Molecular Dynamics Simulations of Ionic Liquid Based Electrolytes for

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Molecular Dynamics Simulations of Ionic Liquid Based Electrolytes for Na-Ion Batteries: Effects of Force Field Piotr Kubisiak, and Andrzej Eilmes J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b08258 • Publication Date (Web): 04 Oct 2017 Downloaded from http://pubs.acs.org on October 6, 2017

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The Journal of Physical Chemistry

Molecular Dynamics Simulations of Ionic Liquid Based Electrolytes for Na-ion Batteries: Effects of Force Field

Piotr Kubisiak and Andrzej Eilmes*

Faculty of Chemistry, Jagiellonian University, Gronostajowa 2, 30-387 Kraków, Poland

Abstract Classical molecular dynamics simulations were performed for Na+ conducting electrolytes based on EMIM-TFSI ionic liquid and NaTFSI salt. Several parameterizations of force fields have been tested, including polarizable fields with dipole polarizabilities or Drude-type polarization. Trajectories up to 1 µs long have been used to estimate viscosities, diffusion coefficients and conductivities of electrolytes with increasing amount of sodium salt. Results have been compared to available experimental data. In most cases the best agreement to measured values has been obtained in non-polarizable simulations. Nevertheless, results have indicated the need for further development of polarizable parameterizations, preferably based on Drude polarization model.

*

e-mail: [email protected]

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1. Introduction Development of efficient energy storage technologies is of paramount importance in order to meet the energy needs of modern society. Rechargeable lithium-ion batteries have become very successful energy storage devices and find numerous technological applications. Substantial progress in their development has been made since first commercial Li-ion battery was released in 1991. Increasing demand for such devices, in particular in the prospect of growing market for electric vehicles, raises concerns about possible shortages in supply of lithium salts. Lithium is not regarded as an abundant element in the Earth’s crust; moreover its distribution is uneven, with most known world’s resources located in South America. On the other hand, sodium is one of the most abundant elements, available everywhere at very low price. Sodium batteries are also environment-friendly, showing in average lower environmental impact per kWh of storage capacity than Li-ion cells.1 Na-ion batteries are therefore seen as a promising alternative for Li-ion power sources and one of possible solutions to meet the challenge of increasing demand in a limited-resources and environmentoriented world and have potential to become an innovative technology of the future. Renewed interest in Na-ion batteries and their prospective importance for sustainable development is reflected in rapidly growing number of research publications and reviews related to the use of sodium in energy storage devices.2,3,4,5,6 As a consequence, also Na+ ion conducting electrolytes receive increasing attention.7 Liquid electrolytes for Na-ion batteries may be based on sodium salts (e.g. NaBF4, NaPF6, NaFSI, NaTFSI) and organic solvents such as acetonitrile, linear or cyclic carbonates or ethers.8,9,10,11,12,13 Several electrolytes were prepared as solutions of Na salts in room temperature ionic liquids (usually based on imidazolium or pyrrolidinium derivatives).14,15,16,17,18,19,20,21,22,23 Another class of extensively studied systems are polymer electrolytes, consisting of a metal salt dissolved in a polymer matrix, e.g. poly(ethylene oxide) (PEO); properties of several Na-ion electrolytes of such a type were reported.24,25,26 Polymer-based Na-conducting electrolytes are often plasticized by low weight molecular solvents or by an admixture of ionic liquid in ternary systems.27,28,29,30 Experimental research on electrolytes for lithium batteries was supported by numerous computational works. Similar studies on Na-ion devices are less common. Quantum-chemical calculations or molecular dynamics (MD) simulations include investigations of Na+ binding to organic carbonates31,32,33,34 or to anions of ionic liquids16 and studies on ion-glyme solvate ionic liquids.35,36,37,38 MD simulations were performed for Na-ion electrolytes based on room temperature ionic liquids.39,40 With substantial experimental effort focused on Na-conducting electrolytes, importance of theoretical investigations on these systems will increase. 2


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In this paper we aim to test the performance of MD simulations in modeling of +

Na /ionic liquid electrolytes for which experimental data became available recently. We will present results of classical molecular dynamics simulations for a system of Na salt/imidazolium ionic liquid studied in an experimental work.16 Importance of accounting for polarization effects has been evidenced for several systems with ions, e.g. polymer electrolytes or ionic liquids,41,42,43,44,45,46,47,48,49 therefore in addition to non-polarizable force fields we will test several variants of polarizable parameterizations. Long-time (up to 1 µs) MD simulations will be used to estimate viscosities and conductivities of electrolytes with increasing concentration of Na+ ions. Calculated values will be compared to experimental data.16

2. Computational details Electrolytes studied in experimental work16 were based on 1-ethyl-3-methylimidazolium (EMIM) bis(trifluoromethylsulfonyl)imide (TFSI) ionic liquid with increasing amount of NaTFSI salt. Accordingly, in our calculations we modeled NaxEMIM(1-x)TFSI systems, where x = 0, 0.1, 0.2 or 0.3 is the molar fraction of NaTFSI. Compositions of simulated systems are listed in Table 1. Initial structures were prepared using Packmol software.50 Main MD simulations were performed in NAMD v 2.12 simulation package.51 Nonpolarizable force field for EMIM-TFSI liquid was based on OPLS parameterization52 with bonded parameters taken from Lopes/Pádua field53 and non-bonded from Köddermann’s work.54 Non-bonded parameters for Na+ were adapted from Ref. 55. We will denote this force field parameterizaton as NP1. Based on NP1 force field we constructed a polarizable field in which polarization effects are introduced via Drude oscillators.56 The polarizability α of an atom is represented by light Drude particle with charge qD connected to the parent atom by a harmonic spring. Without an external electric field average position of oscillating particle coincides with the position of the atom. In a field the particle is displaced from the atom and the pair atom-Drude particle carries a dipole moment. The relationship between the charge of the Drude particle qD, polarizability α of the atom and the force constant of the spring kD is given by q D = k Dα

(1)

In our parameterization we set kD = 1000 kcal·mol-1·Å-2. Drude particles were attached to all non-hydrogen atoms of EMIM and TFSI ions. Atomic polarizabilities were adapted from the APPLE&P polarizable force field for liquids and electrolytes.43 With the set value of kD force

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constant, resulting charges of Drude atoms were in the range of 0.87e to 1.78e. This parameterization will be labeled Dr-P1. Inclusion of polarization in MD simulations increases the computational cost; therefore some cheap ways of effective modeling of polarization effects are sought. One of proposed solutions applied to ionic liquids is the charge scaling,57,58 based on the argument that polarizability of the medium reduces interactions between charged particles, and similar effect may be obtained by reduction of partial charges. In this work we tested such an approach, introducing a non-polarizable field sc-P1, which is the parameterization NP1 with all charges scaled by a factor of 0.7. NAMD simulations with NP1, Dr-P1 and sc-P1 force field were performed in the NpT ensemble at p = 1 atm and two temperatures T = 293 and 333 K with Langevin dynamics and modified Nose-Hoover Langevin barostat.59,60 In Dr-P1 simulations Drude oscillators were coupled to a low temperature bath with T = 1 K. A time step of 1 fs (or 0.5 fs in the case of simulations in Dr-P1 field) was used to integrate equations of motion. Periodic boundary conditions were applied to the system, and electrostatic interactions were taken into account via particle mesh Ewald algorithm.61 For reliable estimates of collective properties (viscosity, conductivity) long MD trajectories are preferred, therefore we obtained approx. 1100 ns trajectory for each system; with the last 1000 ns used for the analysis. In order to test different approaches to polarizability modeling we checked also a classical parameterization based on dipole polarizabilities of individual atoms. The dipolepolarizable force field for EMIM-TFSI was the parameterization used in our recent work62 based on the APPLE&P field43 with small modification of C-S-N-S dihedral angle to get the population of conformers closer to that obtained from ab initio molecular dynamics simulations.63 Non-bonded parameters for Na+ ion are from Ref. 55. For simulations with dipole polarizabilities Tinker v. 7.1 software64 was used. As in Ref. 62, induced dipole moments were calculated iteratively assuming mutual interactions between polarizable atoms until self-consistency was achieved. This parameterization will be denoted as P2-mutual. We tested also a simplified procedure implemented in Tinker in which the dipole moments are calculated in a single step as a response to the electric field of permanent charges (therefore contributions from other induced dipoles to the local electric field are disregarded). This setup of polarizable simulations will be labeled as P2-direct. The bonded and non-bonded parameters in P1 and P2 families of our force fields differ, therefore for completeness, in order to compare results we used another parameterization based on P2-

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mutual field parameters but without atomic polarizabilities. This non-polarizable FF will be called NP2. Tinker MD runs with NP2, P2-mutual and P2-direct FFs were conducted in the NpT ensemble with Nose-Hoover integrator65 at the same pressure and temperature conditions as set in NAMD simulations. The Thole scheme of short-range polarization damping66 was used in polarizable simulations. Without efficient parallel implementation, Tinker simulations were much shorter than NAMD runs. Depending on parameterization we collected approximately 15, 40 and 60 ns of the trajectory for P2-mutual, P2-direct and NP2 parameterizations, respectively; the differences in length reflect the relative speed of simulations. Because of limited the length of the MD trajectories, Tinker simulations will serve mainly as an additional check to the NAMD computations. We should note that the polarizable parameterization underlying the P2-mutual field was originally systematically developed43 and then adapted by us for the use in different software. On the other hand, Drude polarizability in Dr-P1 was added on a top of existing parameterization NP1. This may result of double counting of some interactions already effectively incorporated in the original field. Likewise, simple removing polarization from P2mutual to obtain NP2 force field may result in worse performance than in the case of fully reparameterized FF. We used different variants of FFs in order to obtain insight into effects of polarizability, but limitations of these modified fields should be kept in mind.

3. Results and discussion 3. 1. Structure of electrolytes

Densities of simulated electrolytes were calculated as averages over the last 1000 ns or 10 to 30 ns of the MD trajectory; shorter times were used for Tinker trajectories. Results are displayed in Fig. 1. For most parameterizations the difference between experimental and calculated density does not exceed 0.04 g/cm3. The exception is the force field with scaled charges sc-P1 (not shown in Fig. 1) for which density is significantly smaller and ranges between 1.39 and 1.45 g/cm3 at 293 K or between 1.32 and 1.37 g/cm3 at 333 K. In most cases the NP2 and P2-mutual force fields yield the densities closest to experiment; however, it should be pointed out that the P2-mutual FF was parameterized in Ref. 62 to reproduce the density of neat EMIM-TFSI at 298 K. On the other hand, the P2direct FF apparently overestimates the density. It may be noted in Fig. 1 that most shown FFs predict reasonably well changes of the density with NaTFSI concentration – the calculated 5



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curves are approximately parallel to experimental dependence. A clear exception is the FF with Drude polarizability predicting increase of electrolyte density slower than measured. To analyze structures of electrolytes we calculated radial distribution functions (RDFs) for selected atom pairs as averages over the last 5 ns of the trajectory. Sample Na-O RDFs obtained for x=0.1 at 333 K are shown in Fig. 2. Position of the first sharp peak differs slightly between the two families of FFs. The maximum is located at 2.6 or 2.4 Å for NP1 and NP2, respectively. Effect of polarizability implemented either as Drude polarizability in DrP1 or as dipolar polarizability in P2-mutual is a small shift of 0.08 Å to smaller distances. Shift in the same direction of the second maximum at about 5 Å is larger and simultaneously the height of the peak is reduced. Similar small decrease of metal ion – oxygen distances in polarizable fields has been observed in MD simulations of LiTFSI dissolved in EMIMTFSI.48 P2-direct FF gives the same position of the first maximum as P2-mutual, but the shift of the second peak is much larger (to the position about 3.8 Å) and the peak is much more diffuse. Effect of charge scaling is the opposite to the effect of polarization: in sc-P1 simulations both maxima in Na-O RDF move to larger distances. Coordination numbers predicted in both families of FFs are similar. Average numbers of O atoms at 3.5 Å from the Na+ ion are 5.8 and 6.1 for NP1 and NP2, respectively. Polarization increases the width of the peaks in RDF, therefore reduces the plateau on the running coordination number curve. The numbers of coordinating oxygens are 5.4 and 5.9 for Dr-P1 and P2-mutual, respectively. Values from polarizable FFs (in particular Dr-P1) agree with the experimental16 finding that the sodium cation interacts with three TSFI anions and with the results of quantum-chemical structure optimization of [Na(TFSI)3]2- complex showing preferred coordination by five oxygen atoms.16 In Fig. 3 we display sample distributions of Na+ ions in selected electrolytes. For all concentrations of NaTFSI the system at the nanoscale is inhomogeneous at given moment of time as shown in Figs. 3a-3c. There are parts of the sample free from Na+ cations, while in other regions Na+ concentration is apparently larger than average. However, the structure is dynamic; regions of low and high sodium concentration change positions within the sample (compare Figs. 3a and 3b) and therefore the distribution of ions averaged over longer period of time is uniform and the overall structure of electrolyte homogeneous. Sample RDFs for Na-Na ions are presented in Fig. 4. Two main peaks at about 6 and 12.5 Å are observed in both NP1 and NP2 force fields. In polarizable Dr-P1 and P2-mutual FFs the maxima move towards smaller distances and the height of the first peak is reduced. As shown earlier for Na-O RDFs, charge scaling has the effect opposite to polarizability also 6


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in the case of Na-Na RDFs. The Na-Na RDF obtained in P2-direct field is very different from other distributions. Appearance of the maximum at 3 Å and change of the scale by an order of magnitude suggest dramatic change in the structure of the electrolyte. Indeed, as readily seen in Fig 3d, Na+ ions form aggregates containing closely packed sodium cations. Such an effect may be attributed to the “overpolarization” of the sample. Dipole moments calculated at the first step are too large, and they are reduced by mutual interactions in the next steps of the iterative procedure leading to self-consistency of induced dipoles. However, P2-direct calculations use solely the first step, and overestimate dipole moments. Therefore aggregation of Na+ ions is energetically favorable, because it leads to larger local electric fields and larger stabilization, though at a price of unphysical structure of the system. From the analysis of structures of electrolytes we may conclude that both “cheap” ways of accounting for polarization have failed. This is evident in the case of P2-direct FF yielding completely wrong structures. Nevertheless, we will present some results obtained for this parameterization in tables, in order to show to what extent unphysical structure of electrolyte affects the results. Charge scaling gives too small densities and behaves differently than “truly” polarizable FFs, therefore it is unlikely that this parameterization would yield results close to experiment. On the other hand, NP1 and NP2 behave similarly and polarization effects in Dr-P1 and P2-mutual are comparable, therefore we will focus mainly on these four parameterizations. Another structural property of the electrolyte which we analyzed is the distribution of conformers of the anion. Owing to its flexibility, the TFSI- anion can exist in different conformations. Quantum-chemical calculations and spectroscopic studies indicate that the energy separation between cis and trans conformers is small (about 1 kcal/mol) and both conformations coexist in the liquid with preference for the trans conformer.67 Interactions with Na+ ion are likely to affect the ratio of different conformations of TFSI-, therefore we checked the percentage of anion conformers in electrolytes with increasing NaTFSI concentration. In Fig. 5 we present changes in the distribution of C-S-S-C dihedral angle in the anion with increasing salt content for different force fields. It is evident that while the two nonpolarizable FFs predict large probability of dihedral angle values close to ±180 °, the number of trans conformations decreases in the polarizable P2-mutual field and is reduced to zero in Dr-P1 structures. Lack of trans conformations in a polarizable force field of the P2-mutual type was observed in recent simulations.63 In this work, as described in Sec. 2, some parameters were modified to obtain better agreement to ab initio simulations, therefore trans 7



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conformations are populated in simulations using the P2 family of FFs. Apparently, inclusion of the polarizability decreases abundance of trans conformers, even to zero in the case of DrP1 field (to which no adjustment has been made). Interestingly, the same effect of disappearance of trans conformations is observed in simulations using scaled charges. As seen in Fig. 5, increasing concentration of Na salt decreases probability of large absolute values of CSSC angle and increases amount of anions with CSSC dihedral close to zero. Changes in the percentage of different conformations of the anion are displayed in Fig. 6. For this purpose we classified the cis, gauche and trans conformers as the structures with the CSSC dihedral angle within the interval of ±30° around 0°, ±30° and ± 180°, respectively. Note, that due to shorter trajectories, the averaging is worse for P2 family of FFs. In nonpolarizable NP1 and NP2 FFs, the trans conformations are the most populated. Their number is significantly smaller in P2-mutual field and they vanish completely in the parameterization using Drude polarizabilities. In all fields population of cis conformation grows with increasing amount of Na salt in the electrolyte. This is usually accompanied by decrease of populations of trans and gauche conformers, with the exceptions of P2-mutual FF in which the gauche population remains approximately constant and Dr-P1 parameterization yielding no trans conformations at any salt concentration. The effect of NaTFSI addition to EMIM-TFSI liquid is the increasing probability of finding the TFSI- anion in the cis conformation. Interaction of the anion with small Na+ cation is expected to increase barriers for cis-trans conformational transition, reducing the flexibility of the anion. This will have implications for transport properties, because ion mobility in EMIM-TFSI is coupled to the conformational dynamics of the anion.68,69 It has been shown that artificially increased barriers for conformational changes slow down ion diffusion in MD simulations of ILs with TFSI anion.68 Experimentally measured decrease of TFSI- mobility in EMIM-TFSI under high pressure led to conclusion that twists between two conformations facilitate anion movements through the liquid.69 Hindering of the conformational changes by anion interactions with Na+ cation should therefore reduce the TFSI- diffusion in IL/salt electrolytes at higher salt concentrations.

3. 2. Viscosity

Viscosity of the electrolyte can be calculated from the Green-Kubo relation as the integral over time of the pressure tensor autocorrelation function:

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η=

V kT

∞

∫

Pαβ (t ) Pαβ (0) dt

(2)

0

where Pαβ is the αβ component of the pressure tensor, V is the volume of the system, T is temperature, k stands for the Boltzmann constant and the brackets indicate the ensemble average. To obtain better statistics calculated values were also averaged over independent components of the pressure tensor. Ideally, the autocorrelation function of the pressure tensor decays to zero in the limit of infinite time and the integral approaches a constant value. In practice, this is usually not observed because of the long-time noise causing fluctuations of the integrated value. The viscosity is a collective property, therefore increased number of molecules/ions in the system does not improve statistics; instead, very long trajectories are required. Issue of reliable estimation of viscosity has been discussed in a recent work presenting a time decomposition method.70 Here we applied a simpler approach. The trajectory was divided into N parts and the results of integration according to Eq. 2 were averaged over all parts. The number N has to be such that the length of individual part is sufficient to observe decay of the autocorrelation function to zero value. In case of NAMD trajectories of µs length in most cases we were able to use N equal 100 or 200. For short Tinker simulations N was between 5 and 1. The difference between viscosity values obtained for different N was used as an error estimate. In Fig. 7 we present an example of averaged values of running integrals for electrolytes simulated in the NP1 force field at 333 K. For low concentrations of NaTFSI the plateau of integrated value is reached at about 2 ns. At highest concentration (x = 0.3) the viscosity is the largest, resulting in slow decay of pressure tensor autocorrelation function and approximately constant value of η is reached at the time close to 10 ns. Systems with high viscosities are therefore prone to larger errors of estimated values; the errors are also large for Tinker simulations because of worse averaging. Calculated viscosities are collected in Table 2 and displayed in Fig. 8. Unfortunately, in Ref. 16, viscosities are shown for Na+ concentrations different than for conductivities; therefore comparison with measured data is possible only for small x values. The agreement of NP1 data to the experiment is quite satisfactory. Also NP2 parameterization performs reasonably well, especially at 333 K or at low NaTFSI concentrations. It is also noticeable that only nonpolarizable fields reproduce correctly increase of the viscosity with increasing x. Conversely, viscosities from Dr-P1 field exhibit practically no concentration dependence. Polarizable force fields yield too small viscosities, with underestimation of measured data

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increasing from Dr-P1, through P2-mutual to P2-direct. Scaled-charges sc-P1 force field gives completely wrong values, order of magnitude too small.

3.3. Ion transport

Diffusion coefficients and conductivities of modeled electrolytes were estimated from ion displacements traced in MD trajectories. Diffusion coefficient of ion i was calculated from the slope of the time dependence of its mean square displacement (MSD):

Di = lim t →∞

1 2 R i (t ) − R i (0) 6t

(3)

Conductivity of the system can be calculated using the Einstein formula as71 e2 t →∞ 6tVk T B

λ = lim

∑z z i

j

[R i (t ) − R i (0)][R j (t ) − R j (0)]

(4)

i, j

In the above formulas t stands for time, V is the volume of the simulation box, kB is the Boltzmann’s constant, T is the temperature, e is elementary charge, zi and zj are the charges of ions i and j, Ri(t) is the position of i-th ion at time t and the brackets

denote the ensemble

average. The conductivity is proportional to the collective ion diffusion coefficient: 1 t →∞ 6tN

Dcoll = lim

∑z z i

j

[R i (t ) − R i (0)][R j (t ) − R j (0)]

(5)

i, j

N is the total number of ions in the system. Dcoll would reduce to the average of anion and cation diffusion coefficients Davg = (D– + D+)/2 if there is no correlation between movements of different ions, i.e. when the off-diagonal terms in (5) are negligibly small. In Fig. 9 we display double-logarithmic plots of mean square displacements of ions and the collective MSD obtained in NP1 or Dr-P1 force fields at 333 K and x=0.1. The MSD scales with time as MSD ∝ tβ. For intermediate time scales in viscous liquids, a subdiffusive regime is observed, with β < 1, because ions are trapped in local energy minima. At long times the system approaches diffusive regime and for diffusive motion β = 1. In Fig. 9 the slope of the log(MSD) vs. log(t) line increases with time from subdiffusive to approaching the diffusive motion regime at about 10 ns. For longer times the ideal plot would be therefore a straight line with slope equal one. This behavior is observed for MSD of ions, with some deviations at long times resulting from poorer averaging (the data are averaged over all possible choices of time intervals within trajectory, therefore the number of averaged values

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decreases in the plot from left to right, i.e. from short to long times). Averaging of collective MSD requires even longer times than the displacements of ions; the deviations from straight line are more pronounced and they increase above 100 ns. To calculate the values of diffusion coefficients and conductivity we used therefore the first 10 % of total timescale; errors were estimated as the span of the values obtained in the time interval between 8 and 10 % of the trajectory. For NAMD trajectories this means that we restricted analysis up to 100 ns, i.e. to the time interval in which diffusive motion is observed and deviations from the ideal dependence are small. We should, however, note that this does not mean that only 10 % of the whole 1 µs trajectory was used – in fact time-averaging was done over the whole trajectory and the µs length was crucial to sufficiently sample time intervals up to 100 ns to produce well averaged data. Because of short Tinker trajectories (P2 family of force fields) time used to calculate transport properties from these data was limited to 10 – 30 ns and the results are supposed to have larger error bars. We should also note that the estimates of error bars shown in Table 4 were based on a single trajectory. One may expect that (given limited size of simulation boxes) there would be differences between data obtained for independent simulations of the same system. Such simulations would certainly improve averaging, but their cost was prohibitive. Therefore the error bars shown here are presumably too small. Diffusion coefficients of Na+, EMIM+ and TFSI- ions obtained from non-polarizable and polarizable FFs are compared in Fig. 10. In all cases polarization leads to increase of diffusion; this effect has been observed in several MD simulations of electrolytes.41,44,45,48 P2mutual force field yields diffusion coefficients 2-3 times larger than simulations with NP1, NP2 and Dr-P1 fields, this effect may be partially attributed to smaller viscosity. Nevertheless, diffusion coefficients for all systems are rather small, of the order of 10-11 m2/s. With increasing salt concentration, diffusion decreases, especially in non-polarizable fields; in simulations with Drude polarization this decrease is slower. There is no data on ion diffusion coefficients in experimental study of NaTFSI/EMIMTFSI electrolytes16 therefore we can only compare our predictions to the results for neat EMIM-TFSI liquid.72,73 Table 3 presents experimental values and results obtained in the four parameterizations. Although polarization increases the diffusion coefficients estimated in DrP1 field, all NP1, NP2 and Dr-P1 FFs yield values 2-3 times smaller than measured. On the other hand, P2-mutual parameterization overestimates ion mobility up to 50 %. Calculated conductivities are collected in Table 4 and displayed in Fig. 11. Both nonpolarizable fields yield similar values about two times smaller than experimental data and 11



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correctly reproduce decrease of conductivity in electrolytes with larger amount of Na+ ions. At 293 K the results of Dr-P1 simulations within their error estimates practically do not depend on x and underestimate λ at low salt concentrations while overestimating it in concentrated electrolytes. At 333 K conductivity obtained from Dr-P1 field decreases with x but slower than experimental data, therefore while it agrees with measured values at x = 0.2 or 0.3, it is underestimated for small x. Polarizable P2-mutual parameterization in all cases predicted too large conductivities in agreement with overestimated diffusion coefficients. Consistently with significantly underestimated viscosities, the approach using charge scaling largely overestimates conductivities of electrolytes. Overall agreement between NP1 or Dr-P1 results and measured conductivities is quite satisfactory with a factor of two for largest differences between simulations and experiment. Dr-P1 predictions are in general closer to experiment, but at 293 K the λ vs. concentration dependence is not properly reproduced and the conductivity is almost constant within error bars. In other simulations (except sc-P1 data which are overestimated and with larger errors) conductivity generally decreases with salt content, some deviations are most likely caused by insufficient averaging. NP2 results are not much worse than NP1, therefore both nonpolarizable fields perform comparably (however, parallelized NP1 simulations in NAMD make possible to collect long trajectories). Accuracy of P2-mutual estimates of conductivity still may be acceptable, but such simulations are not recommended given the larger computational effort compared to non-polarizable NP2 field. We tried to get some more insight into the changes of conductivity from the analysis of different components to the values calculated according to Eq. 4. The main contribution to the conductivity (or equivalently to the collective diffusion coefficients) arises from diffusivities of individual ions, given by diagonal terms in Eq. 4. This value is modified by contributions arising from correlations between motions of different ions – off-diagonal terms in Eq. 4. Contributions from anticorrelated motions of ions of same charge, i.e. cation-cation and anion-anion terms are negative; therefore they reduce conductivity of the electrolyte. Offdiagonal anion-cation component is positive and contributes toward increase of conductivity. Therefore the difference between collective diffusion coefficient and the average of diffusion coefficients for ions composing the electrolyte depends on the balance of off-diagonal components. Negative contributions from cation-cation and anion-anion terms may seem surprising at first glimpse, but they are general properties of ILs. It has been shown, that unlike salt solutions in molecular liquids, in ionic liquid motions of ions of the same charge are on 12


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average anticorrelated and movements of ions of opposite charge enhance the conductivity.74 This effect originates from momentum conservation law, which may be satisfied by the movements of neutral solvent molecules in electrolyte solutions, but imposes additional constraint on ion motions in ionic liquids and molten salts composed entirely of ions.74 We have confirmed this behavior in MD simulations for other ionic liquids.75 In Fig. 12 we display stacked charts presenting different contributions to conductivity at 333 K for four force fields. In each panel values are scaled in such a way that 100 % corresponds to the total value for neat EMIM-TFSI (x=0). Note that cation-cation and anionanion contributions (red and orange areas) are negative; therefore they should be subtracted from the sum of other contributions to get the final value. There is a clear difference between non-polarizable and polarizable FFs. In the parameterizations NP1 and NP2 diagonal contributions decrease significantly with salt concentration in accord with the decrease of diffusion coefficients of ions (Cf. Fig. 10). The off-diagonal contributions also become smaller, but decrease of anion-anion and cation-cation components is faster than the decrease of the anion-cation term. As a result, in neat ionic liquid, sum of all off-diagonal terms is negative, reducing the conductivity, while at x > 0, sum of off-diagonal terms is larger than zero, contributing positively to the total value. In Dr-P1 results, on the other hand, sum of diagonal contributions does not decrease with salt concentration, in agreement with slowly changing diffusion coefficients (Cf. Fig. 10). It may be noted that the contribution from Na+ ions, although still small, increases visibly in concentrated electrolytes. In the contrast to non-polarizable fields, anion-anion and cationcation contributions do not decrease with NaTFSI content and their sum is larger than the anion-cation contribution, therefore destructive effect of off-diagonal correlations prevails and increases with x. P2-mutual results are somewhat different compared to Dr-P1 – diagonal components decrease, but not as fast as in nonpolarizable fields. On the other hand, after initial reduction between x=0 and x=0.1, sum of anion-anion and cation-cation does not decrease further with x and dominates the total off-diagonal contribution; therefore, P2mutual data resemble Dr-P2 results rather than NP1 or NP2. We may conclude that even though both non-polarizable and polarizable fields predict decrease of the conductivity of the electrolyte with increasing x, origin of this dependence is different. In non-polarizable fields it results from the decrease of diffusion coefficients and off-diagonal correlations between ion motions contribute constructively toward final value. In polarizable fields, diffusion coefficients (diagonal terms) do not change that much with salt

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concentration and the decrease of the conductivity originates from increasing destructive effect of off-diagonal correlations.

3.4. Discussion In the view of the results presented above there is no simple answer to the question which parameterization is the best for modeling of NaTFSI/ionic liquid electrolytes. For most properties both non-polarizable force fields seem to perform well without major differences between NP1 and NP2. Moreover, they predict correct dependences of simulated properties on Na salt concentration. Polarizable force fields Dr-P1 and P2-mutual failed at reproducing some trends and usually give values farther from experiment than NPx FFs. Dr-P1 field yields the structures with negligible percentage of trans conformer of the anion (although changes in the abundance of cis conformation are similar in all fields). On the other hand, in some cases polarizable FFs perform better than other parameterizations: P2-mutual is the best for diffusion coefficients in neat EMIM-TFSI and Dr-P1 is the closest to experimental values of conductivity at 333 K. Nevertheless, given larger cost of polarizable force fields, their overall performance is not satisfactory. As shown in Sec. 3.1 simulations with P2-direct force field resulted in unphysical structures of electrolyte. Viscosities and conductivities calculated in this FF are, however, not very different from other parameterizations and do not indicate failure of the model, which might have escaped attention without analysis of RDFs or visual inspection of the structure. This stresses the importance of thorough checking the simulated structures for which transport properties have to be computed. The problem with Dr-P1 force field may be related to the way in which polarizabilities were introduced into non-polarizable field NP1 without modification of other parameters. It is therefore reasonable to seek a better parameterization of a polarizable force field in future studies, given that some effects (e.g. related to ion transport) are differently described by polarizable and non-polarizable FFs. Several methodologies to develop polarizable FFs for liquids were presented recently,76,77,78 including approaches employing symmetry adapted perturbation theory used to parameterize intermolecular interactions,76,77 thus in principle enabling one to construct such parameterization on the ground of quantum-chemical calculations without necessity to use experimental data. Based on the results presented in this work and computational efficiency of different parameterization we can suggest that the nonpolarizable force field of the type NP1 is a good starting point for modeling of Na-ion/ionic

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liquid electrolytes and the effort should be invested in the improvement of Drude-type polarizable FF.

5. Conclusions We performed series of molecular dynamics simulations for Na-ion conducing electrolytes NaTFSI/EMIM-TFSI with increasing Na+ concentration to model the effect of salt addition on the properties of electrolytes. Several non-polarizable and polarizable parameterizations of force field were tested in search of a FF yielding good reproduction of experimental data at reasonable computational cost. Structural properties of electrolytes (radial distribution functions or conformations of anions) were analyzed. MD trajectories up to 1 µs long were used to calculate viscosities and ion transport properties. As shown in this work, results obtained within different parameterizations and their agreement with measured values may significantly depend on the type of force field. Predictions of non-polarizable calculations generally agree with available experimental data and reproduce trends observed in electrolytes with increasing salt content, confirming applicability of the methodology used here to the modeling of electrolytes for Na-ion devices. The non-polarizable parameterizations are also less expensive computationally and therefore may constitute reasonable compromise between speed and accuracy. With some exceptions, performance of polarizable force fields was worse. Notably, the inexpensive protocols of modeling of polarization effects: non-iterative computation of induced dipoles or charge scaling failed, with the former leading to seriously under- or overestimated properties and the latter producing unphysical structures. Therefore, only more expensive ways of accounting for polarization yielded reasonable results. Nevertheless, some trends were better reproduced in polarizable simulations suggesting that such FFs are worth investing effort in improving the parameterization. We showed that for some properties, e.g. changes of electrolyte conductivity with salt content, physical origins of observed effects may differ in details between polarizable and non-polarizable simulations. This is another indication that polarization effects may play important role and should be investigated in computational studies of salt/IL electrolytes. Therefore, further development of improved and rigorously constructed force fields (e.g. based on ab initio calculations used to parameterize interactions) is desirable. We hope that our results will provide some directions for future research in this field.

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Acknowledgments This work was supported by the National Science Centre (Poland) grant no. UMO2016/21/B/ST4/02110. The research was supported by PL-Grid computational infrastructure. Part of equipment used in calculations was purchased with the financial support from the European Regional Development Fund in the framework of the Polish Innovation Economy Operational Program (contract no. POIG.02.01.00-12-023/08).

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Figure captions

Fig. 1. Densities calculated for simulated NaxEMIM(1-x)TFSI electrolytes. Experimental data from Ref. 16.

Fig. 2. Radial distribution functions for Na-O atom pairs and running coordination numbers N(r) obtained from MD simulations with different force fields for electrolyte x=0.3 at T= 333 K. Fig. 3. Selected snapshots of simulation boxes; Na+ ions displayed as spheres. (a,b) system with x=0.1 at 333 K in NP1 FF at two points of the trajectory; (c) system with x=0.3 at 333 K in NP1 FF; (d) system with x=0.3 at 333 K in P2-direct FF.

Fig. 4. Radial distribution functions for Na-Na ion pairs obtained from MD simulations with different force fields for electrolyte x=0.3 at T= 333 K. Fig. 5. Distributions of the C-S-S-C dihedral angle in TFSI- anions obtained in different force fields for increasing salt concentration. Fig. 6. Percentage of different conformations of TFSI- anions obtained in different force fields for increasing salt concentration.

Fig. 7. Running values of the viscosity integrated for electrolytes simulated in NP1 field at T= 333 K.

Fig. 8. Viscosities estimated for simulated NaxEMIM(1-x)TFSI electrolytes. Experimental data from Ref. 16.

Fig. 9. Double-logarithmic plot of mean square displacements of ions and collective mean square displacement obtained for x=0.1 electrolyte at T = 333 K.

Fig. 10. Diffusion coefficients obtained from MD simulations. Open symbols and broken lines – non-polarizable FFs; filled symbols and solid lines – polarizable FFs.

24


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Fig. 11. Conductivities estimated for simulated NaxEMIM(1-x)TFSI electrolytes. Experimental data from Ref. 16.

Fig. 12. Contributions to collective diffusion coefficients for NaxEMIM(1-x)TFSI electrolytes at T= 333 K. In each panel (force field) 100 % equals the sum of all contributions for x = 0.

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Table 1. Compositions of NaxEMIM(1-x)TFSI simulation boxes.

x

Na+

EMIM+

TFSI-

total atoms

0

0

142

142

4828

0.1

15

135

150

4830

0.2

32

128

160

4864

0.3

51

119

170

4862

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Table 2. Experimental and calculated viscosities (in Pa⋅s) of NaxEMIM(1-x)TFSI electrolytes. Relative errors are given in parentheses.

293 K x=0

x=0.1

x=0.2

a

a

x=0.3

exp. (Ref. 16)

0.04

0.067

0.127

NP1

0.043 (8 %)

0.061 (2 %)

0.104 (1 %)

0.25 (16 %)

NP2

0.051 (8 %)

0.088 (4 %)

0.36 (9 %)

0.4 (20 %)

Dr-P1

0.026 (2 %)

0.027 (6 %)

0.03 (4 %)

0.032 (4 %)

P2-direct

0.008 (6 %)

0.015 (10 %)

0.013 (8 %)

0.018 (7 %)

P2-mutual

0.011 (7 %)

0.018 (9 %)

0.027 (8 %)

0.035 (22 %)

sc-P1

0.003 (8 %)

0.003 (4 %)

0.001 (8 %)

0.003 (5 %)

x=0

x=0.1

x=0.2

x=0.3

333 K a

a

exp. (Ref. 16)

0.012

0.018

0.029

NP1

0.013 (4 %)

0.016 (2 %)

0.024 (2 %)

0.053 (5 %)

NP2

0.014 (17 %)

0.015 (3 %)

0.025 (3 %)

0.085 (20 %)

Dr-P1

0.008 (6 %)

0.008 (9 %)

0.008 (9 %)

0.008 (9 %)

P2-direct

0.003 (8 %)

0.003 (1 %)

0.004 (6 %)

0.009 (10 %)

P2-mutual

0.005 (10 %)

0.005 (10 %)

0.006 (4 %)

0.007 (10 %)

sc-P1

0.001 (3 %)

0.001 (2 %)

0.001 (4 %)

0.002 (3 %)

a

values estimated from the quadratic fit to the experimental data

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Table 3. Diffusion coefficients calculated for EMIM-TFSI ionic liquid. DEMIM, 10-11 m2/s T = 293 K experimenta

4.1

experimentb

4.7

DTFSI, 10-11 m2/s

T = 333 K 14

T = 293 K 2.5

T = 333 K 9

2.8

NP1

2.0 ± 0.03

5.7 ± 0.09

1.0 ± 0.01

3.1 ± 0.03

NP2

2.0 ± 0.02

7.2 ± 0.03

0.9 ± 0.03

3.7 ± 0.02

Dr-P1

2.2 ± 0.01

7.2 ± 0.08

1.1 ± 0.01

3.9 ± 0.08

P2-mutual

6.2 ± 0.15

17 ± 0.19

3.5 ± 0.14

10 ± 0.14

a

Ref. 72

b

data for T = 295 K from Ref. 73

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Table 4. Experimental and calculated conductivities (in S/m) of NaxEMIM(1-x)TFSI electrolytes. Relative errors are given in parentheses

293 K x=0

x=0.1

x=0.2

x=0.3

exp.

0.89

0.55

0.27

0.24

NP1

0.44 (1 %)

0.27 (2 %)

0.15 (7 %)

0.12 (3 %)

NP2

0.31 (6 %)

0.24 (10 %)

0.14 (9 %)

0.06 (1 %)

Dr-P1

0.39 (5 %)

0.36 (3 %)

0.42 (3 %)

0.38 (4 %)

P2-direct

1.40 (3 %)

1.45 (4 %)

0.69 (4 %)

0.52 (4 %)

P2-mutual

1.05 (2 %)

1.08 (2 %)

0.87 (3 %)

0.61 (6 %)

sc-P1

2.24 (4 %)

2.60 (1 %)

2.35 (3 %)

2.70 (6 %)

333 K x=0

x=0.1

x=0.2

x=0.3

exp.

2.17

1.96

1.18

1.00

NP1

1.01 (3 %)

0.90 (2 %)

0.73 (6 %)

0.51 (4 %)

NP2

1.16 (6 %)

1.13 (3 %)

0.46 (1 %)

0.31 (2 %)

Dr-P1

1.47 (2 %)

1.29 (4 %)

1.02 (1 %)

0.98 (1 %)

P2-direct

3.03 (2 %)

1.39 (16 %)

1.22 (6 %)

1.03 (4 %)

P2-mutual

2.72 (1 %)

2.82 (3 %)

2.04 (1 %)

1.54 (5 %)

sc-P1

5.54 (3 %)

5.05 (2 %)

5.19 (6 %)

5.34 (1 %)

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Fig. 1. Densities calculated for simulated NaxEMIM(1-x)TFSI electrolytes. Experimental data from Ref. 16.

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Fig. 2. Radial distribution functions for Na-O atom pairs and running coordination numbers N(r) obtained from MD simulations with different force fields for electrolyte x=0.3 at T= 333 K.

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Fig. 3. Selected snapshots of simulation boxes; Na+ ions displayed as spheres. (a,b) system with x=0.1 at 333 K in NP1 FF at two points of the trajectory; (c) system with x=0.3 at 333 K in NP1 FF; (d) system with x=0.3 at 333 K in P2-direct FF.

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Fig. 4. Radial distribution functions for Na-Na ion pairs obtained from MD simulations with different force fields for electrolyte x=0.3 at T= 333 K.

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Fig. 5. Distributions of the C-S-S-C dihedral angle in TFSI- anions obtained in different force fields for increasing salt concentration.

34


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Fig. 6. Percentage of different conformations of TFSI- anions obtained in different force fields for increasing salt concentration.

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Fig. 7. Running values of the viscosity integrated for electrolytes simulated in NP1 field at T= 333 K.

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Fig. 8. Viscosities estimated for simulated NaxEMIM(1-x)TFSI electrolytes. Experimental data from Ref. 16.

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Fig. 9. Double-logarithmic plot of mean square displacements of ions and collective mean square displacement obtained for x=0.1 electrolyte at T = 333 K.

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Fig. 10. Diffusion coefficients obtained from MD simulations. Open symbols and broken lines – non-polarizable FFs; filled symbols and solid lines – polarizable FFs.

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Fig. 11. Conductivities estimated for simulated NaxEMIM(1-x)TFSI electrolytes. Experimental data from Ref. 16.

40


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Fig. 12. Contributions to collective diffusion coefficients for NaxEMIM(1-x)TFSI electrolytes at T= 333 K. In each panel (force field) 100 % equals the sum of all contributions for x = 0.

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Molecular Dynamics Simulations of Ionic Liquid Based Electrolytes for

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