Solvation of Mg2+ Ions in Mg(TFSI)2âDimethoxyethane Electrolytes

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C: Energy Conversion and Storage; Energy and Charge Transport 2+

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Solvation of Mg Ion in Mg(TFSI)/Dimethoxyethane Electrolytes – a View from Molecular Dynamics Simulations Piotr Kubisiak, and Andrzej Eilmes J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02460 • Publication Date (Web): 23 May 2018 Downloaded from http://pubs.acs.org on May 23, 2018

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The Journal of Physical Chemistry

Solvation of Mg2+ Ion in Mg(TFSI)2/Dimethoxyethane Electrolytes – a View from Molecular Dynamics Simulations

Piotr Kubisiak and Andrzej Eilmes*

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

*

e-mail: [email protected]

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Abstract

Classical, polarizable molecular dynamics simulations have been performed for a series of Mg(N(SO2CF3)2)2/dimethoxyethane electrolytes with salt concentration varying in the range c = 0.1 – 1.2 M. It has been found that in dimethoxyethane solutions magnesium salt exists as free ions, with metal cations coordinated to solvent molecules. Cation-solvent interactions favor TTT, TGT and TGG’ conformations of dimethoxyethane, modifying population of conformers in the electrolyte. Mg2+ ions form stable solvates with about three dimethoxyethane molecules. Two sets of solvent molecules with different mobility have been detected in simulations: fast diffusing free solvent molecules and dimethoxyethane molecules bound in the solvates, diffusing slowly with magnesium ions. All these findings are in good agreement with recent experimental data.


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1. Introduction Although lithium-ion rechargeable batteries have proved to be very successful energy storage devices, concerns related to sustainable supply of lithium salts and the need to provide high energy densities stimulate interest in alternative chemistries of batteries, such as sodiumion or multivalent ion batteries. Therefore significant effort is invested in experimental and computational studies on magnesium-based devices.1,2,3,4 An important part of this activity is focused on research on magnesium conducting electrolytes, as an electrolyte with optimized properties is a key component of an efficient storage device. Several classes of electrolytes for Mg batteries are investigated, including solutions of magnesium salts in molecular organic liquids. Many of these electrolytes use monoglyme or higher glymes as solvents.5,6,7,8,9,10,11 Measurements of transport properties9,10 are elucidated with help of X-ray scattering structural studies,5,10,11 and the analysis of interactions between ions and solvent molecules based on vibrational spectra,9,10 supported by quantum chemical calculations8,9,10,12,13 and molecular dynamics (MD) simulations.8,13 In a recent paper solutions of Mg(N(SO2CF3)2)2 (Mg(TFSI)2) in dimethoxyethane (DME) in a wide range of salt concentration were studied by means of single-crystal X-ray diffraction and NMR or Raman spectroscopy.14 An unique behavior of the system was observed: in a certain salt content range, Mg(TFSI)2 solution in DME forms two immiscible phases. The two layers differ in Mg2+ concentration and the distribution of DME conformers; the phase with higher concentration of Mg2+ ions is enriched in TGG, TGG’ and TGT conformers, while the dilute phase is rich with DME molecules in TTT and TTG conformations. Analysis of diffraction data and Raman spectra led to the conclusion that in the DME solution salt cations form exceedingly stable Mg2+⋅3DME solvates. Measured selfdiffusion coefficients suggested that the salt exists as free ions and showed that distinct values of diffusivity can be measured for free solvent molecules and those engaged in the cation solvation shell. Quantum-chemical calculations were used in Ref. 14 to support the analysis of Raman spectra. However, molecular dynamics (MD) simulations would be an essential tool in elucidating structural information and transport properties of Mg(TFSI)2/DME solutions. With the help of MD data deeper insight can be gained into physical processes underlying the observed phenomena, providing new information of relevance to electrochemistry and to solution chemistry as well. In this work we report classical molecular dynamics simulations for Mg(TFSI)2 solutions in dimethoxyethane. Collected data will be analyzed in the context of the structure 3 ACS Paragon Plus Environment


of solution, stability of magnesium solvates and estimated diffusion coefficients. Results will be discussed with regard to experimental data reported in Ref. 14.

2. Methods Most of MD simulations reported in this work were performed in NAMD v 2.7b3 simulation package.15 Force field (FF) parameters for TFSI anion were based on the OPLS parameterization16 with bonded parameters taken from Lopes/Pádua force field17 and nonbonded from Köddermann’s work.18 Parameters for DME molecules were adapted from the work of Anderson and Wilson19 except for parameters describing C-C-O-C and O-C-C-O torsional angles which were taken from ref. 20 (we will denote this parameterization as FF1NP) or from GAFF parameterization21 (FF2-NP parameterization). Non-bonded parameters for Mg2+ cation were taken from AMOEBA-PRO-13 force field22 and the depth of the potential minimum was later slightly modified in order to obtain Mg-ODME distances closer to the values calculated quantum-chemically in an implicit solvent study of ion complexation to oligoglymes.23 Based on these two non-polarizable force fields we constructed polarizable parameterizations with polarization effects included via Drude oscillators.24 Drude particles were attached to all non-hydrogen atoms of DME molecules and TFSI anions; because the polarizability of the Mg2+ ion is small, we did not use Drude oscillators for cations. Atomic polarizabilities and charges for TFSI anion were based on the APPLE&P force field25 whereas parameters for DME molecule were taken from the work on poly(ethylene oxide).26 Force field parameterizations with Drude polarizabilities will be denoted as FF1-DP and FF2-DP. Parameters for all FFs are listed in Supporting Information. NAMD simulations were performed in the NpT ensemble at p = 1 atm and T = 293 K with Langevin dynamics and modified Nose-Hoover Langevin barostat.27,28 Time step of 0.5 fs 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.29 Experimental results of ref. 14 show the dependence of the population of DME conformers on salt concentration. To be able to study this effect we had to ensure that our simulations yield correct percentage of conformers in neat solvent. In room temperature the five most abundant conformers in liquid DME are TGT, TGG, TGG’, TTT and TTG (conformations of DME molecule are shown in Supporting Information).30 Populations of DME conformers obtained for different FF parameterizations from about 5 ns of MD simulations for neat DME are displayed in Fig. 1. All parameterizations overestimate 4 ACS Paragon Plus Environment

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abundance of TGT conformers while underestimating percentage of TTx conformations. Abundance of the TGG conformer is similar both in polarizable and non-polarizable fields and agrees well with the experiment. For TGT and TGG’ conformers polarizable FFs perform better than their non-polarizable counterparts. For TGG’ the FF1-DP is better than the FF2DP, for TGT the opposite trend is observed. Most tested FFs show poor agreement with experimental results for TTT and TTG conformations. The FF2-DP parameterization is the sole FF yielding reasonable (although still too low) populations of TTT and TTG conformers. Therefore, most of MD simulations in this work were performed in the FF2-DP polarizable field, because only this parameterization yields non-negligible percentage of TTx conformers in neat DME, allowing us to study the decrease in theirs populations reported experimentally.

Fig. 1. Distributions of DME conformers obtained from MD simulations of neat liquid in different force fields. Experimental data from Ref. 30. To test whether the ratio of different DME conformers may be related to their relative energies we compared energies of different conformations calculated in different FFs and quantum-chemically (Table S2 in Supporting Information). Energy differences are small and although there are some trends noticeable, e.g. the most abundant TGT and TGG’ conformers are the most stable in non-polarizable fields, generally there is no correlation between relative energies and abundance of DME conformers. In particular, in FF2-DP field the TTT conformer appears to be quite stable, but its abundance in experiment and in our simulations is low. However, we should note that although polarization changes relative energies of isolated DME conformers, the full effect of polarization can be observed only when many molecules interact. Therefore we concluded that the proportions of DME conformers in simulations in different FFs reflect not the relative stabilities of isolated conformers but rather



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result from intermolecular interactions and other factors as molecular packing in the bulk liquid or entropic effects. Likewise, we checked relative stabilities of Mg2+ complexes with different DME conformers with frozen geometry of the glyme molecule and optimized position of the ion (Table S3 in Supporting Information). Regardless of the FF there is strong preference for Mg2+ binding to TGT and TGG conformations of DME molecule. As the last test we compared quantum-chemical and FF-based binding energies for Mg2+-TFSI- and Mg2+-DME (Table S4). In non-polarizable fields binding energies both for cation-anion pair and for cation-DME complex are significantly underestimated. On the other hand, in polarizable parameterizations binding energies for Mg2+-TFSI- agree well with quantum-chemical data, while stability of Mg2+-DME is overestimated. Nevertheless, from the NP and DP parameterizations the latter yields better agreement with ab initio data and the FF2-DP variant was used in most simulations.

Table 1. Compositions of modeled electrolytes, densities and concentrations obtained from NpT MD simulations.

n(Mg2+)

n(DME)

atoms

ρ, g/cm3

c, mol/dm3

1

14

1167

19106

0.92

0.11

2

28

1167

19540

0.96

0.22

3

50

1100

19150

1.02

0.40

4

67

1072

19229

1.06

0.52

5

160

889

19184

1.28

1.18

system no.

Five simulation boxes with increasing content of Mg salt were prepared. Compositions of studied electrolytes are described in Table 1. For each system we performed about 130-150 ns of MD run. When the sizes of simulation boxes had stabilized during NpT simulations we calculated actual values of salt concentration in studied electrolytes (Table 1). According to approximate values of molar concentration we will label our model systems as c = 0.1, 0.2, 0.4, 0.5 and 1.2 M. For selected systems (details will be presented in Sec.3) we performed rigid body dynamics simulations with DME molecules frozen in specific conformations. Tinker v. 5.1 package31 was used for this purpose. Because of performance limitations, in order to reduce computational time, in rigid body simulations we used non-polarizable FF2-NP 6 ACS Paragon Plus Environment

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parameterization with the exception of van der Waals parameters for Mg2+ taken from OPLSAA parameterization.32

3. Results and discussion 3.1 Structure of electrolytes Densities of model systems obtained from NpT MD simulations are listed in Table 1. Density of the electrolyte increases with salt concentration and the dependence is almost perfectly linear within the studied concentration range as shown in Supporting Information.

Fig. 2. Snapshots of simulation boxes for c=0.1 M (a) and c=1.2 M (b). Mg2+ ions are displayed as spheres.

Fig. 2 presents two sample snapshots of simulation box for diluted and concentrated electrolyte. Distribution of metal ions in the c=0.1M system is non-uniform, with some parts of the box free of ions which concentrated in the other part. Nevertheless, this separation changes with time and regions of low and high Mg concentration move through the sample; therefore on average the electrolyte is homogenous. As seen in Fig. 2 in concentrated solution Mg ions are distributed rather uniformly. Therefore in MD simulations we do not observe phase separation reported experimentally apart from some tendency for local fluctuations in ion distribution; we will discuss this issue in conclusions. Radial Distribution Functions (RDFs) for Mg-O atom pairs are displayed in Fig 3 separately for oxygen atoms from DME molecules and TFSI anions. Fig 3 shows also the integrated Mg-O RDFs (running coordination numbers of Mg2+) for both types of oxygen atoms. The first maximum in the Mg-ODME RDF, located at 2 Å, is sharp and integrates to about 4.3-4.7 oxygen atoms with only small decrease in more concentrated solution. It is followed by a weak maximum above 5 Å. On the other hand, coordination to the anion oxygen atoms is very weak; for the dilute electrolyte (c=0.2) the first maximum appears at about 6 Å. In the concentrated solution (c=1.2) some OTFSI atoms appear at shorter distances to the cation, nevertheless the average number of OTFSI at 3 Å is about 0.4. Therefore, we can 7 ACS Paragon Plus Environment


conclude that within the studied range of salt concentration the first solvation shell of the magnesium cation consists almost exclusively of the DME oxygen atoms.

Fig. 3. (left) Radial distribution functions for Mg-O atom pairs; (right) integrated Mg-O RDFs (running coordination numbers of Mg2+).

Fig. 4. Radial distribution functions for Mg-Mg ion pairs. Sample arrangements of ions/molecules contributing to observed maxima are shown in the upper part of the plot.

Some additional information on the structure of the electrolyte may be gained through the RDFs for Mg-Mg ion pairs shown in Fig. 4. Smoothing splines were used to reduce the noise in the plot; original data are available in Supporting Information. With increasing concentration of Mg salt maxima in the RDF move toward smaller distances. Even for the 8 ACS Paragon Plus Environment

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most dilute electrolyte there is a noticeable maximum at about 17 Å. Its height gradually increases and the position shifts to about 16 Å with salt concentration growing up to c=0.5 M. Within this concentration range another maximum develops at 13.5 Å. In the most concentrated electrolyte (c=1.2 M) this maximum appears at 12.7 Å, preceded by a lower maximum at about 10 Å. In the MD simulations for Mg(TFSI)2/DME electrolytes we therefore observe in Mg-Mg RDF between 10 and 17 Å a series of maxima, separated by 33.5 Å. It may be noted that the maximum at 16-17 Å seems particularly stable, being observable in a wide range of concentrations. It is the most pronounced in our system c=0.4 M with composition corresponding to the Mg:O ratio equal 1:22 which was suggested in ref. 14 as thermodynamically favored. Given that the Mg-O distance is approximately 2 Å and the “width” of the DME molecule is about 3 Å, the radius of the Mg cation with its first solvation shell is about 5 Å. Then a simple explanation of the pattern of maxima in Mg-Mg RDF is that the maximum at 10 Å corresponds to two cations separated by only two DME molecules belonging to the solvation shells of these two ions. In the case of the two other maxima, the distance increment corresponds to adding one glyme molecule between the cations; therefore the maxima at about 13 and 16 Å correspond to two Mg ions separated by 3 and 4 DME molecules, respectively. Additional analysis of the structure of electrolyte presented in more detail in Supporting Information confirms the validity of the above explanation. Sample snapshots of the structure of the solvent separating magnesium cations are displayed in Fig. 4. Indeed, the most probable numbers of solvent molecules leading to the maxima observed in the RDF are 2, 3 or 4 DME molecules arranged between two Mg cations. We can also note that in the concentrated electrolyte probability of finding a TFSI anion between two cations increases and the second maximum in the RDF obtained for c=1.2 M results not only from separations by 3 DME molecules (like in more dilute solutions) but also from arrangements of 2 DME molecules + 1 TFSI anion. This helps to rationalize the shift of the maximum from 13.5 Å in c=0.5 M electrolyte to 12.7 Å in c=1.2 M solution as the electrostatic attraction between TFSI anion and Mg2+ cations shortens the distance between the cations. Next, we turn our attention to the conformational preferences of solvent DME molecules. Changes in the population of DME conformers in solutions with increasing salt content and conformations of solvent molecules in the coordination sphere of magnesium ion are displayed in Fig. 5. Populations of TTT and TTG conformers decrease with increasing Mg2+ concentration; simultaneously, the total percentage of TGx conformers increases. The latter effect is due to increasing population of TGT conformers; the population of the TGG 9 ACS Paragon Plus Environment


conformations increases for smaller salt concentrations and for c=1.2 M is approximately the same as for c=0.5 M. The amount of TGG’ conformers decreases with increasing salt content over the whole range of concentrations.

Fig. 5. (left) Populations of DME conformers in electrolytes with increasing salt concentration; (right) number of O atoms within 3 Å distance from Mg2+ ion provided by different DME conformers and TFSI anions.

The dependence discussed above is based on the population of the conformers in the whole sample of the electrolyte. In the right panel of Fig. 5 we try to assess the conformational changes induced in the solvation shells of magnesium ions, plotting the number of oxygen atoms coordinating the Mg2+ cation provided by TFSI anion and DME molecules in different conformations; coordinating atoms are counted within the 3 Å distance from the cation. The number of coordinating oxygen atoms from DME molecules in TTx conformations is practically negligible and therefore it would be unnoticeable in the plot. Up to concentration c=0.5 M the total number of oxygens from TGx conformations of DME remains approximately constant, although proportions of different TGx conformers vary little more that their sum. In the most concentrated electrolyte the number of O atoms from DME in TGT conformations apparently increases to more than 3 atoms per Mg ion. Simultaneously the number of TGG and TGG’ oxygens is reduced, therefore the total number of DME oxygen atoms in the first solvation shell of Mg2+ decreases. This change is accompanied by increasing probability of cation complexation to oxygen atoms from TFSI anions, so that on average there are about 0.4 TFSI oxygens coordinating the ion in the c=1.2 M solution. From the above data we can conclude that complexation of Mg cation to DME induces strong preference for TGx conformations of the solvent molecule, and especially for the TGT conformation. On the other hand, TTx conformers are disfavored. The reason for this behavior is that the TGx conformations enable interactions of the cation with both oxygen atoms from 10 ACS Paragon Plus Environment

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the solvent molecule, leading to energetically favorable more dense packing of O atoms in the solvation shell. Conformational preferences in the neighborhood of the Mg2+ ion change the proportions between conformers of DME molecules in solution when the salt concentration changes, resulting in increasing population of TGx and decreasing amount of TTx conformations in more concentrated electrolytes. We should mention at this point that these preferences in simulated systems could not be predicted solely on the basis of relative binding energies (Table S3), because Mg2+ complexes with TGG and TGG’ conformations are found in similar concentrations despite the fact that the stabilization energy for the latter complex is significantly smaller. Apparently, as in the case of conformer abundance in the neat DME, populations of conformers in real system of many interacting molecules can not be simply estimated from relative energies of individual molecules or ion-molecule pairs. To get some additional insight into preferred conformations of DME molecules in the solvation shell of Mg2+ cation we conducted series of simulations using rigid body dynamics to constrain the solvent molecules at specific geometries as described in Sec. 2. Six pairs of simulations were performed: for a box of neat DME solvent consisting of a single conformer or of a mixture of two or three conformations and for a corresponding box of electrolyte containing Mg(TFSI)2 in concentration about c=0.3 M. Conformer compositions used to prepare simulated systems were: (1) 100 % TTT, (2) 100 % TGT, (3) 100 % TGG’, (4) 50 % TGT + 50 % TGG’, (5) 50 % TTT + 50 % TGT and (6) 33.3 % TTT + 33.3 % TGT + 33.3 % TGG’. Information on average numbers of oxygen atoms found within the 3 Å distance from the Mg ion is summarized in Table 2; more data, including interaction energies, is presented in the Supporting Information.

Table 2. Average numbers of oxygen atoms of different parentage within 3 Å distance from the Mg2+ ion obtained in rigid body MD simulations. TTT

TGT

TGG’

TGTTGG’

TTT-TGT

TTTTGTTGG’

nTFSI

3.61

2.4

3.01

2.49

3.22

3.4

nDME(TTT)

1.49

-

-

-

0.01

0.0

nDME(TGT)

-

3.52

-

2.58

2.48

1.65

nDME(TGG’)

-

-

2.91

0.9

-

0.9

ntotal

5.1

5.92

5.92

5.97

5.71

5.95



As seen in Table 2, from the three conformations used in rigid body simulations the most favored in complexation of the magnesium cation is the TGT conformer, second to it is the TGG’ and the least preferred is the TTT geometry. When only one conformer was present in the electrolyte, the TGT and TGG’ conformers provided the number of coordinating oxygens two times larger than the TTT structure. Likewise, in solutions containing a mixture of conformers, the Mg cation preferably coordinated to DME molecules in TGT conformation and there was no coordination to oxygen atoms from TTT conformers. It may be noted that in the TGT-TGG’ system the ratio of coordinating TGT and TGG’ oxygen atoms is similar to that obtained in the main simulations of this work (Cf. Fig. 5). Conformational preferences in the solvation shell of Mg2+ ion are readily visible in Fig. 6, where we show spatial distribution of ions and different conformers of DME molecules. Apparently, in the vicinity of Mg2+ cations only TGT and TGG’ conformers of DME molecules are present and the TTT conformers are pushed away to other parts of the sample. Calculated binding energies per Mg2+ ion (Supporting Information) show in the case of interactions with TGT and TGG’ conformers larger stabilization than for interactions with TTT geometries; therefore they also suggest that coordination to the TTT DME molecules is disfavored.

Fig. 6. Sample structures of the electrolyte obtained from rigid body simulations for the TTT/TGT/TGG’ system. (a) Distribution of ions, Mg2+ shown as pink spheres, sulphur atoms from TFSI anions – yellow spheres; (b) distribution of DME conformers; Mg2+ ions – pink spheres, DME molecules in TTT, TGT and TGG’ conformations shown as red, blue and cyan spheres, respectively. Data in Table 2 show that in rigid body simulations, unlike the main simulations in the FF2-DP force field, there is a significant degree of Mg2+ - TFSI coordination and the average number of anion oxygen atoms in the first solvation shell of magnesium cation is between 2.4 and 3.6, therefore it is comparable or even larger than the number of DME oxygens. This behavior is also noticeable in Fig. 6, where TFSI anions concentrate in the same regions of the simulation box as Mg cations. Partially this effect may be attributed to rigid body dynamics, e.g. in the electrolyte with DME molecules frozen in TTT conformation, complexation to 12 ACS Paragon Plus Environment

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TFSI anions is the sole possible way to increase coordination number of Mg2+. As a test we performed a short Tinker simulation with FF2-NP field removing the rigid body constraints and we observed that the average number of TFSI oxygen atoms coordinating the Mg ion decreased to 2.15. The other difference between NAMD and Tinker simulations in this work was the accounting for polarization effects in FF2-DP field used with NAMD. When we turned off the polarization (that is we used FF2-NP instead of FF2-DP field in NAMD simulations) for c=0.2 M electrolyte, the number of TFSI oxygen atoms within the 3 Å radius from the cation increased from 0 to about 1.9. This is an important observation, showing that inclusion of polarization in the force field may change significantly the balance between coordination of the Mg2+ cation either to solvent DME molecules or to TFSI counteranions. Therefore in the simulations reported in this work, application of the polarizable force field was crucial for reproduction of the experimental result reported in ref. 14 that in Mg(TFSI)2/DME electrolytes salt exists in the form of free ions up to quite high concentrations. In other studies on similar systems there is a substantial coordination of Mg2+ to the anion, e.g. 4 oxygen atoms from TFSI anions coordinating the cation predicted for Mg(TFSI)2 in DME8 or 1-2 anion oxygen atoms (depending on the solvent) for Mg(TFSI)2 solutions in DME, diglyme and tetraglyme.13 Based on our tests described in this section we may attribute the difference between refs. 8,13 and present calculations to the polarizability effects, since a non-polarizable force field parameterizations were used in the former studies.8,13 The observation that polarization reduces Mg2+ - TFSI interactions can be rationalized by the fact that polarization of the medium decreases cation-anion attraction and simultaneously increases stabilization of the anion in the solvent.

3.2 Diffusion Calculated radial distribution functions and average coordination numbers show, in accord with experimental findings of ref. 14, that magnesium cations in Mg(TFSI)2/DME electrolytes are surrounded by a shell of three solvent molecules. Analysis of the MD trajectories (Supporting Information) suggests that these complexes are stable, i.e. occurrences of exchange of DME molecules coordinated to the given cation with other solvent molecules are rather infrequent. In the case of the c=0.1 M electrolyte more than 80 % of DME molecules coordinated to Mg ions remained in contact with the same ion during 150 ns of simulation. As we will see later in this section, stability of Mg2+ solvation shell is reflected in diffusion coefficients calculated for different components of the system.



Fig. 7. Average mean square displacements of ions and solvent molecules for two electrolytes.

In Fig. 7 we display mean square displacements (MSDs) of ions and solvent molecules calculated for a dilute and a concentrated electrolyte. Data are averaged over all ions or molecules in the simulation box and time intervals are averaged over whole MD trajectory. Theoretically, MSD should scale with time as MSD ∝ tα. In the long time limit a diffusive regime is achieved with α = 1. Values of α < 1 indicate subdiffusive motion and typically are observed in intermediate timescale. For both systems shown in Fig. 7 the diffusive regime (straight lines with slope equal to 1) is achieved. For c=1.2 M electrolyte the time range of subdiffusive motion is larger (up to 20 ns) and more pronounced (lower slope of the MSD line, i.e. lower α) which may be rationalized by a larger degree of ion/molecule trapping in local minima in more concentrated, and therefore more viscous, solution. Average diffusion coefficients of ions and solvent molecules were calculated from MSD vs. time dependence in time intervals for which the systems exhibit diffusive motion regime. Diffusion of solvent molecules requires special attention in the view of our simulation results suggesting large stability of Mg2+-DME complexes and the experimental data14 showing two kinds of DME molecules, moving slowly and fast, respectively. In Fig. 8a we plotted square displacements for 10 slowest and 10 fastest solvent molecules in the c=0.1 electrolyte. Up to 10 ns both sets of trajectories are easily distinguishable, but they start to overlap for longer times. To some extent it may be related to (rather infrequent) events when the solvation shell of one of cations changes and one of DME molecules is replaced by another. However, the major reason for this behavior is that the square displacement stops to increase or even starts to decrease for some “fast” molecules as seen in Fig. 8a. This is expectable, because for an individual random walker its trajectory may return toward the starting point, therefore only the MSD averaged over the whole ensemble (red line in Fig. 8a) is proportional to time, but not displacements for individual molecules. 14 ACS Paragon Plus Environment

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Fig. 8. (a) square displacements of fastest and slowest solvent molecules in the c=0.1 M electrolyte; (b) distributions of DME diffusion coefficients estimated in different time intervals for the c=0.1 M electrolyte; (c) distributions of DME diffusion coefficients estimated for 2 ns intervals in electrolytes with increasing salt concentration.

As a result, the distribution of diffusion coefficients calculated using 2 ns intervals is clearly bimodal, whereas the histogram obtained for 60 ns intervals is much broader and has one maximum (Fig. 8b). We stress once again that data for 2 ns were averaged over all possible choices of the time interval over about 150 ns of the MD trajectory, therefore



bimodal character of the distribution shows that given molecule must behave as “slow” or “fast” over a major part of the trajectory. Therefore, to assess differences in mobility of solvent molecules we plotted in Fig. 8c distributions of diffusion coefficients for all DME molecules in investigated systems using averages over 2 ns intervals. In electrolytes up to c=0.5 M there are two distinct groups of molecules differing in their diffusivities and the gap between these two sets is very well pronounced. With increasing salt concentration diffusion coefficients become smaller; the reduction is larger in the case of “fast” molecules. In the most concentrated system with c=1.2 M diffusion coefficients even for fastest DME molecules are in the order of those obtained for slow molecules in less concentrated solutions, nevertheless both sets of solvent molecules still are easily distinguishable. As readily noticeable, the number of “slow” molecules increases with increasing amount of Mg salt in the system. Closer inspection of the data reveals that on average there are about 3.2-3.3 “slow” DME molecules per Mg2+ ion. These findings are in excellent agreement with experimental results of ref. 14 and the explanation that “fast” solvent molecules are free DME molecules, whereas “slow” are the molecules from the first solvation shell of the cation.

Fig. 9. Diffusion coefficients estimated from MD simulations for electrolytes with increasing salt concentration.

Diffusion coefficients for ions and solvent molecules in all modeled electrolytes estimated from mean square displacements are summarized in Fig. 9. All values decrease with increasing salt content and reduction of the mobility is the largest for “fast” solvent molecules. Decreasing diffusivity can be attributed to increasing density and viscosity of electrolyte. Magnesium cations diffuse most slowly, mobility of TFSI anions is about two times larger and the “average” solvent has the largest diffusion coefficient. Diffusivity of “slow” solvent molecules are almost as small as that for magnesium ions, which is another 16 ACS Paragon Plus Environment

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indication that motions of cations and “slow” DME molecules are correlated due to interactions in the solvation shell. On the other hand, mobilities of cations and anions differ, supporting the conclusion of ref. 14 that Mg(TFSI)2 exists in DME-based electrolyte as free ions. Estimated diffusivities can be compared to diffusion coefficients reported in ref. 14 for the lower phase (c=0.35 M) of the biphasic system. For TFSI anions and free DME molecules calculated values (0.1×10-5 and 0.3×10-5 cm2/s, respectively) are about three to four times lower than measured data (0.39×10-5 and 0.96×10-5 cm2/s). In the case of “caging” DME the difference is larger: 0.08×10-5 cm2/s calculated vs. 0.72×10-5 cm2/s measured. There are no experimental data for diffusion coefficient of the Mg ion reported in ref. 14, therefore we can not check whether this is an effect of slower motion of Mg2+/DME complexes in MD simulations. Nevertheless, agreement with experiment is satisfactory, and the feature of “free” and “caging” solvent molecules well reproduced.

4. Conclusions We performed classical MD simulation in polarizable force field for a series of Mg(TFSI)2 solutions in dimethoxyethane with increasing salt concentration. In agreement with experimental study14 we found that the salt exists in these electrolytes as free ions within large range of concentrations. Mg2+ ions form stable solvates with DME molecules and the average number of DME oxygen atoms in cation solvation shell reaches 4.7. We confirmed experimental findings that increasing Mg concentration correlates with increasing population of TGx conformers. Some preferences for Mg-Mg distribution in the electrolyte were detected which may be an indication supporting the existence of suprastructure of solvated Mg2+ ions and solvent molecules postulated in ref. 14. Although in simulations for electrolytes with lower salt content we noticed some local fluctuations of ion distributions resulting in appearance of regions of lower and higher density of cations, we did not observe phase separation reported in 14. This is presumably due to force field parameterization which can be capable of general description of the system but is not able to capture such subtle phenomenon sensitive to delicate balance of interactions. On the other hand, it is also possible that simulations for larger system sizes or/and longer times are necessary to reproduce separation of the electrolyte. Therefore, phenomenon of phase separations may be an interesting subject of future works after necessary improvement of force field is made. With regard to the issue of parameterization we should note that inclusion of polarizability effects in FF may change 17 ACS Paragon Plus Environment


significantly reproduction of some features of the system as shown here for conformer population of the solvent and the structure of the solvation shell of magnesium cation. The key conclusions of this work on Mg(TFSI)2/DME electrolyte can be summarized as follows: (1) Coordination to the Mg2+ imposes TGx conformations of DME molecules; as a result the electrolyte is enriched in TGx conformers while amount of TTx conformers decreases with increasing salt concentration. (2) Free ions are present in the electrolyte; Mg2+ cations form stable solvates with about 3 DME molecules; cation coordination to TFSI anion is suppressed. (3) Motions of “caging” solvent molecules are correlated to cation diffusion and two sets of DME molecules are present in the system: free, moving fast, solvent molecules and DME molecules in Mg-DME solvates diffusing slowly with the cation. (4) A kind of suprastructural order arises in the electrolyte with Mg cations separated by 2, 3 or 4 solvent molecules. These results are in good agreement with the experimental study14 and confirm validity of methodology used here to modeling chemistry of Mg/glyme electrolytes. Prospective future studies may be conducted on more complex systems. e.g. MgCl2/Mg(TFSI)2/DME electrolytes.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Plots of DME conformers, data on population of DME conformers in neat solvent obtained in different force field parameterizations, relative energies of DME conformers and binding energies, changes in 2nd solvation shell with salt concentration, correlation between density and concentration of the electrolyte, structural information on Mg-Mg arrangement, data from rigid body MD simulations, analysis of solvate stability, force field parameters.

Acknowledgment This research was supported by the National Science Centre (Poland) grant no. UMO2016/21/B/ST4/02110.


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Solvation of Mg2+ Ions in Mg(TFSI)2âDimethoxyethane Electrolytes

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Solvation of Mg2+ Ions in Mg(TFSI)2âDimethoxyethane Electrolytes