Molecular Dynamics Simulations of Lithium Doped Ionic-Liquid

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Molecular Dynamics Simulations of Lithium Doped Ionic-Liquid Electrolytes Promit Ray, Andrea Balducci, and Barbara Kirchner J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b06022 • Publication Date (Web): 26 Oct 2018 Downloaded from http://pubs.acs.org on October 28, 2018

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The Journal of Physical Chemistry

Molecular Dynamics Simulations of Lithium Doped Ionic-liquid Electrolytes Promit Ray1 , Andrea Balducci2,3 , and Barbara Kirchner1∗ 1

Mulliken Center for Theoretical Chemistry, Rheinische Friedrich-Wilhelms-Universität Bonn, Beringstr. 4+6, D-53115 Bonn, Germany 2

Institute for Technical Chemistry and Environmental Chemistry,

Friedrich-Schiller-University Jena, Philosophenweg 7a, 07743 Jena, Germany 3

Center for Energy and Environmental Chemistry Jena (CEEC Jena),

Friedrich-Schiller-University Jena, Philosophenweg 7a, 07743 Jena, Germany E-mail: [email protected],Tel:+49228-73-60442

∗

To whom correspondence should be addressed

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ACS Paragon Plus Environment

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Abstract Lithium bis(trifluoromethanesulfonyl)imide (LiNTf2 ) doped ionic liquids (ILs) are investigated herein, as potential electrolytes for lithium-ion batteries, via scaled charge molecular dynamics simulations. Four model ILs based on the [NTf2 ]− anion and heterocyclic ammonium cations were studied with varying concentrations, ranging from 0 to 1 M solutions, of the dissolved lithium salt. The pyrrolidinium ([pyrHH]+ ), piperidinium ([pipHH]+ ), N-butyl-pyrrolidinium ([pyrH4]+ ) and N-butyl-N-methyl-pyrrolidinium ([pyr14]+ ) cations were considered to evaluate the combined effects of increased ring size, as well as the introduction of apolar groups on the nitrogen atom of the cations, on the liquid structure properties of the electrolytes. Among the investigated ILs, [pyr14][NTf2 ] is the only aprotic IL allowing for a comparison of protic and aprotic ILs. The lithium coordination shell is seen to be quite different in the various IL-based systems; networks of lithium ions bridged by [NTf2 ]− ions have interesting consequences on the solvation shells and coordination numbers. Aggregate existence and velocity autocorrelation functions are finally evaluated in order to characterize the caging effect of [NTf2 ]− ions around lithium ions. In conclusion, we find that the lithium mobility and transport is directly proportional to the strength of the inter-ionic interactions within the liquids whereas the ease of solvation shows opposite trends.

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Introduction

Ionic liquids (ILs) have been extensively investigated in the recent past as several ILs often exhibit unique combinations of desirable properties such as incombustibility, negligible vapor pressure, wide temperature stability range, good conductivity, and low viscosity. 1–3 Interactions within ILs can be rationally tuned by the modification of constituent ions 4,5 which has been shown to significantly alter the structure, dynamics, and properties of the ILs. 6–8 ILs have therefore been researched for their use as electrolytes in electrical devices such as dye-sensitized solar cells and supercapacitors. 9–15 In the particular context of lithium-ion bat-

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teries (LIBs), doping ILs and their mixtures with inorganic salts 16–18 has resulted in several high performance electrolytes 19–22 with overall performances at least similar, and superior in most cases, to the conventionally used organic electrolytes. Throughout the article, lithium ions dissolved in ILs will be referred to as [Li]+ in order to be consistent with our previous article. 23 The large-scale use of ILs in LIBs is mainly limited by high viscosities of typically studied ILs and the relatively low mobility of [Li]+ ions in ILs. 19,24,25 Therefore, the improvement of transport properties of [Li]+ ions in IL-based electrolytes is of extreme importance. Moreover, the cost of ILs is still much too high for their efficient use in commercial devices. However, the vast majority of investigations on IL-based electrolytes have utilized aprotic ionic liquids (AILs). 11,19,24,26,27 Protic ionic liquids (PILs) have not been investigated as much although several recent investigations indicate that they can be successfully employed as potential electrolytes in LIBs. 28–30 On account of hydrogen-bond networks reminiscent of that in water, 31,32 PILs often exhibit higher conductivities and fluidities. 33–35 Considering that PILs are often significantly cheaper to synthesize, it seems very imperative to extend preliminary studies on their structural properties 36–38 to their application as potential electrolytes in LIBs. Although ILs and their mixtures have been found to be safe and stable for use in LIBs, 21,22 prediction of performances and properties of IL-based electrolytes is not trivial based on structural considerations alone. Furthermore, several IL anions exist as conformers which can interconvert at room temperature which in turn significantly influences structure and properties of the ILs. 39–41 X-ray and neutron scattering experiments 42–44 have concluded that anions are the most important determinants of the X-ray scattering patterns of ILs. 45–47 In addition to radiation scattering techniques, computer simulations 44,48,49 have also complemented experimental developments in obtaining a reasonable knowledge of the structure of ILs. 6,50 Among different computational methods, classical molecular dynamics (MD) has largely been the method of choice for investigations of both IL structure 51–54 as well as fea-

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tures characterizing electrolyte performance 55–60 as larger accessible time scales allow for significant ion transport. Static quantum chemical calculations and ab initio molecular dynamics (AIMD) have also added valuable insight into solvation mechanisms and energetics of ionic salts in a variety of organic solvents on account of higher accuracy despite the relatively higher computational demands. 17,61–63 Moreover, quantum chemical methods such as density functional theory and semiempirical quantum mechanics 64,65 have been integrated into screening approaches for the development of promising electrolytes beyond the current stateof-the-art. 66,67 However, detailed computational investigations 62,68 along with experimental validation are essential to rationalize the development of new electrolyte materials. We recently carried out preliminary investigations on the physicochemical properties and [Li]+ solvation structures, both experimentally 18 and computationally, 23 of a series of [NTf2 ]− -based ILs doped with 0.1 M LiNTf2 as potential high-performance electrolytes for LIBs. In the present article, we complement our previous findings by studying varying salt concentrations via scaled charged MD simulations at room temperature which also gives us access to important dynamical properties of interest. As in our previous work, the pyrrolidinium ([pyrHH]+ ), N-butyl-pyrrolidinium ([pyrH4]+ ), piperidinium ([pipHH]+ ) and N-butyl-N-methyl-pyrrolidinium ([pyr14]+ ) IL cations are investigated in combination with the [NTf2 ]− anion resulting in four different ILs. Experimental densities of all investigated systems and [Li]+ -[NTf2 ]− coordination numbers, 18 for the 0.1 M [Li]+ doped ILs, are briefly mentioned in order to validate and supplement our simulations. Specific features of the investigated cations; ring size, alkyl chain addition and the presence of two, one or no acidic hydrogen atoms, are evaluated in their influence on [Li]+ solvation on the molecular level thus justifying our choice of model systems. The three protic ionic liquids (PILs); [pyrHH][NTf2 ], [pyrH4][NTf2 ] and [pipHH][NTf2 ], are compared to the structurally similar aprotic ionic liquid (AIL); [pyr14][NTf2 ] in terms of liquid structure and solvation mechanisms of the respective IL-based electrolytes. [pyrH4][NTf2 ], although protic, is believed to be an important case study because it represents a tradeoff between the protic [pyrHH][NTf2 ]

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and aprotic [pyr14][NTf2 ]. We first discuss the details of the simulation methodologies and experimental measurements following which we discuss the influence of salt addition on the liquid structure of each of the ILs. A thorough subsequent discussion of the [Li]+ solvation, shared solvations shells and ion transport via dynamical properties of interest concludes the results section.

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Experimental measurements and computational details

The simulated systems consisting of the pure and LiNTf2 doped ILs were generated from 500 ion pairs of the respective ILs. The pure ILs as well as 0.1 M, 0.5 M and 1 M LiNTf2 solutions were investigated for [pyrHH][NTf2 ], [pyrH4][NTf2 ] and [pyr14][NTf2 ]. In the case of [pipHH][NTf2 ], we investigated the pure IL as well as 0.1 and 0.5 M LiNTf2 solutions as it was experimentally determined that a 1 M solution of LiNTf2 in [pipHH][NTf2 ] is not possible. The doped systems were created by replacement of the adequate number of IL cations by [Li]+ ions. Compositions of all investigated systems are presented and discussed in Table S1 and Section S1 of the ESI. All-atom representations of the constituent ions of the four different ILs are shown in Fig. 1. The text labels below the ball-and-stick representations for the [pyrHH]+ , [pipHH]+ , [pyrH4]+ and [pyr14]+ ions are in black, red, blue and green respectively as these are the colours adopted throughout the manuscript in reference to the ILs formed from these cations and the [NTf2 ]− ion. The experimental determination of the density of the electrolytes was carried out, at room temperature, with a Mettler-Toledo DE40 density meter. The instrument was adjusted with air and deionized H2 O. The estimated maximum error of the density values is 2 %. The densities of the respective pure ILs and the investigated electrolytes, along with densities obtained from the subsequently described force-field based simulations, are discussed in the subsequent section and listed out in Table S2 in Section S1 of the ESI.

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Figure 1: Ball-and-stick representations of the investigated ions. Top panel: [pyrHH]+ and [pipHH]+ ions, middle panel: [pyrH4]+ and [pyr14]+ ions and bottom panel: [NTf2 ]− ion. Hn and Ct denotes H atoms attached to the N atoms and terminal C atoms of the long chains in the respective cations. The most acidic H atoms on the IL cations, labelled Hn , can easily be inferred from the partial atomic charges shown in Fig. S1 of the ESI.

The [NTf2 ]− ion was modeled using the Canongia Lopes–Padua force field parametrized for the anion which is based on the general OPLS-AA 69,70 / GAFF 71 framework. Nonbonded parameters for the heterocyclic ammonium cations were also specified herein while the remaining force field parameters were taken from the OPLS force field for amines. 72 Partial charges were obtained from a restrained electrostatic potential (RESP) 73 fit of the isolated ions at the HF/6-31++G** level downscaled to an absolute value of 0.8. 74 The calculated atomic RESP charges are shown in Fig. S1 of Section S1 of the ESI. Since the ionic nature 6


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of ILs is believed to be largely responsible for the unique properties of ionic liquids, 75,76 it is necessary to account for charge transfer and polarizability resulting in less than unit net charges on the constituent IL ions. 77–80 For enhanced ion dynamics, in particular, polarizable force fields have been developed for several ILs. 76,81 Reduced static charges are an approximate alternative 53,77,82 but depending on the scaling factor, some force field parameters often need to be refined. 83,84 Scaling charges to an absolute value of 0.8 has been shown to reproduce structure and dynamics in reasonable agreement with experiment 53,54 even without refining vdW parameters. 75 However, densities are also evaluated, for the pure ILs, with unit charges in the ESI for comparison. To ensure charge neutrality and compatibility with the IL ions, 6,85 [Li]+ ions were also modeled as single sites of charge +0.8, and their Lennard-Jones parameters were directly taken from the amber force field GAFF. 71 All classical MD simulations described were carried out at 300 K using the LAMMPS 86 program. The standard Ewald sum technique, 87 with an accuracy of 10−5 Hartree beyond the cutoff distance, was used for the treatment of long-range electrostatic interactions. Cut-offs for the Lennard-Jones interactions were taken at 15 Å with tail corrections. The temperature was maintained using the Nosé–Hoover thermostat. 88,89 The timestep used in these simulations was 0.5 fs with trajectories and thermodynamic information saved every 250 steps for later analysis. Starting structures for the simulations were generated with the PACKMOL 90 program. For the simulations in the canonical ensemble, simulation boxes were subsequently compressed to result in the experimental densities. 18 The respective systems were then equilibrated for 5 ns in the canonical ensemble following which another 10 ns in the same ensemble were used for the analysis of trajectories. Simulations were also performed in the isobaric-isothermal ensemble to obtain densities for comparison with the experimental values in order to validate the utilized force field. Furthermore, short 100 ps long simulations were also performed with trajectories written out every 0.5 fs for the evaluation of velocity autocorrelation functions. All structure visualisation was carried out using the VMD 91 and PyMOL 92 programs.

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Analysis of trajectories from the LAMMPS output files has been performed by our in-house code TRAVIS 93 which offers an extensive range of properties, well beyond the standard, evaluated from trajectory files. For more details, the reader is referred to the article which introduces TRAVIS. 93 In particular, we evaluated radial distribution functions (RDFs), diffusion coefficients, residence time autocorrelation functions (ACF) and velocity autocorrelation functions. Self-diffusion coefficients were calculated from the mean square displacements (MSDs) of the respective ions using the Einstein relation: 1 t→∞ 6t

D = lim

(1)

using positions r(t) varying with time. We considered only the data points in the last half of the corresponding mean squared displacement functions (shown in the ESI) for the linear regression. Furthermore, time-dependent autocorrelation functions (ACF)s, c(t), were calculated herein. They have the general form

c(t) =

< c(t0 ).c(t) > < c(t0 ).c(t0 ) >

(2)

with the population variable h and time t. h=1 if the defining criteria (such as a distance or an angle condition) are satisfied, h=0 otherwise. Graphical representations were produced with the GRACE program package.

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Results and discussions

After discussing the densities of the investigated electrolytes and their comparison with densities obtained from constant-NPT simulations, we shift focus to the liquid structure of the different IL-based electrolytes in terms of the impact of [Li]+ salt addition. Subsequently, we discuss [Li]+ solvation highlighting the importance of shared solvation shells and [Li]+ -

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[Li]+ networks in determining ion aggregates within the respective electrolytes. Finally, diffusion, [Li]+ aggregation and velocity autocorrelation functions are discussed in order to link transport properties to structural considerations and specific chemical changes in the cations of the ILs. With reference to transport properties, in particular, it should be acknowledged that polarizable force fields would allow for a more realistic description of diffusion and ion-cage dynamics 58,94 and better comparison to experiment. Meanwhile, DFT-based AIMD 95,96 explicitly considers the electronic structure and, therefore, polarizability is considered implicitly. However, we validate the scaled charge simulations performed herein by benchmarking against experimental densities, available diffusion coefficients, and coordination numbers. Experimental densities are discussed in Table S2 of the ESI while coordination numbers and diffusion coefficients are subsequently discussed in the manuscript. Furthermore, the emphasis herein is placed more on predicting trends in dynamical properties and relating them to the changes in the chemical structure of the IL cations. It is therefore envisaged that in this case, such a description of the systems considered here will not be significantly limited by the approximate treatment of charge transfer as described in the computational details. The [pipHH][NTf2 ] and [pyrHH][NTf2 ]-based systems are seen to exhibit similar structural and solvation characteristics typical of protic ILs while the [pyrH4][NTf2 ] and [pyr14][NTf2 ]based systems exhibit correspondingly similar characteristics. Therefore, in certain instances in the manuscript, only the representative systems are discussed for the sake of convenience. The corresponding properties for all investigated systems can be found in mentioned sections of the ESI.

3.1

Density

Densities obtained from both experimental measurements and constant-NPT MD simulations are depicted in Fig. 2. Experimental densities for the pure ILs are found to be highest for [pyrHH][NTf2 ] followed by [pipHH][NTf2 ] (black and red crosses) which makes sense in that 9



Figure 2: Experimental and theoretical densities of the pure ILs and corresponding [Li]+ doped IL solutions as a function of doping concentration measured at 300 K. The theoretical densities were obtained from simulations in the isobaric-isothermal ensemble.

PILs are known to have high densities at room temperature. The density of the IL drops with the replacement of an acidic proton in [pyrHH][NTf2 ] by a butyl chain as can be seen from the density of [pyrH4][NTf2 ] (blue cross). The density drops even further with the replacement of yet another proton with a methyl chain as can be seen from the density of [pyr14][NTf2 ] (green cross). The drop in densities could be suggestive of the weakening of inter-ionic interactions which we investigate later via coordination environments and ion aggregation lifetimes. Addition of [Li]+ increases the experimental densities in all cases. However, the density increases significantly in [pyr14][NTf2 ] while comparing the pure IL and 0.1 [Li]+ -doped solution. Increase in densities in the other IL-based systems is almost linear as indicated by dotted lines placed in order to guide the eye. Turning to the NPT densities, the simulations reproduce experimental densities for all the pure ILs in excellent agreement with errors less than 2.5 % (compare circles with crosses). The simulation densities of the [Li]+ -doped ILs also compare reasonably well with experimental values with maximum deviations of about 3.4 %. Experimental and NPT densities along with errors, as well as

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densities obtained using unit charges, are provided in Table S2 of Section S1 of the ESI.

3.2

Influence of [Li]+ doping on IL structure

RDFs often provide a fundamental and direct insight into equilibrium liquid structure and, hence, we begin the discussion on IL structure with RDFs. In order to examine the influence of salt addition on the liquid structure of the four ILs, the molecular coordination of ions in the pure ILs and the corresponding [Li]+ -doped electrolytes is examined via ion-ion RDFs. In all our analyses, the center of mass (COM) of the anion was considered the representative coordinate while we considered the center of ring (COR) of the cation. The [pyrHH][NTf2 ] and [pipHH][NTf2 ]-based systems are seen to exhibit similar structural features typical of protic ILs while [pyrH4][NTf2 ] and [pyr14][NTf2 ] show correspondingly similar properties. It is also noteworthy that RDFs are normalized with respect to densities and, therefore, coordination numbers are a better indicator of quantitative coordination environments than peak intensities. We limit the discussion and the representation in the main manuscript to the influence of LiNTf2 addition on the IL structure. RDFs of the inter-ionic and H-bond distances in the pure ILs are depicted in Fig. S2 and Fig. S3 of the ESI respectively. Corresponding discussions can be found in Section S2 of the ESI. Fig. 3 depicts RDFs of cation-anion and anion-anion distances in the representative pure and the corresponding [Li]+ -doped ILs; [pyrHH][NTf2 ] (top panels, graphs shown in black) and [pyr14][NTf2 ] (bottom panels, graphs shown in green). All ion-ion RDFs of the investigated solutions are depicted and discussed in Fig. S4 and Section S3 of the ESI. Introduction of [Li]+ introduces only subtle changes in the appearance of cation-anion RDFs (shown in the left panels of Fig. 3) in that the relative magnitude of the first solvation shell shifts downwards with the peak positions remaining the same, most visibly observed in [pyr14][NTf2 ] (bottom panel, graphs shown in green). The peaks are, however, observed to be a little broader in the [Li]+ doped systems (see subsequent discussion on coordination numbers). The first peak in 11



Figure 3: RDFs depicting inter-ionic distances in the representative pure ILs and the respective electrolytes based on [pyrHH][NTf2 ] and [pyr14][NTf2 ]. Left panels: cation-anion distances and right panels: anion-anion distances in the investigated IL solutions.

the anion-anion RDFs is seen to shift to slightly lower distances in [pyrHH][NTf2 ] (top right panel, graphs shown in black); the most probable anion-anion distance is seen to decrease slightly on account of clustering of [NTf2 ]− ions around [Li]+ ions. The average anion-anion distance, however, is seen to shift to larger distances as evidenced by the appearance of a second peak at around 1.1 nm for the high concentrations of [Li]+ doping investigated. In the case of [pyr14][NTf2 ] (bottom panel, graphs shown in green) the first solvation shell exhibits a more significant split, into two peaks, for [Li]+ concentrations greater than 0.1 M but most visible for the highest concentration investigated. The first of these peaks, at a much shorter distance than in the pure ILs, is sharper with a shoulder and corresponds to [NTf2 ]− ions 12


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bound closely to [Li]+ ions while the second peak is broader and at larger distances corresponding to the average anion-anion distance which increases with [Li]+ doping on account of destruction of structural ordering. Lower anion-anion distances suggests stronger [Li]+ [NTf2 ]− interaction while the shoulder could be indicative of different types of coordinations as we proceed to verify. As the anion is left unchanged and only the cationic component of the respective ILs changes across the systems, differences in the anion-anion RDFs clearly points to the subtle yet important role of the cation in determining the solvation mechanism of [Li]+ ions.

Figure 4: Average number of [NTf2 ]− ions around a cation, in each of the studied systems, as a function of [Li]+ doping.

The average cation-anion coordination number (n(cation-anion)), evaluated at the first minima (around 0.9 nm) of the corresponding RDFs, is plotted in Fig. 4 as a function of concentration of [Li]+ doping in the respective IL-based systems. n(cation-anion) values are the highest in [pyrHH][NTf2 ] followed by [pipHH][NTf2 ] (data points in black and red respectively) which changes upon [Li]+ doping. Turning to the lower n(cation-anion) values, these are higher in [pyrH4][NTf2 ] than [pyr14][NTf2 ] (data points in blue and green respec13



tively) which also changes upon [Li]+ addition. Running coordination numbers are plotted against inter-ionic distance, for the pure and doped ILs, in Fig. S5 of the ESI to demonstrate a reduction in coordination number observed at about 0.5 nm corresponding to the first peak of the RDFs shown in the left panels of Fig. 3. n(cation-anion), however, is seen to exhibit an increase with increasing [Li]+ concentration, most significant in [pyr14][NTf2 ] and [pyrH4][NTf2 ] and least in [pyrHH][NTf2 ], discussed in detail in Section S3 of the ESI. In fact, n(cation-anion) in [pyr14][NTf2 ] increases almost by a value of 1 while comparing the pure IL and the corresponding 1 M [Li]+ doped solution in agreement with simulations performed with a polarizable force field; 58 such an increase is consistent with the observed splitting behavior of the anion-anion RDFs seen in the right panels of Fig. 3 with the average anion-anion separation in the ILs shifted to slightly larger distances on account of increased repulsion. More importantly, this suggests that more [NTf2 ]− ions surround a cation with weak coordination within the first solvation shell while far fewer [NTf2 ]− ions coordinate the [Li]+ ions; such a balance has been discussed to be the energetic penalty concerning [Li]+ salt solubility in the ILs at high levels of [Li]+ doping. 58 In addition to highlighting differences in solvation trends among our investigated systems, this could explain the limited solubility of LiNTf2 in [pipHH][NTf2 ]. Since H-bonding is a crucial determinant of spatial arrangement of ions in protic ILs, RDFs of Hn (cation)-O ([NTf2 ]− ) distances are depicted in the top panel of Fig. 5 for the pure ILs and the corresponding solutions with highest [Li]+ doping. The presence of one acidic proton in [pyrH4][NTf2 ] (blue curves) leads to a significantly different pattern of RDF compared to [pipHH][NTf2 ] and [pyrHH][NTf2 ] (red and black curves respectively), we discuss this aspect in Fig. S3 and Section S2 of the ESI. Addition of [Li]+ leads to a notable reduction of peak intensities up to a distance of 0.6 nm wherein the form of the RDF remains intact with solvation shell heights and minima pushed downwards. The reduction in intensities is most noticeable in the RDFs of pure and doped [pyrH4][NTf2 ]. Beyond Hn (cation)-O ([NTf2 ]− ) distances of 0.6 nm, there is a reversal of trends as can be seen from the dashed lines rising

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Figure 5: RDFs of H-bonding distances in [pipHH][NTf2 ], [pyrHH][NTf2 ] and [pipHH][NTf2 ].

above the solid lines. Hn (cation)-O ([NTf2 ]− ) coordination numbers, n(r), are plotted in the bottom panel of Fig. 5. n(r) is highest in [pyrHH][NTf2 ], followed by [pipHH][NTf2 ] and [pyrH4][NTf2 ] similar to the trends in cation-anion coordination numbers. Trends in n(r), concerning the addition of [Li]+ , support conclusions drawn from the RDFs in that there is a drop in n(r) in the distance range of 0.2 and 0.6 nm beyond which there is a reversal of 15



trends on account of more [NTf2 ]− ions surrounding a cation (see discussion on cation-anion coordination numbers). The average H-bonding coordination number, corresponding to n(r) values at about 0.3 nm (around 1 for pure [pyrH4][NTf2 ] and 2 for the other two ILs), are also seen to drop upon [Li]+ addition pointing to the destruction of the H-bond network brought about by [Li]+ addition. H-bond RDFs, [NTf2 ]− ion conformations and alkyl side chain stacking in the all the investigated IL-based systems are depicted in Fig. S6 of the ESI.

3.3

Solvation of [Li]+ in the ILs

In order to understand the [Li]+ solvation structure in our investigated systems, preliminary insight is once again gained by evaluating RDFs of [Li]+ -[NTf2 ]− distances. [Li]+ -[NTf2 ]− RDFs are followed up with a discussion on types of [Li]+ -[NTf2 ]− coordination and coordination numbers. The [Li]+ -COM ([NTf2 ]− ) RDFs, depicted in the left panels of Fig. 6, exhibit similar appearances for all four IL-based systems with a split first solvation shell centered around about 0.35 nm, predominantly an isomeric effect brought about by different conformations adopted by the [NTf2 ]− ions around the [Li]+ ions. 58,59 As discussed in our previous work, 23 the width and relative intensities of two peaks are directly affected by the cis-trans ratio of the [NTf2 ]− ions which is, in turn, determined by the isomerization of the [NTf2 ]− ion captured by the force field. The split first solvation shell, however, does point to important differences in the [Li]+ -[NTf2 ]− coordination environment in the different IL-based electrolytes; the first pre-peak is relatively weak and not well defined in the case of the electrolytes based on [pipHH][NTf2 ] and [pyrHH][NTf2 ] (two top panels, graphs shown in red and black respectively) in comparison to those based on [pyrH4][NTf2 ] and [pyr14][NTf2 ] (two bottom panels, graphs shown in blue and green respectively). [NTf2 ]− ions seem to approach [Li]+ ions closer in the two latter systems compared to the former. Furthermore, the first solvation shell maximum is observed at slightly larger distances in the [pipHH][NTf2 ] and 16


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Figure 6: RDFs depicting distances between the [Li]+ ions and the [NTf2 ]− ions in the respective lithium-doped ILs. Left panels: [Li]+ - COM ([NTf2 ]− ) distances, right panels: [Li]+ - O ([NTf2 ]− ) distances in the investigated electrolytes.

[pyrHH][NTf2 ] IL-based systems. Increased [Li]+ doping is seen to seemingly increase the intensity of the pre-peak in the [pipHH][NTf2 ] and [pyrHH][NTf2 ]-based systems. In the case of the [pyrH4][NTf2 ] and [pyr14][NTf2 ]-based systems (two bottom panels, graphs shown in blue and green respectively), only minor changes in peak intensities are seen with peak positions remaining intact. Effects of [Li]+ doping are observed in all systems for [Li]+ -COM [NTf2 ]− distances between about 0.5 nm and 0.75 nm. Turning next to the [Li]+ -O ([NTf2 ]− ) RDFs (right panels of Fig. 6), all graphs appear extremely similar with two well-defined peaks at about 0.2 and 0.4 nm. The first of these peaks corresponds to the O atoms on the [NTf2 ]− coordinated by the [Li]+ and the second of these peaks corresponds to the other O atoms on the [NTf2 ]− ion; the presence of two peaks is suggestive of a certain monodentate co-

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ordination in all the investigated systems. It is important to mention that monodentate and bidentate coordinations are not necessarily linked to split peaks observed in the [Li]+ COM ([NTf2 ]− ) RDFs (see subsequent discussion on coordination numbers). The minima separating the two peaks in the [pyrH4][NTf2 ] and [pyr14][NTf2 ]-based systems (two bottom panels, graphs shown in blue and green respectively) are shifted upwards in comparison to the [pipHH][NTf2 ] and [pyrHH][NTf2 ] IL systems (two top panels, graphs shown in red and black respectively) which hints at a more uniform distribution of [Li]+ -O ([NTf2 ]− ) distances in the former systems. Table 1: Average [Li]+ -COM ([NTf2 ]− ) and [Li]+ -O ([NTf2 ]− coordination numbers as well as the total number of [NTf2 ]− uniquely solvating [Li]+ normalized by the number of [Li]+ . System + [pipHH] /[Li]+ (0.1 M) [pipHH]+ /[Li]+ (0.5 M) [pyrHH]+ /[Li]+ (0.1 M) [pyrHH]+ /[Li]+ (0.5 M) [pyrHH]+ /[Li]+ (1.0 M) [pyrH4]+ /[Li]+ (0.1 M) [pyrH4]+ /[Li]+ (0.5 M) [pyrH4]+ /[Li]+ (1.0 M) [pyr14]+ /[Li]+ (0.1 M) [pyr14]+ /[Li]+ (0.5 M) [pyr14]+ /[Li]+ (1.0 M)

[Li]+ -COM ([NTf2 ]− ) [Li]+ -O ([NTf2 ]− ) 3.97 3.98 3.92 3.98 3.96 3.97 3.93 3.97 3.89 3.96 3.77 4.02 3.76 4.01 3.66 3.97 3.61 3.98 3.73 3.98 3.66 3.98

/NLi 3.66 3.34 3.94 3.31 2.94 3.56 3.17 2.55 3.50 2.95 2.62

[Li]+ -[NTf2 ]− coordination in the doped ILs is quantitatively depicted in Table 1. The positions of the first minima in the [Li]+ -COM ([NTf2 ]− ) and [Li]+ -O ([NTf2 ]− ) RDFs (depicted in Fig. 6) were used as cut-off distances in obtaining average coordination numbers (corresponding to distances of 0.52 nm and 0.25 nm respectively). Average [Li]+ -COM ([NTf2 ]− ) coordination numbers range between 3.6 to 4 and are not significantly affected by increased [Li]+ doping. Increase in coordination numbers with increased [Li]+ are only observed at greater [Li]+ -[NTf2 ] distances as depicted in Fig. S7 of the ESI. [Li]+ -O ([NTf2 ]− ) coordination numbers are found to be 4 for all investigated systems with little influence of either the IL cation or [Li]+ doping observed. Running [Li]+ -O ([NTf2 ]− ) coordination numbers are 18


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shown in Fig. S8 of the ESI. Trends in [Li]+ -[NTf2 ]− coordination numbers predicted here are opposite to the trends in experimental coordination numbers, as discussed in detail in our previous work, 18,23 owing to the presence of split [Li]+ solvation shells and shared [NTf2 ]− solvation shells as elaborated subsequently. The presence of shared solvation shells wherein multiple [Li]+ are solvated by a given [NTf2 ]− lead to an underestimation in the experimental determination of [Li]+ -[NTf2 ]− coordination numbers. 23,58,59 Shared solvation shells can be quantified by the evaluation of the total number of [NTf2 ]− ions uniquely solvating all [Li]+ , , normalized by the number of [Li]+ . The formation of [Li]+ -[Li]+ networks with high [Li]+ doping can be inferred from the drop in /NLi as compared to the average [Li]+ COM ([NTf2 ]− ) coordination numbers. Time-averaged coordination environments, of both [Li]+ ions around [NTf2 ]− ions and [NTf2 ]− ions around [Li]+ ions, are shown and discussed under Figures S9 and S10 in Section S4 of the ESI.

Figure 7: [Li]+ -COM ([NTf2 ]− ) running coordination numbers, plotted as a function of [Li]+ COM ([NTf2 ]− ) distances, as obtained from the corresponding RDFs for the 1 M [Li]+ -doped electrolytes.

[Li]+ -[NTf2 ]− running coordination numbers (n(r)) are shown for the each of the doped 19



ILs only the with highest [Li]+ -doping in Fig. 7. Up to [Li]+ -COM ([NTf2 ]− ) distances of about 0.4 nm (representing those [NTf2 ]− ions which can approach [Li]+ ions closely), for n(r) values up to about 2, n(r) is highest in the doped [pyr14][NTf2 ] followed by the doped [pyrH4][NTf2 ] while n(r) values are almost the same in [pipHH][NTf2 ] and [pyrHH][NTf2 ] (green, blue, red and black curves respectively) with marginally higher values in the former within the above mentioned distance range. Ability of [NTf2 ]− ions to approach [Li]+ ions closely reflects on the inter-ionic interactions within the ILs; these trends correlate inversely with the trends in cation-anion coordination numbers in the pure ILs. Both n(r) and the trends therein are in excellent agreement with experimental coordination numbers 18 and our previous simulations 23 with higher n(r) values suggesting that more [Li]+ ions can approach the [NTf2 ]− ions closely in the aprotic IL, consistent with the ratio of intensities of the two peaks in the split solvation shell in the [Li]+ -COM ([NTf2 ]− ) distances. For [Li]+ -COM ([NTf2 ]− ) distances beyond 0.4 nm, the trends get reversed in that n(r) is highest in the doped [pyrHH][NTf2 ] and [pipHH][NTf2 ] solutions followed by [pyrH4][NTf2 ], and is found to be the lowest in the doped [pyr14][NTf2 ] implying that more [Li]+ ions can approach the [NTf2 ]− ions at larger distances in the former ILs. However, as pointed out earlier, [NTf2 ]− ions bound further away from a given [Li]+ would probably be closer to another [Li]+ and would be accounted for twice in the theroretical estimation of coordination numbers. [Li]+ [Li]+ RDFs, for the respective IL-based systems with highest [Li]+ -doping, are shown in Fig. S11 of the ESI.

3.4

Dynamic and transport properties of the electrolytes

In addition to structural changes, the addition of [Li]+ to IL systems has generally been shown to greatly influence the ion dynamics on account of the formation of [Li]+ -anion aggregates. 23,57–59,63 Self-diffusion coefficients of the three ionic species were calculated herein from the mean square displacements of the [Li]+ ions, COMs of the [NTf2 ]− ions and CORs of the respective 20


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cations using the Einstein relation as described in the computational details. Self-diffusion coefficients obtained thereby are shown in Table 2 as function of [Li]+ doping concentration. Self-diffusion coefficients are plotted against [Li]+ concentration in Fig. S12 of the ESI. Furthermore, mean square displacements (both in linear and logarithmic scale) are plotted in Figure S13 of the ESI. It should be pointed out that our production run was 10 ns long following a pre-equilibration of 5 ns and, therefore, slow dynamics such as diffusion and results thereof should generally be treated with appropriate caution. We expect the trends however to remain valid. Overall, our diffusion coefficients are well comparable with diffusion coefficients (from both experiments and simulations) of several [NTf2 ]− -based [Li]+ -doped ILs. 57–59 As mentioned before, however, PILs have not been investigated as widely as AILs. Therefore, experimental diffusion coefficients are available only for [pyr14][NTf2 ] to the best of our knowledge. Our diffusion coefficients of both IL cation and anion in [pyr14][NTf2 ] are in excellent agreement with simulations based on a polarizable force fields. 58 Similar to the polarizable force field, our values deviate from experimental measurements by a factor of 2-3 due to a wide variation in experimental measurements. 97–99 Our values for the suppression in diffusion coefficients of cation and anion upon [Li]+ -doping as well as the diffusion coefficients of [Li]+ are also within the above-mentioned error limits. Considering the pure ILs first, diffusion coefficents of both cations (D(cation)) and anions (D(anion)) are the lowest in [pipHH][NTf2 ] followed by [pyrHH][NTf2 ], [pyrH4][NTf2 ] and [pyr14][NTf2 ]. D values for the respective IL constituents are the highest in [pyr14][NTf2 ] which is justifiable based on the chemical interactions within the ILs. It is also well known that PILs with hydrogen-bonded networks generally exhibit very low diffusion at room temperature; our simulations perfectly reproduce these trends. Interestingly, the diffusion coefficients of the ions of the pure IL are only marginally higher in [pyr14][NTf2 ] than [pyrH4][NTf2 ] which implies that the latter resembles AILs more closely than PILs. In the [pipHH][NTf2 ] and [pyrHH][NTf2 ] IL systems, D(cation) and D(anion) are comparable to each other (within each IL system). However, D(cation) is observed to be larger than D(anion) in the systems

21



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Table 2: Diffusion coefficents D (10−12 m2 s−1 ) of the various ionic species in the investigated IL-based systems. D(cation) and D(anion) represent diffusion coefficients of the cationic and anionic component of the corresponding IL while D([Li]+ ) represents the diffusion coefficient of the [Li]+ ions. System [pipHH]+ [pipHH]+ /[Li]+ (0.1 M) [pipHH]+ /[Li]+ (0.5 M) [pyrHH]+ [pyrHH]+ /[Li]+ (0.1 M) [pyrHH]+ /[Li]+ (0.5 M) [pyrHH]+ /[Li]+ (1.0 M) [pyrH4]+ [pyrH4]+ /[Li]+ (0.1 M) [pyrH4]+ /[Li]+ (0.5 M) [pyrH4]+ /[Li]+ (1.0 M) [pyr14]+ + [pyr14] /[Li]+ (0.1 M) [pyr14]+ /[Li]+ (0.5 M) [pyr14]+ /[Li]+ (1.0 M)

D(cation) 5.39 4.20 3.27 7.36 5.96 3.37 2.29 10.97 10.49 6.79 5.03 13.50 7.81 4.48 5.18

D(anion) 5.83 4.67 2.72 7.06 6.22 2.90 1.99 8.65 7.75 4.64 2.64 11.94 5.71 3.53 2.96

D([Li]+ ) 1.55 0.87 2.99 1.44 1.05 2.94 2.00 1.30 2.36 2.12 1.38

based on [pyrH4][NTf2 ] and [pyr14][NTf2 ] (as observed experimentally 97–99 and from previous simulations 58 ). As observed previously, 57–59 addition of [Li]+ to the systems significantly slows down the dynamics of all ions in general. Furthermore, it is also observed that [Li]+ has a significantly lower self-diffusion than the IL ions which is understandable based on the formation of aggregates discussed earlier. The formation of aggregates needs to be minimized so as to obtain more ’naked ions’ in order to optimize these electrolyte systems. Diffusion coefficients of the [Li]+ ions (D([Li]+ )) are much lower in [pipHH][NTf2 ] than [pyrHH][NTf2 ] for all investigated concentrations although D([Li]+ ) decreases much more noticeably, with [Li]+ doping, in the latter. D([Li]+ ) is seen to be lower in both [pyr14][NTf2 ] and [pyrH4][NTf2 ], at low [Li]+ doping, than in [pyrHH][NTf2 ] which is explained on the basis of stronger [Li]+ [NTf2 ]− interactions. D([Li]+ ) values in [pyrH4][NTf2 ] and [pyr14][NTf2 ] fall less drastically, however, with increased [Li]+ doping which is promising in view of their use as potential

22


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electrolytes. In order to comment on solvated ionic species resulting from aggregation of IL ions around each other and [NTf2 ]− around the [Li]+ ions and their impact on transport properties, 100 continuous residence time autocorrelation (ACF(t)) functions are calculated both for cation-anion and [Li]+ -[NTf2 ]− aggregates. ACF(t) is unity when the distance condition corresponding to coordination or solvation, obtained usually from the first minimum of the RDFs, is satisfied. The ensemble average, as described in the computational details, is taken over all reference ions. ACF(t) decays from unity to zero when the correlation is completely lost in that all reference ionic species have exchanged their solvation or coordination shells (as defined by the criterion) of the observed ionic species. In the below depicted ACFs, the first minima after the solvation shell maxima were considered to depict trends in solvation shell lifetimes. Turning to the cation-anion ACFs in Fig. 8 for the pure ILs (shown in the top panel), solvation shells are seen to be most short-lived in pure [pyr14][NTf2 ] followed by [pyrH4][NTf2 ], [pyrHH][NTf2 ] and [pipHH][NTf2 ] (green, blue, black and red solid lines respectively). The ACFs imply that cations and anions prefer to diffuse as a unit more in [pipHH][NTf2 ] and [pyrHH][NTf2 ] in comparison to other two ILs in agreement with the fact that D(cation) and D(anion) have similar values in these IL-based systems. Although the cation-anion coordination number is higher in [pyrHH][NTf2 ] than in [pipHH][NTf2 ], the ACF decays more rapidly in the former (which changes upon [Li]+ addition). Addition of [Li]+ is seen to increase ion-pair lifetimes in that the corresponding ACFs decay slower than in the pure ILs (compare solid and dashed lines). The difference is most noticeable in [pyr14][NTf2 ] and [pyrHH][NTf2 ] reflected in the reduction in D (cation) in these IL-based systems. Turning next to the [Li]+ -[NTf2 ]− ACFs (shown in the bottom panel), we observe a significant reversal of trends. For the 0.1 [Li]+ doped ILs, the ACFs decay the fastest in [pyrHH][NTf2 ] (black solid lines) followed by [pipHH][NTf2 ], [pyrH4][NTf2 ] and [pyr14][NTf2 ] (black, red, blue and green solid lines respectively). Maximum coordination shell lifetimes in [pyr14][NTf2 ] is well

23



Figure 8: Residence lifetime autocorrelation functions (ACF (t)) plotted with time. Top panel: ACF (t) corresponding to cation-anion coordination in the pure ILs and solutions with highest [Li]+ -doping, bottom panel: ACF (t) corresponding to [Li]+ -[NTf2 ]− coordination in the electrolytes with lowest and highest [Li]+ -doping respectively.

in agreement with the strong [Li]+ -[NTf2 ]− interactions (as observed from the [Li]+ -[NTf2 ]− RDFs) and the relatively low diffusion coefficients of the [Li]+ ions in [pyr14][NTf2 ]. Increasing the [Li]+ -doping concentration reverses the trends for [pyr14][NTf2 ] and [pyrH4][NTf2 ], as for [pyrHH][NTf2 ] and [pipHH][NTf2 ] (although the doping concetrations are different), implying that the addition of [Li]+ tunes the delicate balance between cation-anion and [Li]+ -anion interactions. [Li]+ -COM ([NTf2 ]− ) lifetime ACFs do not decay to zero in the 8 ns that are shown suggestive of very long lifetimes. Increasing the amount of lithium salt leads to a reduced rate of exchange of anions in the first coordination shell of both the [Li]+ 24


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and IL cations suggesting reduced structure diffusion and a greater participation of vehicular diffusion. There exists a negative correlation between the ion-pair decay rates and the [Li]+ -[NTf2 ]− decay rates. Table 3: Residence correlation lifetimes (tau) using the first maximum of the cation-anion RDF as distance cut-off and H-bond criteria defined in the text. Residence lifetimes are expressed in ps. System [pipHH]+ [pipHH]+ /[Li]+ (0.5 M) [pyrHH]+ [pyrHH]+ /[Li]+ (1.0 M) [pyrH4]+ [pyrH4]+ /[Li]+ (1.0 M) [pyr14]+ + [pyr14] /[Li]+ (1.0 M)

tau (cation-anion) 6.76 7.17 4.79 5.38 4.48 4.71 4.45 5.28

tau (H-bond) 4.25 4.35 3.54 3.68 5.48 5.51

The discussed ACFs in the investigated IL-systems, however, decay extremely slowly as is common for [NTf2 ]− -based ionic liquids with cyclic substituted ammonium cations. Furthermore, [Li]+ -[NTf2 ]− correlation has been shown to extend to lifetimes corresponding to over 50 ns in AILs. 58,59,63 In order to evaluate cation-anion lifetimes, the first maximum of the cation-anion RDFs (around 0.5 nm) was considered as a cut-off distance more indicative of ion-aggregate lifetimes. H-bond lifetimes were calculated using the Hn (cation)-O ([NTf2 ]− ) distance cut-off to be 0.3 nm and the N-Hn ..O angle to be be greater than 135 degrees. The evaluated lifetimes are shown in Table 2. Trends in these lifetimes are the same as those already discussed for the solvation shell. The presence of stable aggregates with reasonably long lifetimes is in agreement with previous studies involving [Li]+ ions and AIL anions. 101,102 In particular, investigations in [NTf2 ]− -based electrolytes have concluded that [Li]+ -[NTf2 ]− aggregates are particularly long lived in AILs with large bulky cations giving rise to a caging effect. 58,94 Therefore, a final property of interest is the velocity autocorrelation function which allows the caging and back scattering effect in ILs to be observed. 103–105 The VCF of [Li]+ ions is shown in Fig. 9. As

25



Figure 9: VCFs of the [Li]+ ions in the IL systems with the lowest and highest [Li]+ -doping. Insets showns zoomed in regions of the VCFs. The colour convention for the various IL systems is that same as that adopted throughout the manuscript.

can be seen, the VCFs shows a clear oscillatory behavior after the first collision, and these oscillations become weaker after about 1000 fs but do not get completely damped up to 1.5 ps. [Li]+ ions exhibit a rattling motion in the cages formed by neighboring [NTf2 ]− ions, similar to the previous studies of solutions with AILs. 101 Long-lived oscillations in the VCF indicate periodic reversals in the direction of motion of the [Li]+ ions within the solvation shell during the [Li]+ -[NTf2 ]− lifetimes as can be obtained from distance autocorrelation functions discussed previously. The insets are shown with the aim of observing the decay of the functions to zero as well as observe the first maximum after the minimum. Although the curves appear very similar, the initial reverals in direction of the velocities are more pronounced in the [pipHH][NTf2 ] and [pyrHH][NTf2 ]-based systems (graphs in red and black respectively), which points to the weaker [Li]+ -[NTf2 ]− coordination (see inset on the left), while they are slightly weaker in the [pyrH4][NTf2 ] and [pyr14][NTf2 ]-based systems (graphs shown in blue and green respectively). Except in the case of [pyrHH][NTf2 ], increasing [Li]+ leads to an increase in the oscillations of c(t). The first zero of the respective functions (denoted as the collision times 102,105 ) is denoted in the right inset. Except for [pyrHH][NTf2 ], [Li]+ doping increases the collision time on account of shared solvation shells. Since the inter26


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ionic interactions are too strong in[pyrHH][NTf2 ] for effective solvation shell sharing, this effect is not observed. The collision times are understandably lower than typical IL ions, 105 on account of the small size of the [Li]+ ions, but marginally higher than those observed in [Li]+ doped ethylammonium nitrate. 102

4

Conclusions

In order to rigorously understand the solvation mechanism of [Li]+ ions in four different [NTf2 ]− based ILs with structurally similar cations, we conducted scaled-charge MD simulations of the pure ILs as well as varying concentrations of LiNTf2 dissolved in the various ILs. Solvation of the [Li]+ ions takes place by the gradual destruction of structure and H-bond network in the ILs, clearly observed even for low concentrations investigated, we substantiate these claims by describing coordination environments and ion-coordination lifetimes. However, the anion-anion ordering, in the ILs, is most affected upon [Li]+ ion addition and points to the differences in solvation mechanisms in the various studied IL-based systems. We also found that the ease of solvation, determined by how closely the [NTf2 ]− ions cage the [Li]+ ions, is generally inversely proportional to the inter-ionic interactions within the ILs for all the IL-based systems shown by trends in coordination numbers and structure destruction in the individual ILs. However, [pyrHH][NTf2 ] and [pipHH][NTf2 ] represent an interesting case because cation-anion lifetimes are longer in the latter but with less effective coordination. Solvation characteristics are found to be very similar in [pyrH4][NTf2 ] and [pyr14][NTf2 ] which is encouraging in that PILs are cheaper and easier to synthesize than AILs. [NTf2 ]− ion adopts different conformations when it simultaneously solvates more than one [Li]+ ion. In this context, shared solvation shells are of extreme importance as this affects the experimental determination of coordination numbers. We found that significant [Li]+ -[Li]+ networks are formed in the various ILs from which the experimental coordination numbers

27



can be rationalized. Analyzed VCFs show that [Li]+ ions are trapped in cages formed by the [NTf2 ]− , as in previous investigations, 101 but the fluctuations are more long-lived. The study gives us clear indications that concentration of [Li]+ greatly determines electrolyte performance as does the tuning of interactions within the IL as can be seen in the case of [pyrH4][NTf2 ]. In conclusion, we find that solvation of [Li]+ in ILs is through an inhomogeneous structuring mechanism, which we previously described, 23 considered to be a "universal" ion solvation mechanism but much work is needed to substantiate this hypothesis.

Supporting information The supporting information includes a description of the investigated system sizes, validation of the force field used and additional analysis from the classical MD simulations. This material is available free of charge via the Internet at http://pubs.acs.org/.

5

Acknowledgements

BK and PR would like to thank the support from the Deutsche Forschungsgemeinschaft under the SPP 1708 project KI768/15-1.

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Molecular Dynamics Simulations of Lithium Doped Ionic-Liquid

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