhancing conductivity and thermal stability and suppressing aluminum corrosion.6 Furthermore, mixtures of Nmethyl-N-propylpyrrolidinium bis(fluorosulfonyl)imide (pyr 13 FSI) and N-butyl-N-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide (pyr14TFSI) show higher conductivities and lower melting points due to ion mismatch.7,8 However, only a microscopic understanding of fundamental transport processes would make it possible developing strategies to increase the ionic conductivity. One big challenge in this field is to successfully parametrize force fields to produce theoretical results which correlate with experimental ones. Molecular dynamics (MD) simulations are a powerful tool to elucidate microscopic mechanisms of complex molecular systems like lithium ion transport.9,10 Accurate representation © 2014 American Chemical Society

of intermolecular interactions is important for predicting structural and, especially, dynamic properties of ILs doped with lithium salts. Due to strong polarization of anions by a small lithium cation, it is important to include many-body polarizable terms in the intermolecular potential (force field) used in MD simulations. Previous simulations using an atomic polarizable force field for liquids, electrolytes, and polymer (APPLE&P) have accurately predicted both structural and transport properties of pure ILs and ILs doped with lithium salts.10−14 Previous MD simulations with APPLE&P focused on the pyr-based ILs doped with lithium salts.10,13,14 It has been shown that the coordination does not vary when changing the cation from pyr13 to pyr14.15 Lithium aggregation sharing TFSI anions as bridges were also observed, but the simulations at lower temperatures are too short to break up this aggregation.11,15 For the lithium ion transport, two mechanisms were observed.11 One way is the structure diffusion, which means that lithium ions move by exchanging its first coordination shell. The other way is the vehicular mechanism, where lithium ions move with their first coordination shell. This was investigated in more detail by adding an additional potential function, which stabilized the coordination of TFSI on lithium ions. As a consequence, a slowing down of the TFSI exchange out of the first coordination shell as well as a reduced lithium ion diffusion were observed. The authors suggested that the long-lived Li+− Received: January 30, 2014 Revised: May 1, 2014 Published: June 6, 2014 7367

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with a vacuum oil pump (10 to 3 bar) and for an additional 24 h with a turbo molecular pump.

TFSI aggregates move slower due to reduced anion exchange contribution to the lithium ion diffusion. Both transport possibilities were investigated by Li et al. as a function of lithium ion concentration.10 For this analysis, they identify the lifetimes of the aggregates and determine the mean square displacement (MSD) in this time interval which corresponds to the vehicular mechanism. The remaining part of the MSD is contributed by a structural mechanism. The analysis shows that the vehicular mechanism became more important by decreasing the amount of lithium ions. Furthermore, decreasing the temperature led to an increased mean square displacement of the lithium ions in the lifetimes of Li−TFSI aggregates. Solano et al. used the correlation between experimental and numerical information to characterize the systems pyr14TFSI/ LiTFSI and pyr14FSI/LiFSI.14 Due to the relatively short trajectories of 3 ns used in that work, simulations were restricted to high temperatures and no direct overlap with the experimentally accessible regime was possible. In this work, we investigate systems with different ratios of FSI and TFSI anions, which are promising candidates for electrochemical applications. As cation, we use N-ethyl-Nmethylimidazolium (emim) and lithium ions. This work is motivated by the experience from organic electrolytes in lithium ion batteries.16−18 Due to the complex demands on electrolytes for lithium ion batteries (LIBs), often mixtures of different carbonates are used.17 The most often used mixture is ethylene carbonate:diethyl carbonate (EC:DEC)17 because they supplement each other. EC has the ability to form a solid electrolyte interface (SEI), but the viscosity is very high so DEC is added to reduce the viscosity.19 However, the concept of mixing components to use the advantages of both is the idea of this work. The two investigated anions FSI and TFSI are structurally quite similar, but they also supplement each other because FSI has a film forming ability on the anode while TFSI has a higher thermal stability. Thus, also for ILs the use of anion mixtures may be useful. In this work, we investigate the effect of anion mixtures on the lithium ion dynamics and based on this if the concept of mixing anions is a possibility to improve the properties of electrolytes based on ionic liquids. Among other things, we explicitly study whether the presence of Li+−(T)FSI clusters indeed is a viable mechanism to slow down the lithium diffusivity as suggested in previous work.11 We start with a comparison of theoretical and experimental results to achieve a good basis for the analysis on the atomic scale. For the comparison, we choose system properties like the density, diffusion coefficients, and conductivity. We also determine the experimental viscosity to correct the diffusion coefficients for finite size effects. The diffusion coefficients from PFG-NMR and simulation are compared with data from Hayamizu et al.,20 and also this comparison shows a good agreement. On the basis of the agreement, we carefully examine the lithium ion diffusion mechanism in a variety of solvate types.

Table 1. Composition (in Molecules) of the Five Investigated Mixtures system

TFSI100

TFSI91

TFSI50

TFSI9

TFSI0

emim TFSI FSI Li

180 197 0 17

180 180 17 17

208 114 114 20

180 17 180 17

180 0 197 17

Both viscosity and density measurements were conducted in the dry room. The viscosity measurements were performed between 20 and 70 °C with 10 °C steps by means of an Anton Paar Physica MCR 301 rheometer. The density measurements were conducted in the same temperature range (with 10 °C steps) using a MettlerToledo DE40 density meter. Pulsed Field Gradient-NMR (PFG-NMR). The investigated mixtures were flame-sealed in nuclear magnetic resonance (NMR) tubes inside the dry room to prevent any contamination. To determine diffusion coefficients of different ionic species, we have used a Bruker NMR spectrometer (Germany) with a permanent field strength of 4.7 T. The diffusion probe head was a “Diff30” (Bruker, Germany) with selective rf inserts for 1H, 19F, and 7Li. The maximum gradient strength was technically limited to 1.8 T/min. We changed temperature with the water-cooling unit stepwise from 10 up to 49 °C. Higher temperatures (60 and 70 °C) were reached by additional heated air flow (500 l/h). For the PFG-NMR experiments, we have used the STE and dstegp3s sequences according to the Bruker library (Top Spin 3.0). The dstegp3s sequence is necessary in case of air flow heating to suppress convection artifacts. The echo attenuation was evaluated by a mono exponential fitting. Ionic Conductivity Measurements. The temperature dependence of the conductivity for each mixture was measured by means of an automated conductivity meter (“MaterialMates Italia”) equipped with a frequency analyzer and a thermostatic bath (ΔT = ±1 °C). The mixtures were loaded in sealed conductivity cells (inside the dry room) containing two platinum electrodes previously calibrated using a 0.01 M KCl aqueous solution. The cells were cooled down to −40 °C for 18 h before starting to increase the temperature in 2 °C steps. At each temperature, the samples were left to equilibrate for 1 h. Determination of the Water Content. The water content was measured using the standard Karl Fischer method. The titrations were performed by an automatic Karl Fischer coulometer titrator (Mettler Toledo C30). The Karl Fisher titrant was a one-component (Hydranal 34836 Coulomat AG) reagent provided from Aldrich. To keep the contamination of water from air as low as possible, the Karl Fischer coulometer titrator was located inside the dry room (dew point < −60 °C). All the tools used were also stored inside the dry room. The samples were introduced in the titrator using a syringe dried at 50 °C under a vacuum for at least 24 h. The whole setup and the procedure permit avoiding water contamination from the environment. We experimentally determined that, following this method, we are able to discriminate down to 2 ± 1 ppm of water in the ionic liquid samples. The water content of each sample was less than 4 ppm.

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EXPERIMENTAL SETUP The ionic liquids emimTFSI and emimFSI and the salt LiFSI were purchased from Solvionic, while LiTFSI was purchased from 3M. All compounds were individually dried under a vacuum at room temperature for 24 h with a turbo molecular pump (10 to 7 bar). The four compounds were mixed to make several mixtures, whose compositions are reported in Table 1. Each mixture was further dried at room temperature for 24 h 7368

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Article

Ewald method (Ewald coefficient, 0.27511; grid size, 48 × 45 × 45; interpolation order, 4). The simulation temperature was varied between 298 and 403 K. Our trajectories were sufficiently long to determine the diffusivities in a reliable manner (e.g., 150 ns for T = 333 K). Compared to previous works, we extend the trajectories of more than a factor of 5,10,14 which makes it possible to calculate dynamical properties at lower temperature with accurate statistics. The detailed microscopic analysis was performed at 333 K where we can directly compare with the experimental data. In the following, the systems are characterized by the anion fraction of TFSI (see Table 1).

SIMULATION METHODOLOGY All simulations were performed with the MD simulation package AMBER 10.21 This software was extended by a Buckingham Potential and a Thole screening. These two modifications made it possible to use the many body polarizable force field APPLE&P.13

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Figure 1. Structures of FSI and TFSI. Blue, N; yellow, S; red, O; cyan, C; pink, F.

DIFFUSION COEFFICIENTS The self-diffusion coefficient of each ionic species was determined via PFG-NMR experiments and simulations, using the Einstein−Smoluchowski equation22

The starting structure was produced randomly in the gas phase with a box size of 300 Å, so the box is large enough to avoid bad contacts in the start structure. Then, the simulation cell was shrunk to roughly 47 Å. In this step, the polarization was switched off to accelerate this step. After this, an equilibration run of 10 ns in the NpT ensemble at 1 bar with polarization was performed to obtain a homogeneous system. For the average density, we only use the last 8 ns because the system needs the first 2 ns to handle polarization effects. The averaged density was used for the followed production run in the NVT ensemble. The comparison of experimental densities with the ones from the simulation is shown in Table 2. The

D = lim

Δt →∞

Exp. Sim. Exp.

100 1.507 1.50 16.188

91 1.502 1.50 14.159

50 1.481 1.47 10.48

9 1.442 1.43 8.78

(1)

In eq 1, MSDion is the mean-square displacement of the specific ion, ⟨ ⟩ denotes the ensemble average, Δt is the time interval, and different time origins are used. For the comparison of experiment and simulation, the data from the simulations were corrected for hydrodynamic effects, which show finite size effects.23 It is given by

Table 2. Comparison of Experimental and Simulation Densitiesa TFSI (%) ρ (g/cm3) ρ (g/cm3) η (mPa s)

⟨MSDion ⟩ 6Δt

ΔDFSC = 0 1.435 1.42 9.581

2.837kBT 6πηL

(2)

where kB is the Boltzmann constant, T is the temperature, η is the viscosity, and L is the box length. For the viscosity, the experimental values were used (see Table 2). PFG experiments are limited to a maximum temperature of 343 K due to technical reasons. Thus, the temperature ranges of simulation and experiment do overlap between 298 and 333 K. For low temperatures, sufficient equilibration of the simulated configuration is necessary. In practice, we have fitted the experimental data by the Vogel−Fulcher−Tamann (VTF) relation in order to have a complete overlap with the experimental data. The VTF fit function is given by

a

Also, the experimentally determined viscosity is reported. All values refer to 333 K.

Berendsen thermostat was used to control the temperature, and the Shake algorithm, to constrain the bonds containing hydrogen. The elementary integration step was 1 fs. The electrostatic interactions were calculated via the particle mesh

Figure 2. (a) Diffusion coefficients for the system TFSI100; lines represent the VTF fit to our experimental data (solid lines, experimental temperature range; dashed lines, extrapolation of experimental data), the black data points the simulation results; the colored ones the diffusion coefficients determined by Hayamizu et al.20 (b) Diffusion coefficients depending on the TFSI fraction for T = 333 K; dashed lines connect the experimental data, solid lines the simulated data. 7369

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⎛ ⎞ B D = D0 exp⎜ ⎟ ⎝ (T − T0) ⎠

In eq 4, Nν,i is the number density of the different ions and Di is the diffusion coefficient of each species. In Table 4, the resulting transference numbers are shown. Due to an uncertainty of approximately 8% for the diffusion

(3)

Here, D0 and B are material dependent constants, which can be freely adjusted. T0 is the hold constant for all fits per system to make the results comparable to each other. For the value of T0 the diffusion coefficients of emim are fitted with a freely adjustable T0. The resulting value is used for the fits of other diffusion coefficients and the conductivity of the respective system. Tokuda et al. investigate pure ionic liquids and use the VTF fit to determine T0.24 The values for T0 are in the range 149−164 K, so our values are in good agreement. The fitting parameters for the TFSI100 system, displayed in Figure 2a, are shown in Table 3. The parameters for the other four systems are shown in the Supporting Information.

Table 4. Apparent Lithium Ion Transference Number Depending on the Anion Composition system transference number

DEMI DTFSI DLi

B (K)

T0 (K)

90 ± 7 89 ± 50 89 ± 8 σ0 (mS/cm)

743 ± 13 838 ± 106 913 ± 17 B (K)

161 ± 9 161 161 T0 (K)

713 ± 35

651 ± 8

161

σ

TFSI91 0.019

TFSI50 0.022

TFSI9 0.024

TFSI0 0.024

coefficients, the differences between low and high TFSI content are inside the statistical error. Thus, different anion compositions of FSI and TFSI do not enhance the lithium ion transference number. Jeremias et al. investigated the ionic liquid diallyldimethylammonium-bis(trifluoromethanesulfonyl)imide (DADMATFSI) doped with nearly the amount of LiTFSI as the salt content in our systems and found a transference number of 0.023.26

Table 3. Fit Parameter for the VTF Fit of Diffusion and Conductivity Data for the System TFSI100 D0 (10−10 m2/s)

TFSI100 0.018

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CONDUCTIVITY The Einstein relation σ = lim

t →∞

e2 6tVkBT

∑ zi⟨R i(t ) − R i(0)⟩zj⟨R j(t ) − R j(0)⟩ i,j

(5)

can be used to calculate the ionic conductivity from MD trajectories. In eq 5, e is the elementary charge, t is the time, V is the simulation box volume, T is the temperature, zi,j are the charges of the ions i, j, and Ri, Rj are the positions of the ions i and j, respectively. Due to the cross terms in the sum, this value can only be determined with poor statistics compared to ion self-diffusion coefficients. The part of the conductivity without cross terms reflects the uncorrelated part. It reads

In Figure 2, the experimental and simulation data are compared. For the complete temperature range, good agreement between experiment and simulation can be observed (see Figure 2a). Furthermore, we compare our data with PFG-NMR experiments from Hayamizu et al. and find also a very good agreement for the systems TFSI0 and TFSI100.20 We check that the small deviations between simulation and the experiments are not due to insufficient sampling. In Figure 2b, the dependence of each ionic species on the anion composition is shown. The agreement between experiment and simulation is again very promising. Significant deviations (approximately 20%) are only visible for the lithium ion diffusivity. Experimental values display a stronger dependence on TFSI concentration than simulation results. This significant deviation for lithium ion diffusivity can be observed over the complete temperature range (see the Supporting Information). Thus, it seems that the deviations for low TFSI content are systematic and hold beyond this specific temperature. To estimate the statistical error of the diffusion coefficients, we split the trajectory of the TFSI100 at 333 K in 10 ns intervals and determine the diffusion coefficient. The average value was in good agreement with the one from the long trajectories, and the maximum deviation was 8%. The difference between TFSI0 and TFSI100 for the anion diffusion is roughly 1.1. Solano et al. found a factor of nearly 1.5 for another lithium ion concentration and another cation.14 They also found that the cation diffusion is nearly unaffected by the anion which is in accordance with our data, that emim diffusion is almost unaffected by the anion ratio (see Figure 2b). For electrochemical applications, the transport of lithium ions is of main interest. Therefore, we approximate the contribution of lithium ions to the conductivity via the transference number which is defined as25

t Li =

σuncorr = lim

t →∞ 2

=

e VkBT

∑ zi 2⟨[R i(t ) − R i(0)]2 ⟩

∑ niDi i

i

(6)

where ni is the number of the specific ionic species and Di is the diffusion coefficient of the ionic species. The degree of uncorrelated motion α can be defined as the ratio between σ and σuncorr, i.e., eqs 5 and 6. σ α = lim α(t ) = lim t →∞ t →∞ σuncorr (7) α = 1 means completely uncorrelated ion motion, while α → 0 stands for a complete correlated motion so all cations move together with anions as ion pairs or aggregates. Due to the poor statistic for the long time limit of the cross terms, in the literature, α is determined in the subdiffusive regime by utilizing the first 2−5% of the trajectory.27 To proof this method, we split our trajectory of the TFSI100 system and investigate for which time interval the value of α can be determined with reasonable accuracy. We calculate α in the regime from 0.4 to 1 ns (corresponding to less than 2% of the total simulation). Only in this time regime a reliable determination of α is possible (see the Supporting Information). In Table 5, the averaged values of α are shown. The value of α is independent from the anion composition for the simulations as well as for the experiment. Having in mind the

Nν , iDi ∑ Nν , iDi

e2 6tVkBT

(4) 7370

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Table 5. Averaged α Values from Experiment and Simulation (Simulation Values Have an Uncertainty of 0.1) T (K)

Sim.

Exp.

298 333

0.67 0.76

0.63 0.64

the viscosity is inversely proportional to the equivalent conductivity, i.e., Λη = constant

(8)

In eq 8, Λ is the equivalent conductivity and η is the viscosity. Figure 4 shows the relation between equivalent conductivity and inverse viscosity. The lines represent the linear fit to each data set. The slope increases with increasing amount of TFSI. The values are comparable to the ones reported for the ionic liquid emimBF4 doped with LiBF4 by Hayamizu et al.25 Compared to the ionic liquid 1-butyl-2,3-dimethylimidazolium bis(trifluoromethanesulfonyl)imide (bmmiTFSI) doped with a higher amount of lithium salt investigated by Monteiro et al.,29 our equivalent conductivities are a factor of 4 higher. The classical Walden plot, which is based on eq 8, was established by Xu et al. to classify ionic liquids and to link the viscosity with the conductivity.18 For this classification, the viscosity has to be in units of Poise and the equivalent conductivity in S cm2 mol−1. The reference, a dilute KCl solution,18 was chosen arbitrarily, so the comparison between ionic liquids and this reference is quite questionable.30,31 However, this reference line was used by Xu et al. to divide the diagram into different areas and define properties for each area.18 Therefore, we use this diagram to compare our system with previous work.31,32 Figure 4b enables a classification of our ionic liquids based on the work of Xu et al. All data points are below the reference line. A possible reason for a deviation to lower values compared with the reference can be ion pairing.18 Lee et al. focus on current battery electrolytes like ethylene carbonate−dimethyl carbonate (EC−DMC) doped with lithium salts. 32 All investigated electrolytes are below the reference line in the Walden plot. They explained this with the low ionicity of the systems.32 Our data points are also below the reference line, and this is consistent with the ionicity (degree of ion uncorrelated motion) values around 0.6−0.7 shown in Table 5. A similar behavior was observed by MacFarlane et al. for pure ionic liquids.31

estimated uncertainty for α of 0.1, reported by Li et al. and Borodin et al.,10,27 the agreement between experiment and simulation is very good. The “ideal” conductivity σuncorr (see eq 6) can be calculated from the diffusion coefficients. Under the assumption that α(t) is time-independent for even longer times, as suggested by the data shown in the Supporting Information, we can then determine σ via eq 7. In Figure 3, a comparison of the conductivities is shown. The determined conductivities from simulations differ at most 30%

Figure 3. Conductivity for the experimental data (solid lines) and simulation results (data points).

from the experimental ones and show the same dependence on TFSI concentration. Part of the residual deviations result from the difference in the α-value at the higher temperature. It seems that due to the higher temperature the α-values get a higher uncertainty. Importantly, the two systems with the lowest content of TFSI show a significantly higher conductivity than the other three systems in experiment as well as in simulation. Walden investigated in his work strong electrolytes with a high equivalent conductivity which means the normalized conductivity with respect to the concentration.28 He found that

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LITHIUM ION COORDINATION Lithium Ion Coordination by Anions. Next, we study the lithium ion coordination. In Figure 5a and b, we show the radial distribution function (RDF) of lithium ions with OTFSI and OFSI. In Figure 5a, we observe nearly the same coordination behavior for the two systems containing only one anion species.

Figure 4. (a) Relation between equivalent conductivity and inverse viscosity (fluidity). (b) Walden plot to classify ionic liquids. 7371

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Figure 5. (a) Radial distribution function for lithium ions and anion oxygens for TFSI100 and TFSI0. (b) Radial distribution function for lithium ions and anion oxygens for TFSI91, TFSI50, and TFSI9. Dashed lines, TFSI; solid lines, FSI.

Addition of a small amount of FSI to TFSI100 leads to a dramatic increase of the first coordination shell by a factor of 2. Further addition of FSI results in a decrease of the peak intensity for the TFSI oxygens as well as for the FSI oxygens. Thus, the lithium ion coordination strongly depends on the anion composition. The systems TFSI9 and TFSI91 have opposite anion compositions. Therefore, the TFSI peak for TFSI9 can be compared with the FSI peak for TFSI91 because in both cases the specific anion corresponds to the minority component. Interestingly, the TFSI peak is higher compared with the FSI peak for the minority as well as for the majority situation. However, the total number of oxygens in the first coordination shell of the lithium ions is four for all five systems (see Table 6). This is in accordance with the work of Figure 6. RDF of lithium ions with themselves.

Table 6. Averaged Number of Anions Inside the First Coordination Shell of Lithium Ions

As a compensation, for the system TFSI0, the second coordination shell is much more pronounced. Figure 7 shows a

system

TFSI0

TFSI9

TFSI50

TFSI91

TFSI100

FSI TFSI

4.2 0

3.4 0.8

1.3 2.9

0.1 4

0 4.1

Umebayashi et al.33 The shape of the RDF for the system TFSI100 is comparable to the one reported by Monteiro et al.29 In that work, a much higher lithium ion concentration was analyzed. Table 6 and Figure 5b indicate a strong preference for TFSI compared to FSI. Lithium Dimers. In addition to the lithium ion being solvated by four anions (see Table 6), lithium ions were often found to form aggregates with other lithium ions located nearby which we call lithium dimers.11 For the analysis of these dimers, we determine the radial distribution function of the lithium ions, shown in Figure 6. For all systems the first coordination sphere is well-defined which means lithium dimers are present in all systems but they strongly differ in the amount of lithium ions in the first coordination shell. From 0 to 91% TFSI, the relative intensity of the first coordination sphere increases. The TFSI100 system behaves similarly compared to the TFSI91 system. The strongest relative reduction of the number of direct lithium ions is seen when going from TFSI9 to TFSI0. Compared with the TFSI100 system, the reduction even amounts to a factor of 3. The first and second peak are shifted compared to the simulations of Borodin et al.,11 but the relative heights are very similar. This may be a consequence of the different cation and lithium ion concentration.

Figure 7. Lithium dimer and TFSI as a bridge.

typical configuration of a lithium ion dimer. Here, TFSI acts as a bridge to connect two lithium ions. The distance between these two lithium ions is approximately 4 Å (see Figure 6). FSI can also act as a bridge, but the probability is much lower because TFSI is sterically much more demanding and coordinates stronger. To analyze such dimers, we first determine their lifetimes via identifying the time point when they are formed and the time 7372

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Table 7. Lifetimes of Dimers and Anion Lifetimes When Coordinated to a Dimer or a Single Lithium Ion in ns, Percentage of Lithium Involved in a Dimer system TFSI0 TFSI9 TFSI50 TFSI91 TFSI100

Li−Li 3.0 5.9 18.1 20.8 19.8

± ± ± ± ±

0.4 0.9 2.7 3.0 3.4

TFSIdimer 11.6 14.8 14.9 12.8

± ± ± ±

2.5 1.7 1.3 1.6

TFSIsingle 3.5 4.2 4.3 3.9

± ± ± ±

FSIdimer 2.5 ± 0.2 3.3 ± 0.2 4.3 ± 0.7

0.2 0.1 0.1 0.1

FSIsingle

2*#Li−Li/#Litot

± ± ± ±

18.8 31.0 40.1 35.3 36.3

1.1 1.2 1.2 1.2

0.0 0.0 0.0 0.1

compared with those for which no TFSI exchange is observed in a given time window. Furthermore, the MSDs for lithium ions inside a dimer are determined in the time interval in which the dimer is stable. Figure 8 compares the MSD of dimerized and single lithium ions for the system TFSI100. Moreover, Figure 8 reports the

point when they break. The criterion was determined with the help of the RDF. We use as the critical distance for the formation of a lithium dimer 6 Å and for binding of lithium ion and an anion oxygen 2.75 Å. Furthermore, for the lifetimes of anion−lithium ion coordination, we distinguish whether the anion has one or two lithium ion neighbors and count the time until the distance is beyond the cutoff distance. Short transient residences in the nearest neighbor shell are excluded from the calculation of the lifetimes. For this purpose, we only take into account lifetimes which are larger than 10% of the initially calculated average lifetimes where all transitions were included. In Table 7, the resulting lifetimes and percentage of lithium ions, which are involved in such dimers, are presented. The addition of FSI to TFSI100 does not influence the lifetime of the dimers. However, a dramatic increase of the lifetime by a factor of 6 is observed if TFSI0 and TFSI50 are compared, i.e., upon addition of TFSI. The exchange rates of the anions are comparable to those determined by Li et al.10 These authors sum over all lithium ions without a distinction between dimers and single lithium ions, obtaining exchange rates of the same order of magnitude. Borodin et al.11 determine a lifetime of 7.1 ns for such dimers at T = 393 K using a slightly different force field. Compared to the lifetimes at T = 373 K (roughly 11 ns) and T = 403 K (5 ns) of our simulations, both are in good agreement. The system without TFSI is noticeable because less than 20% of all lithium ions are involved in dimers. A small amount of TFSI increases this fraction to over 30%, indicating that TFSI strongly stabilizes lithium dimers. Furthermore, increasing the amount of TFSI leads to longer lifetimes of FSI in a lithium ion dimer, while different anion compositions have no influence on the lifetimes of TFSI in a dimer and also on the lifetimes of anions close to single lithium ions. The lifetime of TFSI in a dimer for the system TFSI9 is longer than the average lifetime of a dimer. This indicates that two kinds of dimers are present, one stabilized by TFSI and one by FSI. The dimers which are stabilized by TFSI live much longer, but here TFSI is the minority so this leads to a slight increase of the average. In the TFSI50 system, the concentrations of FSI and TFSI are equal. Thus, the probability for TFSI as a bridge is higher because it is the favored partner (see Figure 5b) and hence the dimer lifetime increases. For higher TFSI concentration, FSI is the minority and is no longer present in a dimer (see Table 7). The lifetimes on single lithium ions show a longer lifetime for TFSI inside the first coordination shell compared to FSI. Both are not affected by different anion compositions. Due to the long lifetimes of the dimers and the involved amount of lithium ions especially for high TFSI content, one may wonder about the lithium ion transport in the presence of the dimers. We explicitly determine the MSD for different subensembles of particles. In this way, we can proceed without the addition of an external perturbation as Borodin et al. did.11 The MSDs of the single lithium ions with TFSI exchange are

Figure 8. Comparison of MSD of lithium ions in dimers, single lithium ions, and lithium ions with no TFSI exchange at T = 333 K.

MSD of single lithium ions not exchanging their first coordination shell for 8 ns. It is clearly shown that the TFSI exchange does not influence the lithium ion diffusion. More specifically, the diffusivity of the dimerized and single lithium ions just differ by 10% at the most. These results suggest that the previous observation concerning the slowing down of the lithium ions may be related to the addition of the binding potential,11 giving rise to a significantly modified local structure, rather than to the corresponding increase of the lifetime of the first neighbor shell. Interestingly, as reported by Borodin et al.,11 this addition hardly modified the diffusivity of the large cation. Our results, reported in Figure 2b, show that the emim diffusivity is independent from the anion composition and in this sense somewhat insensitive to the local structure around the anion.

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CONCLUSION In this paper, we have investigated the transport properties, total ionic conductivity, ion diffusion coefficients, and lithium ion transference numbers of ionic liquids doped with lithium salt composed of two anions, bis(fluorosulfonyl)imide (FSI) and bis(trifluoromethanesulfonyl)imide (TFSI), and two cations, N-ethyl-N-methylimidazolium (emim) and lithium ions, via experimental and simulation techniques. The comparison of experimental and theoretical results displays a very good agreement over a wide range of temperatures as well as different anion compositions. The agreement at lower temperatures is especially remarkable because no direct overlap with such long trajectories of simulation and experimental results have been reported so far.10,11,14 On the basis of this 7373

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promising agreement between simulations and experiment (also with the data from Hayamizu et al.20), one may explore the microscopic information on the simulation data in order to elucidate some of the microscopic mechanisms present in these systems. Here, we have studied in particular the lithium ion coordination and the properties of the lithium dimers with respect to lifetimes, exchange rates, and percentage of involved lithium ions. For the minority as well as for the majority situation, TFSI is the favored coordination partner for lithium ions. The analysis of the lifetimes of lithium dimers shows that TFSI stabilizes them. However, the lithium dimers are nearly as fast as single lithium ions for the temperature accessible in this present work. This observation may just follow from the roughly similar size of the lithium dimers and LiTFSI aggregates. Furthermore, lithium ions which do not exchange their first coordination shell are also as fast as the two species. This observation suggests that anion−lithium ion exchange rate does not influence lithium ion transport. This is a different conclusion from the one reached in the previous study that showed that application of the biasing potential to significantly decrease the lithium ion−anion exchange slows down lithium ion transport by 30%.11 One should note, however, that the additional biasing potential also perturbed the IL structure while keeping the average LiTFSI coordination the same.

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ASSOCIATED CONTENT

S Supporting Information *

Diffusion coefficients for the system TFSI0, VTF fit parameters for diffusion coefficients, and time resolved α for different parts of the TFSI0 trajectory. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.J., A.M., and S.P. would like to thank the financial support of BMBF within the project “MEET Hi-END - Materialien und Komponenten für Batterien mit hoher Energiedichte” (Förderkennzeichen: 03X4634A). The work is financially supported by the SafeBatt project from BMBF (Förderkennzeichen: 03X4631N).

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REFERENCES

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