Polarizable Molecular Dynamics and Experiments of 1,2

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

Polarizable Molecular Dynamics and Experiments of 1,2-Dimethoxyethane Electrolytes with Lithium and Sodium Salts: Structure and Transport Properties Thilanga P. Liyana-Arachchi, Justin B Haskins, Colin M. Burke, Kyle M. Diederichsen, Bryan D. McCloskey, and John W. Lawson J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b03445 • Publication Date (Web): 21 Aug 2018 Downloaded from http://pubs.acs.org on August 24, 2018

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The Journal of Physical Chemistry

Polarizable Molecular Dynamics and Experiments of 1,2-Dimethoxyethane Electrolytes with Lithium and Sodium Salts: Structure and Transport Properties Thilanga P. Liyana-Arachchi,†,§ Justin B. Haskins,†,§ Colin M. Burke,‡ Kyle M. Diederichsen,‡ Bryan D. McCloskey,‡ and John W. Lawson∗,¶ AMA Inc., Thermal Materials Protection Branch, NASA Ames Research Center, Moffett Field, California 94035, USA, Department of Chemical and Bimolecular Engineering, University of California, Berkeley, California 94720, USA, and Thermal Materials Protection Branch, NASA Ames Research Center, Moffett Field, California 94035, USA E-mail: [email protected]

∗

To whom correspondence should be addressed AMA Inc., Thermal Materials Protection Branch, NASA Ames Research Center, Moffett Field, California 94035, USA ‡ Department of Chemical and Bimolecular Engineering, University of California, Berkeley, California 94720, USA ¶ Thermal Materials Protection Branch, NASA Ames Research Center, Moffett Field, California 94035, USA § Contributed equally to this work †

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Abstract The structure and transport properties of electrolyte solutions of 1,2-dimethoxyethane (DME) having salts of Li+ with bis(trifluoromethanesulfonyl)imide ([TFSI]− ) or Na+ with [TFSI]− are investigated with polarizable molecular dynamics and experiments. Polarizable force fields for Li+ and Na+ with DME and [TFSI]− were developed based on quantum chemistry calculations, ab initio molecular dynamics simulations, and thermodynamic liquid-state properties. Simulation results for density, viscosity, self-diffusion coefficient, and conductivity of the electrolytes all agree well with the trends and magnitudes of available experimental data for a wide range of salt concentrations. As the concentration of salt increases, the electrolytes become more viscous and molecular species become less mobile. Ionic conductivity does not change monotonically with salt concentration and exhibits a maximum between 0.5-1.0 M for both Li[TFSI] and Na[TFSI] electrolytes. Comparatively, both cations are solvated by 5-6 oxygen DME or [TFSI]- oxygen atoms and exhibit similar diffusivities and conductivities. The solvation shell of Na+ is found to be more weakly bound and to have a lower binding residence time than that of Li+ . The transport of Li+ therefore is more vehicular - through the motion of the solvation shell, while the transport of Na+ is based more on exchange through the replacement of solvating species. The atomistic insight provided by this work can be used as the basis for future rational design of improved electrolyte solvents for lithium-oxygen, sodium-oxygen, and lithium-sulfur batteries.

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Introduction Lithium-sulfur (Li-S), 1–5 sodium-oxygen (Na-O2 ), 6–9 and lithium-oxygen (Li-O2 ) 4,6,10–13 battery chemistries have attracted interest due to their high theoretical energy densities, 1600, 1600, and 3400 Wh/kg, respectively, compared to the state-of-the-art Li-ion rechargeable batteries. 14,15 However, many of the most significant challenges to these battery chemistries achieving greater cycle life and higher capacity are related to limitations of the electrolyte. Unlike Li-ion batteries, most advanced chemistries form reaction intermediates during cycling, and the solubility of these intermediates in the electrolyte can dramatically affect performance. For Li-S batteries, solubility of lithium polysulfide intermediates is common in many electrolytes and leads to the loss of active S and capacity. 16,17 For Li-O2 and Na-O2 , oxygen must be soluble in the electrolyte to allow the formation of sodium superoxide and lithium peroxide discharge products. 6,9,15,18–23 Beyond this for Li-O2 , increases in capacity have been noted when the reaction intermediates are soluble in the electrolyte. The resulting “solution mechanism” leads to non-conformal, lithium-peroxide toroid formation that increases capacity. 18–20,24,25 Due to the challenges in developing electrolytes suitable for advanced battery chemistries, atomistic-level understanding of the thermodynamic, transport, and structural properties of these systems is crucial to designing high performance electrolytes. Detailed information concerning properties such as solvation of both cations as well as reactive intermediates can be useful for understanding electrolyte decomposition and can also suggest strategies to boost the solubility of these species, and therefore increase system capacity. Towards this end, molecular dynamics (MD) simulations are an ideal tool for such investigations. In order to study and compare the interesting and significant differences between Li-cation and Nacation systems at the electrolyte level, we performed MD simulations of the thermodynamic, transport and structural properties of Li[TFSI] (lithium trifluoromethanesulfonylimide) and Na[TFSI] (sodium trifluoromethanesulfonylimide) salts in a 1,2-dimethoxyethane (DME) solvent. These DME based electrolytes are widely used in Li-S, Li-O2 , and Na-O2 batteries 3



and, hence, warrant detailed investigation. 6,18,23,24 A key question for any MD simulation is the quality of the force field used. Many general purpose force fields have been developed, e.g. OPLS, AMBER, etc. 26–29 for use in applications involving organic liquids. While such force fields can provide some valuable understanding for specific systems of interest, significant deviations for electrolytic systems, especially in transport and structural properties, are often seen compared to experimental data. 30 There are exceptions to this, however, such as the recent work of Park and coworkers, 31 who evaluated the properties of DME electrolytes with Li[TFSI] and Li[NO3 ] salts using point charge models with implicit polarization through ion charge scaling. The transport properties resulting from this were in good agreement with experiment at low-to-moderate concentrations. In general, it is very challenging to develop robust, high-fidelity force fields for electrolytes. Polarizable force fields, such as the atomistic polarizable potential for liquids, electrolytes, and polymers (APPLE&P) 32,33 and the atomic multipole optimized energetics for biomolecular simulation (AMOEBA) force field, 34,35 have been developed that can accurately predict the thermodynamic, transport, and structural properties (e.g., density, the heat of vaporization, viscosity, diffusion, conductivity, and solvation shell) of electrolytic systems (solvent combined with salts) or ionic complexes (e.g., ionic liquid), where polarization of the solvent by the ionic constituents is substantial. Successes include a variety of organic electrolytes, such as carbonate electrolytes, 15,36,37 and ionic liquid electrolytes. 38–40 However, available predictive models based on polarizable force fields are typically system specific and require careful parameterization to obtain a high degree of accuracy. In this paper, we develop high fidelity, polarizable force fields for electrolytes of Li[TFSI] and Na[TFSI] in DME, use them to perform comprehensive MD simulations of the structural, thermodynamic and transport properties for these systems, and validate the results against experimental data. Force fields for Li+ and Na+ with DME and [TFSI]− anions are obtained by fitting parameters to both quantum chemistry computations and ab initio 4


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molecular dynamics (AIMD). Force field fitting to AIMD data typically is not done due to the high computational expense. However, we have found that such an approach can result in robust, predictive models. MD simulations were performed for the two electrolytes using these new force field parameterizations to evaluate and compare key thermodynamic and transport properties (i.e., density, heat of vaporization, viscosity, diffusion, conductivity, correlated motion of cations/anions, and residence times between cations and molecules/anions) with varying salt concentration at 298 K. In addition, structural properties (e.g. radial distribution function (RDF), solvation shell) with varying salt concentrations at 298 K were also considered. The temperature dependence of the force field was examined by investigating the ionic conductivity up to 393 K. Complementary experimental data was obtained for density, heat of vaporization, viscosity, species self-diffusion coefficients and conductivity to validate the simulation results.

Methods Polarizable Force Field To describe the atomic interaction between Li+ , Na+ , [TFSI]− , and DME using MD simulation, we employed the functional form of the atomistic polarizable potential for liquids, electrolytes, and polymers (APPLE&P) developed by Borodin and coworkers. 15,32,33,38 The interactions consist of intramolecular bonds, angles, and torsions as well as intermolecular repulsion, dispersion, coulomb, and polarization terms. The repulsion and dispersion energy (U rd ) is given by a modified version of an exponential-6 Buckingham potential, rd

−Bij r

U (r) = Aij e

− Cij r

−6

+ Dij

12 Bij r

12 ,

(1)

where r is the distance between two atoms having types i and j; A and B are coefficients of repulsion; C governs dispersion; and D provides a hard wall interaction at small distances and 5



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was assigned a value of 5 × 10−5 kcal/mol for all pair interactions. 32,33 The cross interaction (i 6= j) repulsion and dispersion parameters of all species except those that involve Li+ or Na+ were determined using the Waldman-Hagler (WH) combination rules 41 as given by Aij = Bij = Cij =

p

Aii Ajj

Bii−6 p

Bij6 3 Bii3 Bjj !1/6

2 −6 + Bjj

,

(2)

Cii Cjj

where ii and jj indicate single element parameters and ij indicates a mixed parameter. The Coulomb interactions (U coul ) between all components were represented by partial point charges assigned to atomic centers and off-atom, “dummy” force centers, U coul =

1 qi qj 2 4π0 rij

(3)

where 0 is the vacuum permittivity and qi and qj are partial point charges assigned to atomic and off-atom force centers. Off-atom, force centers are added to the nitrogen of [TFSI]− , bisecting the S-N-S angle, and the oxygen atoms of DME to improve the electrostatic potential. This improves the description of the electrostatic potentials of the molecules. 32,42,43 Two force centers were used for each DME oxygen atom, while a single force center was used for the [TFSI]− nitrogen; more details are provided in Figures 1, S1, and S2. Polarization energy (U pol ) is given by 1 U pol (ri ) = − µi · E 0 (ri ), 2

(4)

where µi is the atomic dipole and E 0 is the electric field produced from charges only. The atomic dipoles are proportional to the total electric field at the atom site µi = αE(ri ), where the proportionality factor is the isotropic atomic polarizability (α). Because the electric field includes contributions from evolved dipoles, polarization energy was determined iteratively using a self consistent method. Thole screening was used to damp dipole-dipole interactions 6


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and prevent the “polarization catastrophe.” 44 Bonded interactions consisted of harmonic bonds and angles, while torsions were represented by an order-N harmonic series. Repulsive-dispersive and Coulombic interactions were excluded between atoms participating in bond (1-2 interactions) or angle (1-3 interactions). Induced dipole interactions were scaled by 0.2 between atoms separated by three bonds (1-4 interactions).

Polarizable Molecular Dynamics Simulations Molecular dynamics (MD) simulations were performed using a modified version of the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package. 43,45 All MD simulations were conducted using the 3-2-1 reversible reference system propagation algorithm (rRESPA), that allows splitting the force calculations within each time step (longrange Ewald summation of the charge = 3 fs, long-range Ewald summation of the dipole interactions = 3 fs, local charge = 1.5 fs, repulsive-dispersive = 1.5 fs, dihedral interactions = 1.5 fs, bonds = 0.5 fs, and angles = 0.5 fs). 46 MD simulations were conducted using a cutoff distance of 10 Å for non-bonded interactions and 6 Å for 1.5 fs rRESPA step interactions. The long-range charge-charge and charge-dipole interactions were handled with the Ewald summation, while the dipole-dipole interactions were treated with a reaction field formalism. The systems used for the calculation of thermodynamic, structural, and dynamical properties contained 433 DME molecules and up to 95 Li[TFSI] or Na[TFSI] ion pairs and are given in Table 1. MD simulations were performed on these systems at 298 K and 1 atm for calculation of thermodynamic, structural, and dynamical properties. The property simulations consisted of a temperature and pressure equilibration period of 20 ns, which was followed by production runs of up to 100 ns. All simulations were performed using the Nosé Hoover thermostat and barostat. A similar procedure was undertaken at 423 K and 1 atm for smaller liquid systems of 20 DME molecules and one Li[TFSI] or Na[TFSI] salt pair.

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Ab Initio Molecular Dynamics All ab initio molecular dynamics (AIMD) simulations were performed with the Vienna Ab Initio Simulation Package (VASP) 47–49 using the frozen-core, all-electron projector augmented wave (PAW) method and the generalized gradient approximation of Perdew, Burke, and Ernzerhof with the D2 correction for dispersion as parametrized by Grimme. 50,51 Gamma-point computations with an energy cutoff of 400 eV, an electronic energy convergence criteria of 1E-4 eV, and a time step of 1.0 fs were used for ab initio molecular dynamics simulations. AIMD simulations were performed on liquid systems containing 20 DME molecules and one ion pair of Li[TFSI] or Na[TFSI]. These simulations were performed at 423 K, where the temperature was controlled using the Langevin thermostat for a duration of 50 ps.

Quantum Chemistry Calculations Quantum chemistry calculations were performed using the Gaussian 09 (G09) software package 52 at a number of different levels of theory, which include density functional theory computations using the hybrid B3LYP functional 53 with the augmented correlation consistent polarized double zeta basis set (aug-cc-pvDz) of Dunning and coworkers 54,55 as well as second order Møller-Plesset perturbation theory (MP2) with the aug-cc-pvDz basis set. These approaches were used to carry out computations on complexes of Li+ and Na+ DME molecules and [TFSI]− anions.

Experimental Materials and Methods Lithium bis(trifluoromethanesulfonyl)imide and dimethoxyethane were obtained from BASF and used as received. Sodium bis(trifluoromethanesulfonyl)imide (99.7%) was obtained from Sigma Aldrich and used as received. Whatman QM-A filter paper was purchased from VWR and was rinsed with isopropyl alcohol and acetone and dried in a vacuum oven at 110◦ C prior to bringing it into the glove box.

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Electrolytes of Li[TFSI] in DME and Na[TFSI] in DME were prepared by mixing moles of salt with milliliters of solvent toward concentrations of 0.5, 1.0, 1.5, and 2.0 mole salt/liter solvent in an argon glove box. Due to volume expansion upon mixing, this underestimates the concentration of the solutions. The exact concentrations of the Li[TFSI] in DME samples were measured via 7Li+ NMR comparisons to standard solutions of LiCl in D2O prepared via volumetric flasks. Conductivities for Li[TFSI] in DME were measured with a Metrohm 5-ring conductivity measuring cell in an argon glove box, with an aluminum block for temperature control. Conductivity measurements for Na[TFSI] in DME were obtained using impedance in small volume Swagelok-type two-electrode cells. This was performed to minimize the amount of expensive Na[TFSI] in each sample. Swagelok cells consisting of two stainless steel current collectors sandwiching two pieces of

1 00 2

diameter Whatman QM-A filter paper and 160 µL

of electrolyte were prepared in an argon glove box. The cells were sealed using perfluorinated elastomer O-rings as described previously. 24 Cells were removed from the glove box and placed in an oven at 25.0 ◦ C. Potentio electrochemical impedance spectroscopy (PEIS) was performed with an amplitude of 10 mV, a frequency range of 100 kHz to 10 Hz, and eight points per decade, to obtain the bulk electrolyte resistance. Li[TFSI] in DME controls compared with the 5-ring conductivity measuring cell results were used to determine the cell constant for calculating conductivity. Conductivities were normalized against pure dimethoxyethane. The experimental data for Li[TFSI] in DME matches well with previous values in the literature. Conductivities are comparable of those measured for Li[TFSI] in DME over the range of concentrations at 30 ◦ C by Zhang et al. 56 Diffusion coefficients for lithium and fluorine for Li[TFSI] in DME and fluorine for Na[TFSI] in DME were obtained using diffusion-ordered spectroscopy (DOSY) NMR on a Bruker 600 MHz instrument fitted with a 5 mm Z-gradient broad-band probe and a variable temperature unit maintained at 25 ◦ C throughout the measurement. Samples were prepared inside the glovebox and kept air free during the experiment using sealed caps and 9



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parafilm. The gradient was calibrated to the known values of H2 O, H2 O in D2 O, 57 H-DMSO in d6-DMSO, 58 dimethyl carbonate, 59 and 0.25 M and 4 M LiCl in H2 O. 57 A recycle delay sufficient to allow full relaxation based on measured T1 values was used. The Bruker dstebpgp3s pulse program was used for all measurements, which utilizes a double stimulated bipolar gradient pulse sequence to compensate for any convection in the sample. 60 The signal intensity as a function of gradient strength was fit to 5δ I 2 2 2 = e−γ g δ D(∆− 8 −τ ) . I0

(5)

This equation includes a correction for the sine-shaped gradient pulses used. 61 Diffusion delays between 0.08 and 0.25 seconds and gradient pulse lengths between 1.2 and 3 ms were used. Sixteen experiments of varying gradient strength were used for each measurement and each experiment showed a fitting error below 1%. Based on variability within the calibration, an actual error of 5% is estimated. Repeat experiments with varied diffusion delay times showed no change in the measured diffusion coefficient. Sodium diffusion could not be measured for Na[TFSI] in DME due to sodium’s short T1 relaxation time ( D(Cation) ≈ D([TFSI]− ). The relatively lower diffusion coefficient values observed for [TFSI]− are due to the higher molecular weight of [TFSI]− 14


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compared to DME. The lower diffusion coefficients observed for cations, as compared to those for DME or [TFSI]− , can be attributed to the strong coordination of cations with either DME molecules or [TFSI]− anions in the system. We also computed the ionic conductivity (λ) from MD simulations using an expression similar to the Einstein relation, e2 λ = lim t→∞ 6V kB T

2 + * all X [qi ri (t) − qi ri (0)] ,

(9)

i

where e and T are elementary charge and temperature. The Li+ or Na+ contribution to ionic conduction (λ+ ) may be obtained from the ratio of the diffusion coefficients and the net ionic conductivity, 43 λ+ = λ

N+ D + , N+ D+ + N− D−

(10)

where N is the number of given ion in the system and subscripts of + or − indicate cations or anions, respectively. The ratio of diffusion coefficients that scales net ionic conductivity in Eq. 10 is the transference number. The conductivities obtained from MD simulations for Li[TFSI] in DME and Na[TFSI] in DME for room temperature as a function of salt concentration are presented in combination with experimental data in Figure 5a. 58,62 For the room temperature data, our MD simulation data agrees well with available experiments, with an average deviation of less than 15%. The largest deviation from experiment is 35% for 2M Li[TFSI] in DME. However, this deviation could be attributed to uncertainties in the experimental ionic conductivity, which are estimated at roughly 0.3 Sm−1 . We note a few trends concerning electrolyte concentration and the comparison between the Na+ and Li+ systems. First, the λ of both systems increases at low salt concentrations and then decreases with increasing salt concentrations, with λ having a maximum between 0.5 and 1.0 M Li[TFSI] in DME and between 1.0 and 1.5 M Na[TFSI] in DME. The peak in λ observed in this work can be related to the balance between the diffusion of cation, which decreases with increasing salt concentrations, and the 15



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total number of cations, which increases with increasing salt concentrations. The product of these two quantities provides a similar trend to the concentration-dependent conductivity. This implies that at some limit, increases in conductivity due to the addition of more charge carriers are outpaced by the reduction in ion mobility. The origin of this is explored further in a later discussion of structure. Furthermore, similar values of λ were observed for Li[TFSI] and Na[TFSI] in DME, which parallels the previous observations made for the diffusion coefficients of these solutions. The transference numbers, given in Table 3, show little variation with salt concentration. The average transference numbers for solutions of Li[TFSI] in DME and Na[TFSI] in DME are 0.48 and 0.47, respectively. The conductivities as a function of temperature at 1M salt in DME are presented in Figure 5b. An increased temperature leads to an increase in conductivity, with the characteristic inverse temperature versus logarithmic conductivity plot providing a nearly linear relationship. As with the room temperature salt concentration study, the temperature dependent conductivity is similar for both salt systems. For matters of electrochemical device performance, relatively minor changes in temperature lead to quite large increases in conductivity. By increasing the temperature from 298 K to 333 K, the conductivity of both salt systems increases by a factor of two. To comment on the mechanism of ion transport in DME, we computed the ratio of ionic conductivity to uncorrelated ionic conductivity (ions moving independently of their counterions) (α) as a function of salt concentration at 298 K. The uncorrelated conductivity (λuc ) is given by ions

λuc

N e2 X i 2 i i (β ) D N , = V kB T i

(11)

where β i and N i are the net charge and number, respectively, of ionic species i. From the values of α provided in Table 3, no significant variations between Li+ and Na+ systems are evident for a given salt concentration. We find that the estimated α values for both Li+ and Na+ systems vary between 0.42-0.53.

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To better understand the noted trends in transport, we investigate the residence time of cation bonds (i.e., the average time a cation remains coordinated to a given species) with the oxygen atoms of DME and [TFSI]− . The residence time (τ ) is determined from the neighbor (H i,j ) function,

   0,    H i,j (rk,l , t) = 1,      ,

i,j if rkl > rcut

(12)

i,j if rkl ≤ rcut

and the neighbor autocorrelation (S i,j ) function,

S i,j (t) =

N i PN j i,j i,j k=1 l=1 H (rkl , t)H (rkl , 0) PN i PN j i,j i,j k=1 l=1 H (rkl , 0)H (rkl , 0)

*P

+ (13)

S i,j (t) = Ae−t/τ , where atoms type k and l of species i and j, respectively, are considered to be bonding if i,j their separation is less than (rcut ), which is defined to encompass the first solvation shell of

species i and j. The residence times are presented in Figure 6 as a function of salt concentration at 298 K. Comparatively, the residence times are longer for Li+ than for Na+ , which follows expectations from the differences in binding energy shown in Figure S4. The long residence times suggests that Li+ transport is more vehicular (diffusing with its solvating molecules) than Na+ . A more vehicular transport mechanism is associated with slower rates of diffusion than alternative mechanisms (like solvent or anion exchange). 43 Both cations show a longer residence time with the oxygens of DME than with the oxygens of [TFSI]− , which is reflective of the favorable solvation of the cation by the solvent. Short residence times of cations with anions is a hallmark of a “good” electrolyte, one that minimizes the cation correlation to the anion and thereby maximizes the cation contribution to conductivity (larger α). The residence times of both cations with [TFSI]− are small (< 3 ns).

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Structural Properties To assess the influence of salt concentration and cation on the molecular coordination in the electrolyte, we computed the radial distribution functions g(r) between the cations and oxygen atoms of DME and [TFSI]− , as given in Figure 7. Increasing the Li/Na-salt concentration significantly affects the g(r) of the cation with oxygen atoms of [TFSI]− , with the relative magnitude of the first solvation shell significantly increasing, which indicates higher coordination of oxygen atoms around the cations in the first solvation shell. Alternatively, the g(r) of cations with the oxygen atoms of DME exhibits only small changes, with the magnitude of the first solvation shell slightly decreasing with increasing salt concentrations, which indicates a lower coordination of oxygen atoms around the cations in the first solvation shell. Furthermore, the first solvation shell peak between Li+ and the oxygen atoms of DME or [TFSI]− is around r = 2.1 Å, whereas for Na+ the first peak is around r = 2.4 Å, which can be attributed to the larger size of Na+ compared to Li+ . The coordination of DME and [TFSI]− around the cations was investigated by computing the average number of oxygen atoms from DME and [TFSI]− in the first solvation shell of the cations, which is presented in Figure 8. For all systems, the cations are primarily coordinated to oxygen atoms from DME. For the concentration range investigated in this work, the coordination number of Li+ and Na+ with the oxygen atoms of DME varies between 4.65.1 and 3.7-4.7, respectively. Alternatively, the coordination number of Li+ and Na+ with the oxygen atoms of [TFSI]− varies between 0.2-0.5 and 1.0-1.8, respectively. Increasing the salt concentrations slightly increases the coordination number of cations to the oxygen atoms of [TFSI]− in the first solvation shell. Conversely, the coordination number of cations to the oxygen atoms of DME in the first solvation shell exhibits a slight decrease. This may be simply explained by considering that the [TFSI]− that are coordinated to Li+ and those that are “free” in solution are in equilibrium. Increasing the salt concentration will increase the chemical potential of the “free” [TFSI]− . At sufficiently high concentrations, this will overcome free energetic barriers to increasing the cation coordination to more [TFSI]− . 18


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Similarly, this explains the decrease in cation coordination to oxygen atoms from DME. The trend discussed above also qualitatively agrees with the g(r) distributions between cations and oxygen atoms of DME and [TFSI]− . In order to investigate the variations in coordination of DME and [TFSI]− around the cations, we evaluated the number of DME and [TFSI]− that coordinate to Li+ or Na+ with a single oxygen atom (monodentate configuration, see Figure 9) as well as those having a two coordinating oxygen atoms (bidentate configuration, see Figure 10). From Figure 10, the bidentate configuration of DME with both Li+ and Na+ tends to be more probable, with close to 85-90% of the oxygen atoms of DME that are binding to a cation being involved in bidentate configurations. We find that the fraction of these oxygen atoms involved in bidentate configurations not to vary significantly with salt concentration. The Li+ solvation shell was found to have a slightly lower percentage of bidentate DME molecules than that of Na+ . For [TFSI]− solvating Li+ and Na+ , monodentate configurations tend to be more stable, with 25-40% of the binding oxygen atoms being involved in bidentate configurations. We find that increasing Li/Na-salt concentrations significantly increases the fraction of oxygen atoms of [TFSI]− involved in bidentate configurations. Again, this can be related to the increase in the chemical potential of [TFSI]− in the solution, which makes the displacement of DME binding to Li+ by [TFSI]− more favorable. The most common solvation structures observed at low concentrations from our simulations are provided in Figure 9. Overall, we find that the most common solvation shells of Li+ have five oxygen bonds. The oxygen bonds originate from either three DME, with two in bidentate configurations and one in a mondentate configuration, or from two DME and a [TFSI]− , with the DME being in bidentate configurations and the [TFSI]− being in a monodentate configuration. For Na+ , the most common solvation shells have six oxygen atoms. In this case, the oxygen atoms can originate from three DME, where all three DME are in bidentate configurations, or from two DME and one [TFSI]− , where all species are in bidentate configurations. 19



As a final evaluation of the coordination of molecules and anions around cations, we investigated the tendency of Li+ or Na+ cations to aggregate into clusters by evaluating the networks of cations bound by shared or bridging oxygen atoms of DME and [TFSI]− (see Table 4). We did not observe a significant presence of either Li+ or Na+ clusters. For solutions of either Li[TFSI] or Na[TFSI] in DME, as the salt concentration increases, the cluster size slightly increases, with the probability of finding a Li+ not associated with a cluster decreasing from 100% at low concentrations (0.5 M) to 97.6% at high concentrations (2.0 M), and the probability of finding a Na+ not associated with a cluster decreasing from 93.3% at low concentrations (0.5 M) to 73.3% at high concentrations (2.0 M). There size of the cations appear to be correlated to the prevalence of clusters, as Na+ is involved in more clusters than Li+ . The lack of widespread aggregation could explain the noted maximum in ionic conductivity as a function of concentration in Figure 5a. Electrolytes that readily form large aggregates with Li+ and Na+ , like ionic liquids, 43,68,69 often exhibit monotonic decreases in conductivity with increasing salt concentration. For low salt concentration DME electrolytes, no aggregation means that adding more salt will increase the number of available charge carriers and not significantly impact ion mobility, which increases conductivity. For high salt concentration DME electrolytes, aggregation is still limited, but the ratio of cation-complexed DME to DME free in the volume is high, which leads to large reductions of the vehicular contribution to ion mobility and results in the decrease of conductivity.

Conclusions Detailed understanding of the thermodynamic, transport, and structural properties of electrolytes for advance batter chemistries is crucial for discerning the underlying mechanisms that govern these complex systems. This work provides atomistic-level insights into key thermodynamic, transport, and structural properties of the primary electrolytes (Li[TFSI]

20


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in DME and Na[TFSI] in DME) used for Li-S, Li-O2 , and Na-O2 battery applications. High fidelity, polarizable force fields were developed by fitting parameters to quantum chemistry and ab initio molecular dynamics simulation for these two electrolyte systems. We computed the density, heat of vaporization, viscosity, self-diffusion coefficient, and ionic conductivity for a wide range of salt concentrations. Molecular dynamics simulation predictions are found to be in good agreement with experimental results for the entire concentration range investigated. With increasing salt concentrations, both systems exhibited increasing density and viscosity and decreasing diffusion coefficients. In contrast, the ionic conductivity initially increased with salt concentration, reached a saturation point, and then decreased. This behavior is related to a balance between decreasing diffusion coefficients and increasing number of cations with increasing salt concentrations. We also found that the correlated cation and anion diffusion slightly increased with increasing salt concentrations, which is reflected in increases in residence times observed between cations and anions with increasing salt concentrations. The Li+ and Na+ residence times with the oxygen atoms of DME were significantly greater than those with the oxygen atoms of [TFSI]− . Transport property differences also were described by differences in the residence times of the cations with the oxygen atoms of DME, with the less mobile Li+ having a much longer residence time than Na+ . Structural properties were also analyzed as a function of salt concentration. Both Na+ and Li+ were found to be solvated predominately by 2-3 DME and up to one [TFSI]− . The coordination number between the cations and [TFSI] increased while that between the cations and DME decreased with increasing salt concentration. For both Li+ and Na+ with DME and Na+ with [TFSI]− , bidentate configurations were more likely, while for Li+ with [TFSI]− , monodentate configurations were revealed to be more likely. No significant evidence of cation/anion clustering was observed. In general, an improved understanding of the properties of the electrolytes studied in this work should lead to the design of better formulations with enhanced performance relevant to advanced battery applications. 21



Supporting Information Structure and energetic comparisons of the force field to quantum chemistry computations and values of MSD as a function of time may be found in the Supporting Information.

Acknowledgement This work was supported by funding from the NASA Aeronautics Research Mission Directorate’s (ARMD) Convergent Aeronautics Solutions (CAS) Project.

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Table 1: Summary of the number of DME molecules, ion pairs, and simulation times (tsim in ns) used for the room temperature electrolytes. Molarity DME Li/Na[TFSI] tsim 0.5 1.0 1.5 2.0

433 411 364 327

23 47 71 95

31


20 20 40 60


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Table 2: Experimental (EXP) 32,61–63,66 and molecular dynamics (MD) thermodynamic and transport properties of 1,2-dimethoxyethane at 298 K and 1 atm. Density, heat of vaporization, diffusion coefficient, viscosity, and static dielectric constant are represented by ρ, ∆H, D, and µ, respectively. ρ (g/cm3 )

∆H (kcal/mol) D × 1010 (m2 /s) µ (mPa·s)

MD 0.841±0.01 8.86±0.06 EXP 0.861 8.82

32.1±0.6 31.5

32


0.57±0.09 0.41

6.5 7.2

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Table 3: Ratio of ionic conductivity to uncorrelated ionic conductivity (α), cation contribution to ionic conductivity (λ+ ), and transference numbers as a function of salt concentration at 298 K. Molarity α(Li+ ) α(Na+ ) λ+ (Li+ ) (S/m) 0.5 1.0 1.5 2.0

0.42 0.48 0.53 0.42

0.44 0.43 0.47 0.46

0.53 0.75 0.57 0.21

λ+ (Na+ ) Transference(Li+ ) Transference(Na+ ) (S/m) 0.57 0.58 0.48 0.18

33


0.47 0.47 0.49 0.48

0.47 0.45 0.46 0.50


Page 34 of 45

Table 4: Percent of Li+ and Na+ atoms participating in a cluster of a given size as a function of salt concentration at 298 K. Cluster Size Molar Concentration Li+ -Cluster (%) Na+ -Cluster (%) 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.5 1.5 1.5 1.5 2.0 2.0 2.0 2.0

100 .00 0.00 0.00 0.00 99.64 0.36 0.00 0.00 98.95 1.05 0.05 0.00 97.57 2.43 0.04 0.00

34


93.3 6.56 0.1 0.00 90.2 9.4 0.4 0.00 79.1 18.8 2.1 0.00 73.3 21.7 4.4 0.6

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(a)

(b)

Figure 1: Atomic representation of (a) DME and (b) [TFSI]− . The atom types are colored as follows: carbon is gray, hydrogen is white, oxygen is red, fluorine is cyan, sulfur is yellow, and “dummy” force centers representing long pairs are green.

35


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Cation Binding Energy (kcal/mol)


Li[TFSI] in DME

1.2

Na[TFSI] in DME

3

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

Density (g/cm )

(a)

1.05

0.9

0

1

0.5

1.5

2

-50

-100

-150

Salt Molar Concentration Figure 2: Density of Li[TFSI] in DME (circles) and Na[TFSI] in DME (squares) as a function of salt concentration at 298 K. Computational results are given as filled symbols, while experimental values are given as open symbols. 56 Simulation error bars are smaller than the symbol sizes and thus not presented in the figure.

36


(b)

5


10

Viscosity (mPa·s)

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)

1 Li[TFSI] in DME Na[TFSI] in DME

0.1 0

0.5

1

1.5

2

Cation Binding Energy (kcal/mol)

Page 37 of 45

-50

-100

-150

Salt Molar Concentration Figure 3: Viscosity of Li[TFSI] in DME (circles) and Na[TFSI] in DME (squares) as a function of salt concentration at 298 K. Computational results are given as filled symbols, while experimental values are given as open symbols. 56,64,67 Simulation error bars are smaller than the symbol sizes and thus not presented in the figure.

37


(b)

5


DME

DME 10

Dx10

-10

2

(m /s)

(a)

Li[TFSI] in DME Na[TFSI] in DME

1

+

(b)

Li or Na

+

Dx10

-10

2

(m /s)

10


0.1

[TFSI]

(c)

-

-10

2

(m /s)

10

Dx10

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 38 of 45


0.1

0

0.5

1

1.5

2

2.5

Salt Molar Concentation Figure 4: Diffusion coefficients of Li[TFSI] in DME (circles) and Na[TFSI] in DME (squares) as a function of salt concentration for (a) DME, (b) Li+ or Na+ , and (c) [TFSI]− . Computational results are given as filled symbols, while experimental values taken for this work and those previously measured 56 are given as open symbols. Simulation error bars are smaller than the symbol sizes and thus not presented in the figure.

38


Page 39 of 45

10

Ionic Conductivity (S/m)

2


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) 1.5

1

0.5

0


0.5

1

1.5

2

2.5

(b)


1

2.6

2.8

3

3.2 -1

Salt Molar Concentration

1000/T (K )

Figure 5: Ionic conductivity of Li[TFSI] in DME (circles) and Na[TFSI] in DME (squares) as (a) a function of salt concentration at 298 K and (b) a function of temperature at 1M Li[TFSI] or Na[TFSI] in DME. Computational results are given as filled symbols, while values from the experiments performed in this work are given as open symbols. Simulation error bars are smaller than the symbol sizes and thus not presented in the figure.

39


Dx

Li[TFSI] in of DME The Journal Physical Chemistry Na[TFSI] in DME

1

100

(a)

DME

τ (ns)

10


0.1 10

[TFSI]

(b)

τ (ns)

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 40 of 45

-

1


0.1

0

0.5

1

1.5

2

2.5

Salt Molar Concentation Figure 6: Residence time (τ ) for (a) bonds of Li+ and Na+ with oxygen atoms in DME molecules, and (b) bonds of Li+ and Na+ with oxygen atoms in [TFSI]− as a function of salt concentration at 298 K. The red symbols denote relevant residence times of Li+ cations and blue symbols denote residence times of Na+ cations.

40


Dx

Li[TFSI] in DME The Journal of Physical Chemistry Na[TFSI] in DME

10

0 40

(a)

Radial Distribution

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

DME

30

+

0.5 M 1.0 M 2.0 M

Li

+

Na

20

10

0 30

Radial Distribution

Page 41 of 45

[TFSI]

(b)

25

-

+

Na

20 15

0.5 M 1.0 M 2.0 M

+

Li

10 5 0

1

2

3

4

r (Å) Figure 7: Radial distribution function (g(r)) at T = 298 K as a function of salt concentration for (a) Li+ or Na+ with the oxygen atoms of DME, and (b) Li+ or Na+ with the oxygen atom of [TFSI]− . The red lines denote the Li+ -oxygen radial distribution functions and blue lines denote the Na+ -oxygen radial distribution functions. The solid line denotes the 2.0 M salt concentration, the dashed-dotted line denotes the 1.0 M salt concentration, and the dashed line denotes the 0.5 M salt concentration simulation data.

41


D


1

Coordination Number

6

(a)

DME


2 2.5

Coordination Number

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 42 of 45

[TFSI]

(b)

-


1.5 1 0.5 0

0

0.5

1

1.5

2

2.5

Salt Molar Concentation Figure 8: Coordination number of (a) Li+ and Na+ with the oxygen atoms of DME and (b) Li+ and Na+ with the oxygen atoms of [TFSI]− as a function of salt concentration at 298 K. The circles denote coordination numbers between Li+ and oxygen atoms and the squares denote coordination numbers between Na+ and oxygen atoms.

42


Page 43 of 45 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


(b)

(a)

Li

+

Na

(c) bidentate

(d) Na

Li

+

+

+

monodentate

Figure 9: Depiction of the most probable solvation shells of (a,c) Li+ and (b,d) Na+ from molecular dynamics simulation. Solvation shells composed of only (a,b) DME and (c,d) both DME and [TFSI]− are shown. The cations and ligand bonds with the cations are given as orange. Solvation shell molecules coordinating to the cations through monodentate and bidentate bonds are indicated.

43


D


Bidentate Cation-Ligands

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

Bidentate Cation-Ligands

1

Page 44 of 45

(a)

90

DME

88

Na[TFSI] in DME Li[TFSI] in DME

86

[TFSI]

(b)

-

40


20 0

0.5

1

1.5

2

2.5

Salt Molar Concentation Figure 10: Distribution of bidentate bonds to Li+ or Na+ from (a) the oxygen atoms of DME and (b) the oxygen atoms of [TFSI]− as a function of salt concentration. The circles denote Li+ and the squares denote between Na+ .

44


Radial Distributi

30

+

0.5 M

Li

1.0 M of Physical Chemistry The Journal

+

Na

20

2.0 M

10

0 30

Radial Distribution

[TFSI]

(b)

25

-

+

Na

20 15

0.5 M 1.0 M 2.0 M

+

Li

10 5 0

1

2

4

3

r (Å) 2 Figure 7: Radial distribution function (g(r)) at T = 298 K as a function of salt10 concentration for (a) Li+ or Na+ with the oxygen atoms of DME, and (b) Li+ (a) or Na+ with the oxygen atom + of [TFSI] . The red lines denote the Li -oxygen radial distribution functions and blue lines 1.5 denote the Na+ -oxygen radial distribution functions. The solid line denotes the 2.0 M salt concentration, the dashed-dotted line denotes the 1.0 M salt concentration, and the dashed line denotes the 0.5 M 1 salt concentration simulation data.

0.5

0


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 45 of 45


0.5

1

1.5

2


1

2.5

(b)

+

+

Li2.6and Na Shells 2.8 Solvation 3 3.2 -1

Salt Molar Concentration

1000/T (K )

41

45


Polarizable Molecular Dynamics and Experiments of 1,2

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