Ion Pairing and Diffusion in Magnesium Electrolytes Based on Mag

Subscriber access provided by READING UNIV

Article

Ion Pairing and Diffusion in Magnesium Electrolytes Based on Magnesium Borohydride Devon Samuel, Carl Steinhauser, Jeffrey G. Smith, Aaron Kaufman, Maxwell D Radin, Junichi Naruse, Hidehiko Hiramatsu, and Donald J. Siegel ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b15547 • Publication Date (Web): 14 Nov 2017 Downloaded from http://pubs.acs.org on November 17, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Applied Materials & Interfaces is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Applied Materials & Interfaces

Ion Pairing and Diffusion in Magnesium Electrolytes Based on Magnesium Borohydride Devon Samuel,Ñ, § Carl Steinhauser,^ Jeffrey G. Smith,† Aaron Kaufman,† Maxwell D. Radin,& Junichi Naruse,§ Hidehiko Hiramatsu,|| and Donald J. Siegel*,†,Ñ,‡,^,# Mechanical Engineering Department, ÑMaterials Science & Engineering, ‡Applied Physics Program, &Department of Physics, ^Electrical Engineering and Computer Science, and ^Michigan Energy Institute, University of Michigan, Ann Arbor, Michigan 48109, United States †

#

Joint Center for Energy Storage Research (JCESR)

§

North America Research & Development, DENSO International America, Inc., 24777 Denso Drive, Southfield, Michigan 48086, United States ||

Research Laboratories, DENSO Corporation, 500-1, Minamiyama, Komenoki-cho, Nisshin, 470-0111, Japan

ABSTRACT: One obstacle to realizing a practical, rechargeable magnesium-ion battery is the development of efficient Mg electrolytes. Electrolytes based on simple Mg(BH4)2 salts suffer from poor salt solubility and/or low conductivity, presumably due to strong ion pairing. Understanding the molecular-scale processes occurring in these electrolytes would aid in overcoming these performance limitations. Toward this goal, the present study examines the solvation, agglomeration, and transport properties of a family of Mg electrolytes based on the Mg(BH4)2 salt using classical molecular dynamics. These properties were examined across five different solvents (THF and the glymes G1, G2, G3, and G4) and at four salt concentrations ranging from the dilute limit up to 0.4 M. Significant and irreversible salt agglomeration was observed in all solvents at all non-dilute Mg(BH4)2 concentrations. The degree of clustering observed in these divalent Mg systems is much larger than that reported for electrolytes containing monovalent cations, such as Li. The salt agglomeration rate and diffusivity of Mg2+ were both observed to correlate with solvent self-diffusivity: electrolytes using longer-(shorter-)chain solvents had the lowest (highest) Mg2+ diffusivity and agglomeration rates. Incorporation of Mg2+ into Mg2+-BH4- clusters significantly reduces the diffusivity of Mg2+, by restricting its displacements to localized motion within largely-immobile agglomerates. Consequently, diffusion is increasingly impeded with increasing Mg(BH4)2 concentration. These data are consistent with the solubility limitations observed experimentally for Mg(BH4)2-based electrolytes, and highlight the need for strategies that minimize salt agglomeration in electrolytes containing divalent cations. KEYWORDS: Magnesium batteries, molecular dynamics, electrolyte, diffusivity, contact ion pairs, agglomeration INTRODUCTION The development of battery chemistries that out-perform stateof-the-art Li-ion systems remains an unmet challenge.1–6 A promising candidate amongst these so-called ‘beyond Li-ion’ chemistries involves the substitution of a multi-valent metal, such as magnesium,5,6 for lithium. Magnesium is an attractive negative electrode material as it is safer, less expensive, and offers a higher energy density than anodes based on lithium or intercalated graphite (3833 mAh/cm3 for Mg vs. 2046 mAh/cm3 for Li metal and 760 mAh/cm3 for graphite-based Li-ion anodes).7–9 One obstacle to achieving a viable Mg-ion battery is the development of efficient and stable Mg electrolytes.8,10–12 Gregory et al.10 first examined the feasibility of a rechargeable Mg-ion battery in 1990, by examining compounds allowing intercalation of Mg and the deposition and dissolution of Mg metal. Aurbach et al.13 reported a magnesium-ion battery with improved efficiency in the year 2000 using an electrolyte composed of organohaloaluminate Mg salts in THF. These electrolytes exhibited highly efficient Mg deposition and stripping, but are corrosive to metals such as steel.11 Since Aurbach’s study, several new Mg electrolyte systems have been proposed.12,14– 28 The most promising avoid halide components (and their attendant corrosiveness) while exhibiting high stability.

Noteworthy examples of recently reported Mg electrolytes include those based on Mg-salts such as Mg(BH4)223,27,29 and Mg(TFSI)2.25 Mohtadi et al.23 demonstrated electrolytes based on Mg(BH4)2 in THF and dimethoxyethane (DME). These systems exhibited reversible Mg plating and stripping, and achieved up to 94% coulombic efficiency with the addition of LiBH4. Using diglyme, the efficiency of an Mg(BH4)2/LiBH4 electrolyte was shown to increase to approximately 100%,29 with the increase attributed to enhanced chelation of Mg2+ (compared to DME and THF) and synergistic effects arising from LiBH4 addition.29,30 While exhibiting high efficiency, the solubility of Mg(BH4)2 is relatively low, ranging from 0.01 to 0.1 M in DME (increasing to 0.1-0.18 M with 0.6 M LiBH4)29,31, 0.01 M in diglyme (increasing to 0.1 M with 1.5 M LiBH4)29, and 0.5 M in THF.31 The limited solubility of Mg(BH4)2 in DME and diglyme prompted Tuerxun et al.27 to test a tetraglymebased (G4) electrolyte. The use of a longer-chain G4 solvent was shown to enable a higher concentration of Mg(BH4)2 (0.5 M vs. 0.1 M in diglyme, both with 1.5 M LiBH4), while maintaining close to 100% coulombic efficiency. The presence of LiBH4 in Mg(BH4)2-based electrolytes may facilitate dissociation of the Mg(BH4)2 salt, or equivalently, retard the recombination of Mg2+ and BH4- ions into contact ion pairs or larger

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 12

Figure 1. Illustration of the five solvents and Mg(BH 4)2 salt used in the present study. Mg(BH 4)2 was simulated as three separate ionic units (different from the illustration above), two BH 4- anions and one Mg2+ cation.

agglomerates.32 This would improve the solubility of the salt, and increase conductivity.31 For example, in an Mg(BH4)2/THF electrolyte containing no LiBH4 additions, Mohtadi et al. observed strong ion pairing and a low conductivity of 0.01 mS/cm; the conductivity of an Mg(BH4)2/DME electrolyte was found to be similarly low.33 The addition of LiBH4 increased ion dissociation and improved ionic conductivity to 2 mS/cm in the Mg(BH4)2/DME electrolyte.23,33 Similar results appear in other reports, with conductivities of 2-3 mS/cm reported for Mg(BH4)2/LiBH4 in DME, diglyme, or THF29 (values comparable to Li-ion battery electrolytes13), and about 9 mS/cm in tetraglyme.27 The electrochemical activity of the LiBH4-containing electrolytes was attributed to magnesium, as lithium was not observed in XRD, XPS, or NMR studies of electrodeposits.29,31,33 Furthermore, LiBH4/DME solutions have been reported as electrochemically inactive,31 although more recent work suggests this may depend on the limiting cathodic potential employed.30 While secondary salt additions are beneficial for some Mg-electrolytes, the development of more general strategies to improve performance will be aided by an understanding of the fundamental properties of the parent electrolytic solution (single salt + solvent), including: (i.) the solubility and agglomeration of Mg salts, (ii.) the mechanisms responsible for efficient plating/stripping of Mg, and (iii.) the mobility of Mg2+ ions in solution. Computational models of Mg electrolytes have begun to contribute to this understanding.9,28,32 For example, Rajput et al. used classical molecular dynamics and first-principles methods to characterize the interaction between various Mg salts and solvents.28,32 In addition, Chadwick et al.9 developed an approach for simulating cyclic plating and stripping of Mg, and for determining Mg-ion diffusivities in Mg electrolytes. Building on these earlier computational models, the present study uses classical molecular dynamics to examine the connection between four properties of Mg(BH4)2- based electrolytes: Mg salt concentration, solvent composition, ion diffusivity, and contact ion pair formation (i.e., salt agglomeration). These properties were examined across five different solvents, THF and four glymes (G1, G2, G3, and G4), and at four salt concentrations ranging from the dilute limit up to 0.4 M. Irreversible salt agglomeration was observed at all non-dilute Mg(BH4)2 concentrations, and in all solvents. The rate of agglomeration and magnitude of diffusivity of Mg2+ were both observed to correlate with solvent self-diffusivity: electrolytes based on longer (shorter) chain solvents had the lowest (highest) Mg2+ diffusivity and rate of salt agglomeration. Agglomeration of Mg2+-BH4- clusters significantly reduces the long-range transport

of Mg2+ by restricting diffusion to regions within, or around, a given agglomerate. Consequently, the tendency for enhanced agglomeration at higher salt content increasingly retards diffusion at higher concentrations. These observations are qualitatively consistent with the solubility limitations observed experimentally for Mg(BH4)2based electrolytes. We conclude that efforts to improve these electrolytes should focus on techniques for reducing the degree of agglomeration between divalent magnesium and borohydride anions. METHODS The dissolution of Mg(BH4)2 was explored in five solvents: DME (G1), diglyme (G2), triglyme (G3), tetraglyme (G4), and THF, illustrated in Figure 1. Four salt concentrations were examined: 0.01 M, 0.1 M, 0.4 M, and the ‘dilute limit,’ comprised of one salt formula unit per simulation cell. Classical molecular dynamics (MD) simulations were used to calculate the diffusivity of the Mg2+ ion in each solvent/concentration combination, measure the rates of salt agglomeration into contact ion pairs and larger clusters, and to characterize the solvation structure of the Mg2+ ion. Simulations at the dilute limit were used to estimate the diffusivity of lone Mg2+ ions, which was difficult to isolate in calculations employing higher salt concentrations due to salt agglomeration. Molecular dynamics was performed using the LAMMPS code.34 The OPLS-AA force field35–38 was used to describe all interatomic interactions, with two modifications: (1) customized partial charges were calculated using the ESP scheme in Gaussian at the B3LYP/6311G level39 (see Table S1), and (2) Coulomb interactions were evaluated using dielectric constants specific to each solvent investigated.40,41 Lennard-Jones non-bonding interactions were truncated at 10 Å. A time step of 1 femtosecond was used in all simulations. Packmol was used to create initial configurations in cubic simulation cells.42 The number of atoms present in the computational cells, including salt and solvent, ranged from ~83,000 to ~93,000; the number of Mg(BH4)2 formula units used was: 0 (pure solvent), 1 (dilute limit), 6, 60, or 240, (for 0.01 M, 0.1 M, and 0.4 M concentrations, respectively). Production runs involving salt and solvent used a cubic simulation cell with linear dimension of 100 Å, which allowed for sufficient quantities of Mg(BH4)2 to obtain reliable statistics, even at low concentrations such as 0.01 M. The number of solvent molecules in each system (solvent + salt) was based on the calculated density of the pure solvent. Finite size effects were examined using pure tetraglyme, the largest molecule studied, with increasingly larger cubic simulation cells of 40, 60, 80, and 100 Å on a side. For simulations on the pure solvents, the following sequence of calculations was performed: initial


Page 3 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


energy minimization, NPT MD at 400 K for 0.5 ns, NPT cooling to 298 K for 0.5 ns, and then NVT equilibration at 298 K for a further 0.5 ns. Finally, the mean squared displacement (MSD) was recorded over a three-ns window in the NVT ensemble, and the self-diffusivity D was calculated using the Einstein relation: 𝑥 𝑡 − 𝑥$ % = 6𝐷𝑡 . 1 For each solvent, a total of ten runs with different initial conditions were performed. To validate the force field, the density and self-diffusion coefficients of each solvent were evaluated and compared with measured values. (See Results Section). Similar to the pure solvent calculations, simulations on Mg electrolytes were initiated with an energy minimization step. Afterwards, random velocities were assigned corresponding to a temperature of 298 K, and the system was run for 50 picoseconds (ps) in the NVT ensemble. This was followed by a 500-ps equilibration run in the NPT ensemble. Finally, NVT simulations were run for 5 ns. In selected cases, longer 30 ns runs were used to confirm results obtained from the shorter 5 ns simulations. Throughout, the borohydride ions were treated as internally-rigid bodies: translation and rotation were allowed, but not vibration. To improve the statistics, ten MSD runs were performed for each solvent/salt combination and concentration.43 The average and standard deviation of the Mg2+ diffusion coefficient in each electrolyte was calculated using the ‘leave-one-out’ method of Wang and Hou43 The drift in the system’s center of mass was subtracted before calculating the MSD of the ions. The degree of ion clustering in each electrolyte as a function of simulation time was assessed by post-processing the trajectory files to identify associated (agglomerated) ions. Two ions were considered agglomerated if they were within 4 Å of each other. Each cluster was categorized according to its size (number of ions) as either: an isolated Mg2+ or BH4-, a MgBH4+ ion pair, a Mg(BH4)2 ion pair, or as larger ion clusters. The cumulative agglomeration of Mg2+ and BH4ions into clusters over time was plotted for each electrolyte composition as an ‘agglomeration profile.’ The diffusion coefficient of Mg2+ in each run was calculated using the Einstein relation (Eq. 1) with the MSD during the last nanosecond of the simulation. This time window corresponded to a state of quasi-equilibrium in the agglomeration profile, during which only limited changes in cluster size was observed. Radial distribution functions (RDFs) were evaluated over the last 0.5 ns of the simulations, and were used to quantify the solute structure. Fifty bins were used in the RDF plot, which extended to a maximum distance of 15 Å. Representative images of Mg2+ ions’ solvation shells, and of agglomerated ion clusters present at the end of the simulations, were generated for the 0.4 M electrolytes.

Table 1. Density and self-diffusivity of pure tetraglyme as a function of simulation cell size. Side Length of Cubic Simulation Cell

Density40 (g/cm 3)

40 Å

0.93 ± 0.002

Self-Diffusivity44 (10-7 cm 2/s) 6.1 ± 0.5

60 Å 80 Å 100 Å

0.93 ± 0.001 0.93 ± 0.002 0.93 ± 0.001

7.1 ± 0.3 7.3 ± 0.2 6.5 ± 0.3

Experiment

1.01

11.34

RESULTS AND DISCUSSION Properties of Pure Solvents. To assess and minimize finite size effects, the density and self-diffusion coefficient of pure tetraglyme were evaluated for multiple sizes of simulation cells. As the largest molecule in this study, tetraglyme (G4) has the smallest number of molecules in a given simulation volume. Consequently, it is the system most likely to exhibit finite-size effects. Table 1 summarizes the calculated density and self-diffusivity of G4 for cubic simulation cells with dimensions ranging from 40 to 100 Å. The data indicates that the density is well converged for the smallest system investigated (40 Å). Similarly, the self-diffusivity is converged to within about 10% for systems with a cell side of 60 Å or larger. Table 2 summarizes the calculated density and self-diffusivity for each of the five pure solvents investigated, using a cell size of 60 Å. These data are compared to experimental values40,44–46 and earlier calculations by Rajput et al.32. (Rajput et al. employed the General Amber Force Field47 (GAFF), which differs from OPLS-AA in the form of the torsion term and the potential’s parametrization.) Our calculations predict densities that are approximately 7-10% smaller than the measured values. Importantly, the trend in the calculated densities with respect to solvent type is identical to that found experimentally. For the self-diffusivity, the predicted values correlate with molecular size, consistent with the experimental trends in diffusivity and viscosity.48,49 Our calculated diffusivities overestimate the experimental value for G1, yet slightly underestimate the measurements for G2, G3, and G4, with an average deviation from experiment of 37%. In comparison, calculations from Rajput et al.32 tend to underestimate the diffusivity. Agglomeration of Mg(BH4)2. Regarding the properties of the Mg(BH4)2-based electrolytes, we observed that Mg2+ and BH4- ions agglomerated to some degree in all of the solvents examined, despite being well-separated at the start of each simulation. The progression

Table 2. Comparison of the calculated densities and self-diffusion coefficients for the pure solvents with their measured values. Solvent THF

Density (g/cm3) Calculated 0.79 ± 0.001

Experiment

Experiment

45

0.851

453.6 ± 12

315

0.942

110.5 ± 2

13044

0.77 ± 0.002

0.86

0.87 ± 0.002

0.9445

0.91 ± 0.001

0.98

40

1.01

46

0.93 ± 0.001

Calculated

0.88

G2 G4

Ref. 32

32

G1 G3

Self-Diffusivity (10-7 cm 2/s) 0.889

-1.025

404.8 ± 6

28.2 ± 0.1 7.1 ± 0.3

Ref. 32

300

44

211.34 ± 19.2

44

230 ± 4.85 (303 K) 70.4 ± 4.2 (303 K)

61

44

11.34

-32

8.34 ± 1.8 (312 K)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 12

Figure 2. Agglomeration rate of Mg2+ and BH 4- ions into clusters of different sizes as a function of salt content and solvent composition, over the course of 5.5 ns MD simulations.

of agglomeration in each electrolyte is shown in Figure 2 during the course of 5.5-nanosecond simulations; Figure S1shows similar data for selected compositions that have been run for longer, 30-ns simulations. At 0.01 M, the rate of agglomeration varies substantially as a function of the solvent used. In the solvents with the most compact molecular structure, DME and THF, Mg(BH4)2 and larger clusters form

very rapidly: These agglomerates (depicted by the orange and green curves in Fig. 2) are the dominant species from about 1.5 ns onward. By the end of the 5.5 ns MD window essentially no isolated Mg2+ or BH4- ions remain: all have been incorporated into larger agglomerates. In contrast, the rate of salt agglomeration is much slower in the largest solvents, triglyme and tetraglyme. Here, isolated Mg2+ and BH4- ions remain the most prevalent species for the entire duration


Page 5 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a)

b)

Figure 3. (a) Representative structure of a 0.4 M Mg(BH 4)2/DME electrolyte at the end of a 5-ns MD simulation, and (b) radial distribution function (RDF) calculated during the last 0.5 ns of MD. Dotted vertical lines in the RDF indicate Mg-H and Mg-B distances in crystalline Mg(BH 4)2.

of the simulations. The percentage of unpaired ions equilibrates at values of roughly 45% in G3, and at 70% in G4, Fig. 2. Figure S1 shows that at longer simulation times the percentage of unpaired ions continues to decrease, albeit more slowly, until approximately 15% (G3) and 30% (G4) of ions are unpaired after 30 ns of simulation time. As expected, the agglomeration behavior of G2, whose molecular size lies between the smallest (DME, THF) and largest solvents (G3, G4), falls roughly between these extremes. A nearly equal balance of isolated and agglomerated ions is present at the end of the 5.5-ns MD window for the G2-based system. By 18 ns (Fig S1), all ions are paired. Upon increasing the concentration to 0.1 M and 0.4 M, larger salt clusters quickly become the main equilibrium species in every electrolyte, regardless of solvent composition (Fig. 2). Consequently, the percentage of free Mg2+ ions is nearly zero in all of these systems. (The only exception is 0.1M G4, where the Mg2+ percentage hovers around 10% at 5.5 ns, and falls to approximately zero by 10 ns, Fig. S1.) These larger clusters differ significantly in size between electrolytes, however: in DME and THF relatively few, large agglomerates form, while numerous, but smaller agglomerates are preferred in triglyme and tetraglyme. For example, examination of the intermediate concentration (0.1 M) electrolytes revealed that the average agglomerate has a diameter of 16.1 Å in the DME-based electrolyte, whereas the G4-based system exhibited clusters that are on average less than half that size, 7.5 Å. The structure of these agglomerates is illustrated in Figure 3 for a representative 0.4 M DME system at the end of a 5-ns simulation.

(Additional images of salt agglomerates in other 0.4 M electrolytes along with their RDF plots are shown in Figs. S2-S6). Here, the Mg2+ and BH4- ions have coalesced into five large clusters, leaving only a small number of free magnesium ions. The accompanying radial distribution function (RDF), Fig. 3b, confirms that the Mg2+ ions are in close proximity to BH4- anions: the first two peaks in the RDF correspond to Mg-H (salt) and Mg-B distances, and occur at about 2.0 and 2.6 Å, respectively. These distances are similar to the associated distances in crystalline Mg(BH4)2 (shown as vertical dashed lines in Fig. 3b), indicative of structure reminiscent of the solid salt.50 The presence of additional peaks at larger distances in the RDF indicates the presence of ordering within the clusters over a relatively long range. To visualize the dynamics of agglomeration, trajectories for the Mg2+ and BH4- ions in the G3-based electrolytes were generated at each concentration. These trajectories are shown in Figure 4 for 0.2 ns windows at increasingly later stages of the MD simulation, for two concentrations: 0.01 and 0.4 M. (Fig. S7 shows the trajectory for the 0.1 M case.) In the early-time panels of Fig. 4, the ion trajectories are relatively delocalized. However, as the simulation progresses these trajectories localize as the ions combine into clusters. This coincides with the appearance of increasingly larger regions dominated by the solvent alone (grey coloring). At the later MD stages, displacements associated with isolated ions are less common, with most ion trajectories localized (i.e. orbiting around or within) ion-paired clusters. When agglomeration does occur, it appears to be permanent. This is supported by the nearly monotonic nature of the agglomeration profiles in Fig. 2, and the images in Fig. 4, which show only instances of cluster growth, and little evidence of dissociation.

Table 3. Experimental properties of each solvent and solubility of Mg(BH4)2. Solvent

Mg(BH 4)2 Solubility

THF DME Diglyme Triglyme Tetraglyme

0.5 M23 0.01 M29, 0.1 M23 0.01 M29 Not reported >0.1 M, < 0.5 M27

Dielectric Constant 7.441 7.0740 7.4040 7.6340 7.7840

Dipole Moment (D)61

Viscosity (cP)

1.7562 1.62,45 1.61,63 1.59,64 1.71 (in benzene)64 1.91,45 1.92,63,64 1.87,65 1.97 (in benzene)64 2.16,63,64 2.22 (in benzene)64 2.44,64 2.4540,64

0.4648 0.4649 0.9849 3.8049 4.0549



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 12

a) Trajectories for 0.01 M electrolyte showing gradual agglomeration from distinct, isolated ions to a mix of small contact ion pairs and lone ions.

b) Trajectories for 0.4 M electrolyte exhibiting agglomeration of Mg(BH4) 2 salt into large clusters with no remaining isolated ions. Figure 4. Ion agglomeration in triglyme in (a) 0.01 M and (b) 0.4 M Mg(BH 4)2. Yellow represents magnesium, blue is boron. Each image depicts the ion trajectories over a 0.2-ns window, with images starting at 0, 1, 2, 3, 4, and 5.4 ns. For clarity, solvent molecules are not shown.

Based on the present data, and those of previous reports indicating significant ion pairing of borohydride compounds in solution,23,29,51 it is reasonable to expect that agglomeration plays a role in the low solubility23,27,29,33 of Mg(BH4)2 in glymes and in THF. The variation in agglomeration rate across solvents (at a fixed concentra-

tion) closely follows the trend in the Mg diffusion coefficient (discussed below): agglomeration occurs the most rapidly in the solvents that have the highest Mg diffusion coefficients. This suggests that the agglomeration of Mg(BH4)2 is diffusion limited. Other correlations between the agglomeration rates and the self-diffusivity, dielectric constant, and dipole moment of each solvent (Table 3) may


Page 7 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


be considered. These data suggest that the agglomeration rate (at a fixed concentration) approximately follows the trend in self-diffusivity of the solvents, Table 2. Similarly, agglomeration rate and cluster size follow the dipole moments of the solvents: DME, with the lowest dipole moment, exhibits the most rapid agglomeration of Mg2+ and BH4- into large ion clusters, followed (in order) by THF, G2, and the larger glymes. Conversely, the dielectric constant does not appear to have a large effect on agglomeration. This may be because all the solvents considered have similar values, ranging from 7.1 to 7.8. Solvation Structure of Mg2+ Ions. Radial distribution functions were computed for Mg-Mg, Mg-O, Mg-B, and Mg-H (H from BH4) distances to reveal the solvation structure of the Mg2+ ion. The RDFs were evaluated over the last 0.5 ns of the MD runs, at which point the agglomeration process had equilibrated in all systems except those based on the longest chain solvents (G3, G4) and the lowest concentrations (0.01 M). Representative RDF plots are shown in Figure 5. Based on the coordination of Mg2+ by BH4- anions indicated by the RDFs, three solvation scenarios were identified: solvent-separated ion pairs (Mg2+ coordinated by 0 to 1 anions), contact ion pairs (1-2 coordinating anions), and clusters (coordination by more than two anions). The prevalence of these coordination scenarios as a function of salt concentration is described below. At 0.01 M concentration, all the solvent systems exhibit peaks in their RDFs between Mg-B/H at distances slightly less than 2 Å, indicative of the presence of contact ion pairs. The sharpness of the Mg-B and Mg-H peaks point to strong association between cations and anions. Further support for the direct interaction of Mg cations and BH4 anions is provided by the presence of Mg-B peaks as a major

Table 4: Coordination number of selected atoms about Mg2+ ions as a function of solvent composition in 0.4 M electrolytes. Solvent THF DME Diglyme Triglyme Tetraglyme

O 0.2 0.1 0.6 1.1 2.8

Mg 8.6 8.5 6.9 4.3 1.9

B 5 5 4.5 4.9 3.7

H 7.5 8.3 8.8 5.4 4.5

feature in all systems, but with distances slightly longer than those for Mg-H. Mg-Mg peaks are observed in DME, diglyme, and THF-based electrolytes, but not in the longer G3/G4-based systems. These features indicate that contact ion pairs involving multiple Mg2+ ions, such as Mg2BH43+ or larger clusters, are present in these solvents. Finally, a weak Mg-O peak (black curve in Fig. 5) is present in the RDF for all electrolytes. (An inset illustrates this feature for the DMEbased electrolyte.) This peak reflects Mg2+ coordination by solvent molecules; the small magnitude is due to the tendency to form ion pairs in all solvents except the longer-chain systems. Indeed, this peak only becomes visible (at the scale used to depict cation-anion RDFs) in the RDF for the G4-based system. The absence of secondary peaks in the Mg-O RDF at larger separations suggests that the solvent molecules beyond the first solvation shell are disordered. A unique feature in the RDFs for 0.1 M concentrations (compared to the 0.01 M systems) is the appearance of prominent Mg-

Figure 5. Radial distribution functions between magnesium and O, Mg, B, and H (from BH 4-) for each solvent and concentration, averaged over the last 0.5 nanoseconds of molecular dynamics.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 12

Mg peaks in triglyme and tetraglyme at 4.5 to 5 Å. The lack of secondary peaks in these solvent systems indicates a lack of long-range order, suggesting that the clusters formed are relatively small. In contrast, secondary Mg-Mg RDF peaks appear in the DME, diglyme, and THF-based electrolytes at average separations of approximately 10 Å, consistent with the agglomeration of larger clusters.

molecules, as suggested by the coordination number of oxygen, generally was observed to increase with increasing size/length of the solvent molecule. Similarly, the propensity for agglomeration, as suggested by coordination with Mg, B, and H (due to the presence of neighboring Mg2+ and BH4- groups), decreases with solvent size/length.

Finally, at 0.4 M, the RDFs indicate the presence of significant long-range cation-anion ordering in all systems except those based on tetraglyme. The RDF peak positions are similar across the solvents, with Mg-BH4 peaks at about 2 Å and Mg-Mg peaks about every 5 Å. (DME and THF also show additional Mg-Mg peaks at about 8.5 Å.) The long-range structure of the RDFs is consistent with the formation of larger clusters at these higher concentrations.

Figure 6 provides a real-space picture of representative solvation structures for lone Mg2+ ions across the five solvent systems examined. In all cases, electrostatic interactions with Mg2+ result in nearest-neighbor pairs involving negatively-charged oxygens from the solvents. Typical Mg-O distances are ~2.3 Å, consistent with the RDF data in Fig. 5. The number of molecules coordinating Mg2+ was evaluated for each solvent system; the trend in coordination number was observed to correlate with the size of the solvent. For example, 4 molecules of THF – the smallest solvent considered – coordinate Mg2+, while three molecules participate in the case of larger DME

Table 4 summarizes the calculated coordination numbers for Mg2+ ions by O, Mg, B, and H of BH4- as a function of solvent, assuming a salt concentration of 0.4 M. Coordination of Mg2+ by solvent

THF

DME

Diglyme

Triglyme

Tetraglyme

Figure 6. Representative images of the solvation of a lone magnesium ion (viewed along two directions) in each solvent examined. Nearestneighbor distances (in Å) between Mg2+ and Oxygen are highlighted.


Page 9 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7. Mean squared displacement (MSD) of Mg2+ ions in DME as a function of concentration. (Left) Raw MSD data from the last nanosecond of ten independent MD calculations; (Right) Average MSD evaluated from the ten MD calculations using the leave-one-out method,43 and a linear fit to that average (the latter used to calculate the diffusion coefficient).

and diglyme. Finally, only two triglyme and tetraglyme molecules are required to solvate a lone Mg2+. Solvents that are better able to chelate metal ions have been observed to exhibit superior plating and stripping behavior of the metal, and higher Coulombic efficiencies (CE).23,29 In a previous study, diglyme was found to have better chelating ability than DME, which in turn was better than THF, as a result of kinetic and thermodynamic factors.29 Our results (Fig. 6) indicate that the number of chelating oxygens roughly increases with solvent size: THF (4 chelating oxygens), DME (3), diglyme (6), triglyme (7), and tetraglyme (7). By this metric, tetraglyme and triglyme would be expected to exhibit superior CE and stripping behavior compared to the other solvents examined. Diffusivity of Mg2+ Ions. The mobility of charge-carrying ions within the electrolyte is a critical factor for battery performance. Figure 7 shows the calculated mean squared displacements (MSD) for Mg2+ in the DME-based electrolytes as a function of salt concentration. (MSD plots for the other solvent systems can be found in the Supporting Information, Figures S8-S11.) To improve the statistical accuracy of the calculations, 10 independent simulations were performed for each concentration. The diffusion coefficients, D, were calculated using Eq. 1 and the mean MSD of the independent simulations, while the error was calculated using the leave-one-out method, as described by Wang and Hou.43 Figure 7 shows that the leave-one-out average yields linear squared displacements, and that the magnitude of the displacements decreases with increasing salt

concentration. The resulting diffusion data are summarized in Table 5, along with comparisons to previous calculations conducted at 0.4 M32 and to experiments at 0.075 M.9 The tendency for Mg2+ and BH4- ions to associate during MD timescales implies that the calculated diffusion coefficient will likely depict Mg mobility around or within a Mg-BH4 cluster. While characterizing diffusion for the agglomerated-salt scenario is certainly of relevance for these electrolytes, the diffusivity of a lone Mg2+ ion (coordinated only by solvent) is also of intrinsic importance. Thus, the diffusion of a nominally-isolated Mg2+ ion was evaluated by running simulations containing a single formula unit of Mg(BH4)2 in the various solvents. These data are reported in Table 5 as the ‘dilute limit.’ Despite the dilute nature of these simulations, in some cases the salt ions associated before the end of the simulation. In these instances, the MSD was recorded over an earlier 1-ns window that excluded the regime in which ion pairs had formed. The trends in the calculated diffusion coefficients reported in Table 5 closely follow those for the self-diffusivity of the solvents, Table 2. Except for the THF dilute limit, Mg2+ diffusion decreases monotonically as the salt concentration or solvent size increases. Lone Mg2+ ions (i.e., in the ‘dilute limit’) generally exhibited higher diffusion coefficients. [To confirm the dilute limit behavior of THF, we calculated the diffusivity for Mg2+ ions in the agglomerated state at the same concentration and found that it was indeed higher (~400×10-07 cm2/s) than for isolated Mg2+.]



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 12

Table 5. Calculated diffusion coefficients for Mg2+ (units: 10-7 cm2/s) as a function of solvent composition and salt concentration. Solvent

Dilute Limit

0.01 M

0.1 M

0.4 M

Ref. 32 (0.4 M)

THF

243.1 ± 15.9

345.9 ± 11.3

139.5 ± 9

70.4 ± 2

28 ± 8

DME

338.4 ± 29.1

321 ± 20.1

124.3 ± 5.1

69.3 ± 3.4

25 ± 3

Diglyme

130.2 ± 13.3

104.7 ± 5.5

69.4 ± 1.1

40 ± 1.1

18 ± 2

Triglyme

20.6 ± 1.8

19.1 ± 0.9

16.4 ± 0.3

8.8 ± 0.1

--

Tetraglyme

6.2 ± 0.8

4.7 ± 0.2

4.6 ± 0.1

3.8 ± 0.1

1

Experiment: 0.075 M9 in DME

100 – 160

Calculation: 0.075 M in DME (interpolated from 0.01M and 0.1M calculations)

179

To our knowledge molecular dynamics simulations have not been reported for these electrolytes at 0.1 M, 0.01 M, and the dilute limit. However, Rajput et al. previously performed simulations at higher concentrations of 0.4 M.32 Comparing the present diffusion coefficients to that work, we see that our results are ~183% higher on average. The difference in the 0.4 M results comes in part from the different force fields employed. The work in Ref. 32 used the General Amber Force Fields47, while the present work is based on the OPLSAA with dielectric constants specific to each solvent examined. Compared to the present study, the data from Ref. 32 shows better agreement with experimental solvent densities, but worse agreement with solvent self-diffusivities. Regarding experimental data, Chadwick et al.9 reported a value of 100 – 160×10-7 cm2/s for the diffusion coefficient of magnesium in a 0.075 M electrolyte of Mg(BH4)2 in DME. A linear interpolation between our 0.01 M and 0.1 M diffusion coefficients was performed to compare the present calculations to these measurements. The diffusivity calculated this way, 179 × 10-7 cm2/s, is close to the value reported by Chadwick et al. For comparison, the diffusivity of Li+ in common Li-ion battery electrolytes (typically employing salt concentrations of ~1 M) falls in the range of 7 – 77 × 10-7 cm2/s.44,52–54 We note that this range for Li+ diffusivity overlaps strongly with the range of diffusivities calculated here for Mg2+ in the 0.4 M electrolytes, 4 – 70 × 10-7 cm2/s. Nevertheless, we emphasize that the calculated values correspond to Mg2+ migration within the confines of large, and mostly-immobile agglomerates of Mg2+ and BH4- ion pairs. It is therefore likely that displacements observed for ion-paired Mg2+ will not contribute to macroscopic charge transfer. A more reliable estimate of ionic transport in these electrolytes is given by the dilute limit simulations. It is helpful to compare the present Mg-based systems, which show a strong tendency for ion clustering, to the behavior of monovalent systems, such as those based on Li salts. The formation of small ion clusters has been discussed by several authors in Libased systems.55–60 For example, Tenney and Cygan analyzed ion clusters in Li-ion electrolytes comprising LiPF6 salt and ethylene carbonate (EC), dimethylene carbonate (DMC), and EC/DMC mixtures.60 [The DMC-based system provides the most relevant comparison to the present results, as it has a dielectric constant (4) and viscosity (0.6 cP) similar to the THF, DME, and G2 solvents examined here.] Clustering in DMC was found to be more significant than in the EC or EC/DMC mixtures; nevertheless, the size of these clusters – which generally contained two Li+-PF6- pairs – is much smaller than those observed for the present Mg system. Taken together, these data suggest a greater tendency for ion

agglomeration in multivalent Mg-based electrolytes compared to those based on monovalent Li. CONCLUSION Molecular-scale simulations of salt agglomeration and ion transport in Mg electrolytes based on Mg(BH4)2 salts have been presented. These electrolytes suffer from poor salt solubility and/or low conductivity, presumably due to their tendency to undergo ion pairing reactions that scavenge the primary ionic charge carriers, solvated Mg cations. The present study takes a step towards understanding these reactions, and their impact on transport, across a family of Mg electrolytes based on five different solvents (THF and the glymes G1, G2, G3, and G4) and at four salt concentrations, ranging from the dilute limit up to 0.4 M. Our calculations reveal significant and irreversible salt agglomeration in all solvents examined and for all non-dilute salt concentrations. The degree of ion clustering observed in these divalent Mg systems is much larger than that reported for electrolytes containing monovalent cations, such as Li. The salt agglomeration rate and diffusivity of Mg2+ were both observed to correlate with solvent self-diffusivity, which itself tracks solvent size: electrolytes using longer(shorter-)chain solvents had the lowest (highest) Mg2+ diffusivity and agglomeration rates. Incorporation of Mg2+ into Mg2+-BH4- clusters significantly reduces the diffusivity of Mg2+. Once these clusters are formed, the displacements of Mg ions are restricted to localized motion within (or around) these agglomerates. Because the clusters are relatively immobile, these ion displacements do not contribute to long-range charge transport. Moreover, diffusion is increasingly impeded with increasing concentration, as higher concentrations increase the rate of cluster formation. These data are consistent with the solubility limitations observed experimentally for Mg(BH4)2based electrolytes, and highlight the need for strategies that can minimize salt agglomeration in electrolytes containing divalent cations.

ASSOCIATED CONTENT Supporting Information Partial charges used in MD simulations; agglomeration plots for longer duration MD simulations; ion trajectories showing clustering in triglyme at a salt concentration of 0.1 M; radial distribution functions and cluster morphologies in the various solvents at a salt concentration of 0.4 M; mean squared displacement plots for the various solvents as a function of salt concentration. The Supporting Information is available free of charge on the ACS Publications website.


Page 11 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]; Tel: 734-764-4808

ACKNOWLEDGMENT This work was supported by the Joint Center for Energy Storage Research, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, by DENSO International America, Inc., and by the U.S. National Science Foundation, grant no. CBET-1336387.

REFERENCES (1) Bruce, P. G.; Freunberger, S. A.; Hardwick, L. J.; Tarascon, J.-M. Li–O2 and Li–S Batteries with High Energy Storage. Nat. Mater. 2011, 11 (2), 19–29. (2) Bruce, P. G. Energy Storage Beyond the Horizon: Rechargeable Lithium Batteries. Solid State Ionics 2008, 179 (1), 752–760. (3) Hassoun, J.; Scrosati, B. Review—Advances in Anode and Electrolyte Materials for the Progress of Lithium-Ion and beyond LithiumIon Batteries. J. Electrochem. Soc. 2015, 162 (14), A2582–A2588. (4) Thackeray, M. M.; Wolverton, C.; Isaacs, E. D. Electrical Energy Storage for Transportation—approaching the Limits Of, and Going Beyond, Lithium-Ion Batteries. Energy Environ. Sci. 2012, 5 (7), 7854–7863. (5) Armand, M.; Tarascon, J.-M. Building Better Batteries. Nature 2008, 451 (7179), 652–657. (6) Besenhard, J. O.; Winter, M. Advances in Battery Technology: Rechargeable Magnesium Batteries and Novel Negative-Electrode Materials for Lithium Ion Batteries. ChemPhysChem 2002, 3 (2), 155–159. (7) Saha, P.; Datta, M. K.; Velikokhatnyi, O. I.; Manivannan, A.; Alman, D.; Kumta, P. N. Rechargeable Magnesium Battery: Current Status and Key Challenges for the Future. Prog. Mater. Sci. 2014, 66, 1–86. (8) Yoo, H. D.; Shterenberg, I.; Gofer, Y.; Gershinsky, G.; Pour, N.; Aurbach, D. Mg Rechargeable Batteries: An on-Going Challenge. Energy Environ. Sci. 2013, 6 (8), 2265–2279. (9) Chadwick, A. F.; Vardar, G.; DeWitt, S.; Sleightholme, A. E. S.; Monroe, C. W.; Siegel, D. J.; Thornton, K. Computational Model of Magnesium Deposition and Dissolution for Property Determination via Cyclic Voltammetry. J. Electrochem. Soc. 2016, 163 (9), A1813–A1821. (10) Gregory, T. D. Nonaqueous Electrochemistry of Magnesium. J. Electrochem. Soc. 1990, 137 (3), 775–780. (11) Muldoon, J.; Bucur, C. B.; Oliver, A. G.; Sugimoto, T.; Matsui, M.; Kim, H. S.; Allred, G. D.; Zajicek, J.; Kotani, Y. Electrolyte Roadblocks to a Magnesium Rechargeable Battery. Energy Environ. Sci. 2012, 5 (3), 5941–5950. (12) Doe, R. E.; Han, R.; Hwang, J.; Gmitter, A. J.; Shterenberg, I.; Yoo, H. D.; Pour, N.; Aurbach, D. Novel, Electrolyte Solutions Comprising Fully Inorganic Salts with High Anodic Stability for Rechargeable Magnesium Batteries. Chem. Commun. (Camb). 2014, 50 (2), 243–245. (13) Aurbach, D.; Lu, Z.; Schechter, A.; Gofer, Y.; Gizbar, H.; Turgeman, R.; Cohen, Y.; Moshkovich, M.; Levi, E. Prototype Systems for Rechargeable Magnesium Batteries. Nature 2000, 407 (6805), 724–727. (14) Morita, M.; Yoshimoto, N.; Yakushiji, S.; Ishikawa, M. Rechargeable Magnesium Batteries Using a Novel Polymeric Solid Electrolyte. Electrochem. Solid-State Lett. 2001, 4 (11), A177–A179. (15) Girish Kumar, G.; Munichandraiah, N. Poly(methylmethacrylate) - Magnesium Triflate Gel Polymer Electrolyte for Solid State Magnesium Battery Application. Electrochim. Acta 2002, 47 (7), 1013–1022. (16) Aurbach, D.; Gizbar, H.; Schechter, A.; Chusid, O.; Gottlieb, H. E.; Gofer, Y.; Goldberg, I. Electrolyte Solutions for Rechargeable Magnesium Batteries Based on Organomagnesium Chloroaluminate Complexes. J. Electrochem. Soc. 2002, 149 (2), A115–A121. (17) Aurbach, D.; Weissman, I.; Gofer, Y.; Levi, E. Nonaqueous Magnesium Electrochemistry and Its Application in Secondary Batteries. Chem. Rec. 2003, 3 (1), 61–73.

(18) Gofer, Y.; Chusid, O.; Gizbar, H.; Viestfrid, Y.; Gottlieb, H. E.; Marks, V.; Aurbach, D. Improved Electrolyte Solutions for Rechargeable Magnesium Batteries. Electrochem. Solid-State Lett. 2006, 9 (5), A257–A260. (19) Amir, N.; Vestfrid, Y.; Chusid, O.; Gofer, Y.; Aurbach, D. Progress in Nonaqueous Magnesium Electrochemistry. J. Power Sources 2007, 174 (2), 1234–1240. (20) Mizrahi, O.; Amir, N.; Pollak, E.; Chusid, O.; Marks, V.; Gottlieb, H.; Larush, L.; Zinigrad, E.; Aurbach, D. Electrolyte Solutions with a Wide Electrochemical Window for Rechargeable Magnesium Batteries. J. Electrochem. Soc. 2008, 155 (2), A103–A109. (21) Sheha, E.; El-Mansy, M. K. A High Voltage Magnesium Battery Based on H2SO4-Doped (PVA)0.7(NaBr)0.3 Solid Polymer Electrolyte. J. Power Sources 2008, 185 (2), 1509–1513. (22) Guo, Y.; Zhang, F.; Yang, J.; Wang, F.; NuLi, Y.; Hirano, S. Boron-Based Electrolyte Solutions with Wide Electrochemical Windows for Rechargeable Magnesium Batteries. Energy Environ. Sci. 2012, 5 (10), 9100– 9106. (23) Mohtadi, R.; Matsui, M.; Arthur, T. S.; Hwang, S. J. Magnesium Borohydride: From Hydrogen Storage to Magnesium Battery. Angew. Chemie - Int. Ed. 2012, 51 (39), 9780–9783. (24) Carter, T. J.; Mohtadi, R.; Arthur, T. S.; Mizuno, F.; Zhang, R.; Shirai, S.; Kampf, J. W. Boron Clusters as Highly Stable Magnesium-Battery Electrolytes. Angew. Chemie - Int. Ed. 2014, 53 (12), 3173–3177. (25) Ha, S.; Lee, Y.; Woo, S. W.; Koo, B.; Kim, J.; Cho, J.; Lee, K. T.; Choi, N. Magnesium ( II ) Bis ( Tri Fl Uoromethane Sulfonyl ) Imide-Based Electrolytes with Wide Electrochemical Windows for Rechargeable Magnesium Batteries. ACS Appl. Mater. Interfaces 2014, 6 (Ii), 4063–4073. (26) Tutusaus, O.; Mohtadi, R.; Arthur, T. S.; Mizuno, F.; Nelson, E. G.; Sevryugina, Y. V. An Efficient Halogen-Free Electrolyte for Use in Rechargeable Magnesium Batteries. Angew. Chemie - Int. Ed. 2015, 54 (27), 7900–7904. (27) Tuerxun, F.; Abulizi, Y.; Nuli, Y.; Su, S.; Yang, J.; Wang, J. High Concentration Magnesium Borohydride/tetraglyme Electrolyte for Rechargeable Magnesium Batteries. J. Power Sources 2015, 276, 255–261. (28) Shao, Y.; Rajput, N. N.; Hu, J.; Hu, M.; Liu, T.; Wei, Z.; Gu, M.; Deng, X.; Xu, S.; Han, K. S.; Wang, J.; Nie, Z.; Li, G.; Zavadil, K. R.; Xiao, J.; Wang, C.; Henderson, W. A.; Zhang, J. G.; Wang, Y.; Mueller, K. T.; Persson, K.; Liu, J. Nanocomposite Polymer Electrolyte for Rechargeable Magnesium Batteries. Nano Energy 2015, 12, 750–759. (29) Shao, Y.; Liu, T.; Li, G.; Gu, M.; Nie, Z.; Engelhard, M.; Xiao, J.; Lv, D.; Wang, C.; Zhang, J.-G.; Liu, J. Coordination Chemistry in Magnesium Battery Electrolytes: How Ligands Affect Their Performance. Sci. Rep. 2013, 3, 4–10. (30) Chang, J.; Haasch, R. T.; Kim, J.; Spila, T.; Braun, P. V.; Gewirth, A. A.; Nuzzo, R. G. Synergetic Role of Li+ during Mg Electrodeposition/dissolution in Borohydride Diglyme Electrolyte Solution: Voltammetric Stripping Behaviors on a Pt Microelectrode Indicative of Mg-Li Alloying and Facilitated Dissolution. ACS Appl. Mater. Interfaces 2015, 7 (4), 2494–2502. (31) Mohtadi, R.; Mizuno, F. Magnesium Batteries: Current State of the Art, Issues and Future Perspectives. Beilstein J. Nanotechnol. 2014, 5 (1), 1291–1311. (32) Rajput, N. N.; Qu, X.; Sa, N.; Burrell, A. K.; Persson, K. A. The Coupling between Stability and Ion Pair Formation in Magnesium Electrolytes from First-Principles Quantum Mechanics and Classical Molecular Dynamics. J. Am. Chem. Soc. 2015, 137 (9), 3411–3420. (33) Tutusaus, O.; Mohtadi, R. Paving the Way towards Highly Stable and Practical Electrolytes for Rechargeable Magnesium Batteries. ChemElectroChem 2015, 2 (1), 51–57. (34) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. Journal of Computational Physics. 1995, pp 1–19. (35) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. Optimized Intermolecular Potential Functions for Liquid Hydrocarbons. J. Am. Chem. Soc. 1984, 106 (22), 6638–6646. (36) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118 (45), 11225–11236.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(37) Jorgensen, W. L.; Ulmschneider, J. P.; Tirado-Rives, J. Free Energies of Hydration from a Generalized Born Model and an All-Atom Force Field. J. Phys. Chem. B 2004, 108 (41), 16264–16270. (38) Resende Prado, C. E.; Gomide Freitas, L. C. Molecular Dynamics Simulation of the Room-Temperature Ionic Liquid 1-Butyl-3Methylimidazolium Tetrafluoroborate. J. Mol. Struct. THEOCHEM 2007, 847 (1–3), 93–100. (39) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenb, D. J. Gaussian 09, Revision A.02. Gaussian, Inc.: Wallingford CT 2016. (40) Riadigos, C. F.; Iglesias, R.; Rivas, M. A.; Iglesias, T. P. Permittivity and Density of the Systems (Monoglyme, Diglyme, Triglyme, or Tetraglyme + N-Heptane) at Several Temperatures. J. Chem. Thermodyn. 2011, 43 (3), 275–283. (41) Carvajal, C.; Tölle, K. J.; Smid, J.; Szwarc, M. Studies of Solvation Phenomena of Ions and Ion Pairs in Dimethoxyethane and Tetrahydrofuran. J. Am. Chem. Soc. 1965, 87 (24), 5548–5553. (42) L. Martínez, R. Andrade, E. G. Birgin, J. M. M. Packmol: A Package for Building Initial Configurations for Molecular Dynamics Simulations. J. Comput. Chem. 2009, 30 (13), 2157–2164. (43) Wang, J.; Hou, T. Application of Molecular Dynamics Simulations in Molecular Property Prediction II: Diffusion Coefficient. J. Comput. Chem. 2011, 32 (16), 3505–3519. (44) Hayamizu, K.; Aihara, Y.; Arai, S. Pulse-Gradient Spin-Echo 1 H, 7 Li, and 19 F NMR Diffusion and Ionic Conductivity Measurements of 14 Organic Electrolytes Containing LiN(SO 2 CF 3 ) 2. J. Phys. Chem. B 1999, 103 (3), 519–524. (45) Lago, A.; Rivas, M. A.; Legido, J.; Iglesias, T. P. Study of Static Permittivity and Density of the Systems {(n-Nonane + Monoglyme or Diglyme)} at Various Temperatures. J. Chem. Thermodyn. 2009, 41 (2), 257–264. (46) Rivas, M. A.; Iglesias, T. P.; Pereira, S. M.; Banerji, N. On the Permittivity and Density of the Systems {tetraglyme + (N-Nonane or NDodecane)} at Various Temperatures. J. Chem. Thermodyn. 2006, 38 (3), 245–256. (47) Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and Testing of a General Amber Force Field. J. Comput. Chem. 2004, 25 (9), 1157–1174. (48) Das, B.; Roy, M. N.; Hazra, D. J. Densities and Viscosities of the Binary Aqueous Mixtures of Tetrahydrofuran and 1,2-Dimethoxyethane at 298, 308, and 318 K. Indian J. Chem. Technol. 1993, 1, 93–97. (49) Tobishima, S.; Morimoto, H.; Aoki, M.; Saito, Y.; Inose, T.; Fukumoto, T.; Kuryu, T. Glyme-Based Nonaqueous Electrolytes for Rechargeable Lithium Cells. Electrochim. Acta 2004, 49 (6), 979–987. (50) Filinchuk, Y.; Cerny, R.; Hagemann, H. Insight into Mg (BH4) 2 with Synchrotron X-Ray Diffraction: Structure Revision, Crystal Chemistry, and Anomalous Thermal Expansion. Chem. Mater. 2009, 21 (5), 925–933.

Page 12 of 12

(51) Shirk, a. E.; Shriver, D. F. Solvent and Cation Dependence of the Tetrahydroborate, BH4-, Raman Spectrum. J. Am. Chem. Soc. 1973, 95 (18), 5901–5904. (52) Hayamizu, K. Temperature Dependence of Self-Diffusion Coefficients of Ions and Solvents in Ethylene Carbonate, Propylene Carbonate, and Diethyl Carbonate Single Solutions and Ethylene Carbonate + Diethyl Carbonate Binary Solutions of LiPF 6 Studied by NMR. J. Chem. Eng. Data 2012, 57 (7), 2012–2017. (53) Nishida, T.; Nishikawa, K.; Fukunaka, Y. Diffusivity Measurement of LiPF6, LiTFSI, LiBF4 in PC. ECS Trans. 2008, 6 (18), 1– 14. (54) Valo̸en, L. O.; Reimers, J. N. Transport Properties of LiPF6Based Li-Ion Battery Electrolytes. J. Electrochem. Soc. 2005, 152 (5), A882– A891. (55) Tsunekawa, H.; Narumi, A.; Sano, M.; Hiwara, A.; Fujita, M.; Yokoyama, H. Solvation and Ion Association Studies of LiBF4−Propylenecarbonate and LiBF4−Propylenecarbonate−Trimethyl Phosphate Solutions. J. Phys. Chem. B 2003, 107 (39), 10962–10966. (56) Matsuda, Y.; Morita, M.; Yamashita, T. Conductivity of the LiBF4∕Mixed Ether Electrolytes for Secondary Lithium Cells. J. Electrochem. Soc. 1984, 131 (12), 2821–2827. (57) Takeuchi, M.; Kameda, Y.; Umebayashi, Y.; Ogawa, S.; Sonoda, T.; Ishiguro, S. ichi; Fujita, M.; Sano, M. Ion-Ion Interactions of LiPF6 and LiBF4 in Propylene Carbonate Solutions. J. Mol. Liq. 2009, 148 (2–3), 99– 108. (58) Takeuchi, M.; Matubayasi, N.; Kameda, Y.; Minofar, B.; Ishiguro, S. I.; Umebayashi, Y. Free-Energy and Structural Analysis of Ion Solvation and Contact Ion-Pair Formation of Li+ with BF4- and PF 6- in Water and Carbonate Solvents. J. Phys. Chem. B 2012, 116 (22), 6476–6487. (59) Borodin, O.; Smith, G. D. LiTFSI Structure and Transport in Ethylene Carbonate from Molecular Dynamics Simulations. J. Phys. Chem. B 2006, 110 (10), 4971–4977. (60) Tenney, C. M.; Cygan, R. T. Analysis of Molecular Clusters in Simulations of Lithium-Ion Battery Electrolytes. J. Phys. Chem. C 2013, 117 (47), 24673–24684. (61) Tang, S.; Zhao, H. Glymes as Versatile Solvents for Chemical Reactions and Processes: From the Laboratory to Industry. RSC Adv. 2014, 4 (22), 11251–11287. (62) Barton, T. J.; Roth, R. W.; Verkade, J. G. Directions of the Dipole Moments of Aromatic Heterocyclopentadienes. J. Am. Chem. Soc. 1972, 94 (25), 8854–8857. (63) Abboud, J.-L. M.; Notari, R. Critical Compilation of Scales of Solvent Parameters. Part I. Pure, Non-Hydrogen Bond Donor Solvents. Pure Appl. Chem. 1999, 71 (4), 645–718. (64) Kimura, K.; Fujisiiiro, R. The Dipole Moments of the Oligether of Ethylene Glycol. Bull. Chem. Soc. Japan 1966, 39 (3), 608–610. (65) Nakai, H.; Soejima, H.; Tamura, K.; Ogawa, H.; Murakami, S.; Toshiyasu, Y. Thermodynamic Properties of 2,5,8-Trioxanonane + NOctane Mixture at 298.15 K. Thermochim. Acta 1991, 183 (C), 15–27.

Table of Contents artwork


Ion Pairing and Diffusion in Magnesium Electrolytes Based on Mag

Recommend Documents