Insight into the Solvation Structure of Tetraglyme-Based Electrolytes

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Insight into the Solvation Structure of Tetraglyme Based Electrolytes via First-Principles Molecular Dynamics Simulation Yang Sun, and Ikutaro Hamada J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b07098 • Publication Date (Web): 09 Oct 2018 Downloaded from http://pubs.acs.org on October 13, 2018

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The Journal of Physical Chemistry

Insight into the Solvation Structure of Tetraglyme based Electrolytes via First-Principles Molecular Dynamics Simulation Yang Sun1 and Ikutaro Hamada*,1,2 1

Global Research Center for Environment and Energy based on Nanomaterials Science

(GREEN), National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan 2

Department of Precision Science and Technology, Graduate School of Engineering,

Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan

ABSTRACT Glyme-lithium salt equimolar mixtures, as solvate ionic liquid electrolytes for rechargeable lithium secondary batteries, are of great interest, due to the desirable properties such as high oxidative stability, low vapor pressure, and non-flammability. However, the fundamental understanding of the solvation shell structure in glyme electrolytes have not been clearly established. Herein we employ first-principles molecular dynamics (FPMD) simulation to study the lithium bis(trifluoromethylsulfonyl)-amide (LiTFSA) and tetraglyme (G4) electrolyte system. For the case of equimolar ratio, a positive correlation between the total coordination number of Li+ ions and the phase stability is clearly established. At the ground state of equimolar LiTFSA-G4 electrolyte, most of Li+ ions are coordinated to four O atoms of a curled G4 molecule and one O atom of a TFSA− anion, equivalent to the second most stable contact ion pair in gas phase cluster calculations. By contrast, Li+ ions prefer to be coordinated by two G4 molecules and not in direct contact with TFSA− anions at a low concentration of Li salt. The significantly increased probability of pairing between the Li-G4 complexes and TFSA− anions at the equimolar ratio could be highly relevant to its ionic-liquid-like properties.

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1. INTRODUCTION The booming electric vehicle market stimulates the scientific research for new battery system with higher energy density than the current state-of-the-art Li-ion batteries (LIBs).1-3 For the beyond Li-ion chemistries, e.g., the Li-O2 battery with highest theoretical energy density,4 however, a severe challenge is to develop satisfactory safe and stable electrolyte.5 Glyme–Li salt complexes were firstly developed as LIB electrolytes by the Watanabe and coworkers.6-9 It was assumed that the glyme-Li salt equimolar complexes can serve as a kind of room-temperature ionic liquids (RTILs), where the Li+ ion solvated by a glyme molecule is equivalent to a complex cation [Li(glyme)]+. Later, various glyme–Li electrolytes have been successfully implemented into the next generation battery technologies such as Li-S10-12 and Li-O2 systems.13-16 The experimental studies show that the equimolar mixing of glyme solvent molecules and Li salts exhibit negligible vapor pressure, which makes it more attractive for the open system like Li-O2 batteries. Moreover, it was proposed that the oxidative stability of glyme molecules could be enhanced by the complex formation with Li ions.7 However, the optimal ratio between glyme molecules and Li-salts is still not very clear. Contrary to the equimolar mixing scheme, Li et al. argued that the highest rechargeability of Li-O2 batteries could be achieved when the molar ratio of the LiTFSA to G4 is 1:3 or 1:4.13 To have a better understanding of the structural properties of glyme-based electrolytes and to improve the electrochemical performance, the mechanistic study of the solvation structure in glyme-based electrolytes is urgently needed. In a recent study, Callsen et al. performed density functional theory (DFT) based firstprinciples molecular dynamics (FPMD) simulations on the solvation structure of lithium ions in LiTFSA−triglyme (G3) electrolyte.17 This study revealed that lithium ions are solvated mainly by crown-ether-like curled G3 molecules and the Li-G3 complex is in direct contact with an TFSA− anion in the equimolar ratio. In contrast, the Li solvation shell does not exhibit significant preference at the low concentration of Li salts. The ground-state of Li+ solvation structure is determined to be 5-fold coordinated,17 however, a G3 molecule only has 4 coordinating O sites. In the equimolar ratio, it was found that the most stable solvation shells of Li+ ion is the 4-fold coordinated Li(G3)1 in contact with TFSA−. Compared with the G3, the G4 solvent is more popular in Li-air batteries probably due to the lower vapor pressure. From a structural point of view, the G4 molecule has 5 coordination O sites, which may satisfy the desirable 5-fold coordination of Li+ ions. Tsuzuki et al. have analyzed the difference in physicochemical properties between the LiTFSA−G3 and LiTFSA−G4 electrolytes.18-19 The


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results suggest that the attraction between the [Li(G4)]+ and TFSA− is weaker than that of between [Li(G3)]+ and TFSA−, accounting for the faster diffusion of the [Li(G4)]+ complex. Another report by Chaodamrongsakul et al. investigated the solvation structure of K+ ions in G4 electrolyte through a combined molecular dynamic simulation and X-ray absorption spectroscopy.20 Despite the above research efforts, a thorough study of the real G4 electrolyte system at the DFT21-22 level is still lacking. We here employ DFT based on FPMD to study the Li+ solvation structure in LiTFSA−G4 electrolytes, at both low (1mol/L) and high (equimolar) concentration of Li salt. Our calculation results show that at a low concentration of Li salt, the coordination number of Li+ ions is independent of the initial model structure, which however determines the detailed solvation structure and thus affects the binding energy slightly. In contrast, simulation results of the equimolar electrolyte with different initial structures vary considerably. At the ground-state of equimolar LiTFSA−G4 electrolyte, the G4 molecule prefers a crown-ether-like structure enclosing one Li+ ion, and then the [Li(G4)1]+ complex is found to further pair with an adjacent TFSA− anion. The stable contact ion pairs ([Li(G4)1]+TFSA−) distinguish the equimolar LiTFSA-G4 electrolyte from its low Li-salt concentration counterparts.

2. METHODS DFT calculations were performed by using the Vienna ab initio simulation package (VASP)23-24 with the projector augmented-wave (PAW) formalism.25 The PAW potentials generated with Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) 26 were used. The van der Waals (vdW) forces was taken into account by using the rev-vdW-DF2 functional,27-30 which has been proven accurate in predicting structure and energetics of a variety of systems, including those with dominant vdW bonding.31-35 The plane wave cut-off was set to 700 eV. Calculations of gas-phase molecules/complexes were performed in a 20 × 20 × 20 Å3 cubic box. In the simulations of low concentration LiTFSA@G4 electrolyte, we used a cubic supercell with the cell edges of 18.8 Å, containing 4 LiTFSA and 13 G4 molecules (545 atoms), equivalent to ~ 1.0 mol/L and 1.0 g/cm3. In the case of the equimolar concentration electrolyte, we used a cubic supercell with the cell edges of 18.8 Å, containing 11 LiTFSA and 11 G4 molecules (583 atoms), equivalent to ~ 2.75 mol/L and 1.4 g/cm3, consistent with experimental values.36 Initial structures were constructed using the Packmol software.37 For instance, the electrolyte of 1mol/L was constructed using 4 Li+-G4 complexes, 4 TFSA− anions,



and 9 G4 molecules. The Γ point was used for the Brillouin zone sampling. The FPMD simulations were performed in a canonical ensemble (NVT) by using a Nosé thermostat at 300 K,38-39 with a time step of 1 fs. The molecular graphics were created by using the VESTA software.40

3. RESULTS AND DISCUSSION 3.1 Gas-phase Li+-G4 complexes. The polydentate G4 molecule with 5 O sites can provide up to 5-fold coordination to a Li+ ion. The 5-fold coordination of Li+ ions in both G3 and G4 electrolytes was proposed in previous reports.17, 19 [Li(G4)1]+ complexes with different lithium coordination numbers (CNs) were constructed by changing the curvature of G4 molecule. For instance, a linear G4 molecule can only afford the 1-fold coordination to the Li+ ion, while a completely curled G4 molecule may provide the full 5-fold coordination. The optimized geometries of [Li(G4)1]+ complexes with different CNs are shown in Figure 1a, where the c1 to c5 denote the CNs. A lower/higher CN of Li-ion in the [Li(G4)1]+ complex corresponds to a less/more curved G4 molecule. The CN would be increased when the [Li(G4)1]+ complex is in contact with a TFSA− anion. In the optimized geometry of [Li(G4)1]+TFSA− pairs (Figure 1b), the Li+ ion prefers to be coordinated by two O atoms of the TFSA− anion (OTFSA), with exception of the c4-[Li(G4)1]+TFSA− pair where only one OTFSA is in direct contact with the Li+ ion. The 5-fold coordinated Li+ ion in the c5-[Li(G4)1]+ complex becomes 6-fold coordinated (four O atoms from the G4 molecule (OG4) and two OTFSA, respectively) in the c5[Li(G4)1]+TFSA− pair, consistent with a recent computational study using a different exchangecorrelation functional.41 Note that the length of one Li-OG4 bond in the c5-[Li(G4)1]+TFSA− pair is ~ 2.6 Å, much longer than that of other three Li-OG4 bonds (~ 2.1 Å). Thus, the c5[Li(G4)1]+TFSA− pair can be regarded as a 5-fold coordination structure, if only the short LiO bonds with stronger interactions are considered. Comparison of total energies for all optimized geometries mentioned above can be seen in Figure 1c. The energies of G4 molecules are calculated by removing the Li+ ion from the corresponding [Li(G4)1]+ complexes. Calculation results show that the total energy of G4 molecule changes very little with the conformation (curved or linear), while the stability of [Li(G4)1]+ complexes considerably increases with increasing CN and the c5-[Li(G4)1]+ complex is the most stable one. When coordinated with two G4 molecules (the [Li(G4)2]+ complex), the Li+ ion still prefers a 5-fold Li-O coordination (Supporting Information Figure


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S1). The G4 molecule of the most stable [Li(G4)1]+TFSA− pair also adopts the c5 conformation (c5-[Li(G4)1]+TFSA− in Figure 1b). In the second most stable contact ion pair (c5’[Li(G4)1]+TFSA−), the Li+ ion is also 6-fold coordinated (one Li-OTFSA and five Li-OG4 bonds), with one Li-OG4 bond (~ 2.6 Å) much longer than the other four (~ 2.1 Å). Similarly, the coordination number would be 5 when we just consider the tight/short Li-O bonds.

[Li(G4)1]+

(a) C

O

c1 Li

[Li(G4)1]+TFSI−

(b) N

c4

c2

S

c1

H

F

c2 c5

c4

c3 c3

(c) Relative Energy (eV)

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


G4 [Li(G 4)1 ]+ [Li(G 4)1 ]+ TFSI−

2.5 2.0

c5

1.5 1.0

c5’

c5’

0.5 0.0 c1

c2

c3

c4

c5

Figure 1. Structures and energetics of gas-phase [Li(G4)1]+ complexes and [Li(G4)1]+TFSA− pairs. (a) Optimized geometries of different [Li(G4)1]+ complexes of cN (N=1-5), where N represents the coordination number of the Li+ ion. (b) Optimization geometries of the corresponding [Li(G4)1]+TFSA− pairs. (c) Calculated relative total energies of G4 molecules, [Li(G4)1]+ complexes, and [Li(G4)1]+TFSA− pairs, in different conformations. All energies are referenced to the values of the most stable c5 conformations (c5-G4, c5-[Li(G4)1]+, and c5[Li(G4)1]+TFSA−).

3.2 Tetraglyme electrolyte with low LiTFSA concentration. Next we construct models of



the electrolyte using the optimized gas-phase clusters, and perform FPMD simulation to study the stability of different Li+ ion solvation structures. To simulate the liquid tetraglyme electrolyte with low concentration of LiTFSA salt, 4 [Li(G4)1]+ complexes, 4 TFSA− anions, and 9 G4 molecules are randomly distributed in a cubic box. We construct three different initial models to see the consequent difference. 1mol/L-Conf1: c5-[Li(G4)1]+ complexes (Figure 1a) and c5-G4 molecules, both of which are the ground-state conformations. 1mol/L-Conf2: c1[Li(G4)1]+ complexes and c1-G4 molecules, both of which are energetically unfavorable conformations. 1mol/L-Conf3: c5-[Li(G4)1]+ complexes and c1-G4 molecules, an intermediate between the 1mol/L-Conf1 and the 1mol/L-Conf2. For each model, the MD simulation is performed until the convergence of total energy is achieved. From the time evolution of total energy shown in Figure 2a, we may see that the 1mol/LConf1 system almost reaches the equilibrium after 10 ps. A snapshot of the system at 30 ps is shown in Figure 2b, wherein the c5 structure of [Li(G4)1]+ complexes have remained almost the same as the initial model. In all four c5-[Li(G4)1]+ complexes, only one was changed to the [Li(G4)2]+ (in which the Li+ ion is coordinated by four O atoms from one G4 molecule and one O atom from the second one) during simulation. After being equilibrated, no significant diffusion is observed, suggesting that the Li-O bonds formed during equilibration can hardly be broken at a simulation temperature of 300 K. The simulation data of last 10 ps was used to analyze the equilibrated radial distribution function (RDF) and CN of Li+ ions. During the MD simulation, only O atoms are observed in the first coordination shell of Li+ ions, and therefore the RDF/CN of other species are not provided. The O atoms from both G4 molecules (OG4) and TFSA anions (OTFSA) are analyzed separately. As shown in Figure 2c, the RDF peak of LiOTFSA bonds appears at ca. 2.03 Å, slightly larger than that of the Li-OG4 bonds (1.94 Å). The calculated CN from OG4 atoms is 4.76 (Figure 2d), much larger than the value from OTFSA atoms (0.25). That is, only one in four TFSA− anions is in direct contact with the solvated Li+ ion.


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(a)

-2640

Avg. over 1.5 ps

(b)

Energy (eV)

-2642

Li C O H F S N

-2644 -2646 -2648 -2650 -2652 0

5

10

15

20

25

30

Simulation Time (ps)

(d)

(c)

5

30

Li-OG4 Li-OTFSA

25

NC (r)

15

4.76

Li-OG4 Li-OTFSA

4

20

g (r)

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


3 2

10

1

5 0 0.0

0.25 0.5

1.0

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r (Å)

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3.5

4.0

0 0.0

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4.0

r (Å)

Figure 2. MD simulation of the 1mol/L-Conf1 electrolyte. (a) The total energy as a function of the simulation time. (b) A snapshot of the simulation system at 30 ps. Magnified views provide details of the typical solvation structures. (c) Average radial distribution function g(r) of Li centers over the simulation time from 21 to 31 ps. (d) Coordination number of Li+ ions NC(r) as a function of distance averaged over the simulation time from 21 to 31 ps. For the case of 1mol/L-Conf2, which is constructed with energetically unfavorable [Li(G4)1]+ complexes and G4 molecules, a quite long simulation time is needed to reach the equilibrium (Figure 3a) due to the relatively unreasonable initial structures. At the end of the MD run, all four Li+ ions are coordinated by two G4 molecules (Figure 3b), i.e., forming the [Li(G4)2]+ complexes (4 + 1 or 3 + 2 fold coordinated). Still we found that only one Li+ ion is in direct contact with the TFSA− anion. The equilibrated RDFs/CNs of Li+ ions are very close to the case of 1mol/L-Conf1 (Figure 3c,d). Detailed analysis on the solvation structure of different simulation periods indicates that the CNs of Li-OG4 and Li-OTFSA bonds increase and decrease with increasing simulation time (Supporting Information Figure S2), respectively, suggesting that the direct contact between Li+ ions and TFSA− anions is energetically unfavorable for the tetraglyme electrolyte at a low concentration of LiTFSA salt.



Energy (eV)

(a)

-2641 -2642 -2643 -2644 -2645 -2646 -2647 -2648 -2649 -2650 -2651

(b) Avg. over 1.5 ps

0

10

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30

40

50

60

70

Li C O H F S N

80


(d)

(c)

5

30

Li-OG4 Li-OTFSA

25

NC (r)

15 10

3 2 1

5 0 0.0

4.77

Li-OG4 Li-OTFSA

4

20

g (r)

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

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0.25 0.5

1.0

1.5

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r (Å)

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3.5

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0 0.0

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r (Å)

Figure 3. MD simulation of the 1mol/L-Conf2 electrolyte. (a) The total energy as a function of the simulation time. (b) A snapshot of the system at 80 ps. (c) Average radial distribution function g(r) of Li centers over the simulation time from 70 to 80 ps. (d) Coordination number of Li+ ions NC(r) as a function of distance averaged over the simulation time from 70 to 80 ps.

We further performed MD simulation of another model 1mol/L-Conf3 (Figure 4), which is constructed using the [Li(G4)1]+ complexes in 1mol/L-Conf1 and G4 molecules in 1mol/LConf2. Analogous to the case of 1mol/L-Conf1, the total energy converges quickly (Figure 4a), indicative of a reasonable initial structure. In the equilibrated structure (at 33 ps), all four Li+ ions in 1mol/L-Conf3 are coordinated by single G4 molecules (Figure 4b), slightly different from the case of 1mol/L-Conf1. The calculated RDF (Figure 4c) and CN (Figure 4d) of Li+ ions are very close to the other two models, that is, Li+ ions are predominantly solvated by G4 molecules.


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(a)

-2642

(b)

Avg. over 1.5 ps

Energy (eV)

-2643

Li C O H F S N

-2644 -2645 -2646 -2647 -2648 -2649 0

5

10

15

20

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30


(d)

(c) 35

5

Li-OG4 Li-OTFSA

30

4.84

Li-OG4 Li-OTFSA

4

NC (r)

25

g (r)

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


20 15

3 2

10 1

5 0 0.0

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0 0.0

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r (Å)

r (Å)

Figure 4. MD simulation of the 1mol/L-Conf3 electrolyte. (a) The total energy as a function of the simulation time. (b) A snapshot of the simulation system at 33 ps. Magnified views provide details of typical solvation structures. (c) Average radial distribution function g(r) of Li centers over the simulation time from 23 to 33 ps. (d) Coordination number of Li+ ions NC(r) as a function of distance averaged over the simulation time from 23 to 33 ps. From above MD simulation results, we may see that the 1mol/L LiTFSA-G4 system with different initial structures result in very similar RDFs and CNs. Even starting from an unreasonable initial structure (1mol/L-Conf2), the obtained solvation structure of Li+ ions is still 5-fold coordinated mainly by OG4, despite a much longer simulation time required to reach equilibrium. The low probability of forming Li-OTFSA bonding indicates that the direct contact between [Li(G4)1]+ complex and TFSA− anion is unfavorable in the G4 electrolyte at a low concentration of Li salt. To compare the stability of the configurations considered above, we calculated the binding energy defined by17 𝐸𝑏 =

1 𝑛

sys

TFSA G4 Li [𝐸tot − 𝑛𝐸tot − 𝑛𝐸tot − 𝑛G4 𝐸tot ], sys

TFSA G4 Li where 𝐸tot is the total energy of the electrolyte solution, 𝐸tot , 𝐸tot , and 𝐸tot are the total

energies of Li atom, TFSA radical, and G4 molecule in their ground states in the gas phase, respectively, and n is the number of the LiTFSA pairs. Calculated Eb’s in the equilibrium (the last 10 ps) is shown in Figure 5. We can see that the 1mol/L-Conf2 with the most unstable initial structure has the lowest binding energy after being equilibrated. The binding energy of 1mol/L-Conf1 is slightly lower (on average, by +0.05 eV/Li) than that of 1mol/L-Conf2, while 1mol/L-Conf3 yields a significantly higher binding energy (on average by +0.2 eV/Li) than the



other two. Considering the difference in Li+ ion solvation structures among all three models, the [Li(G4)2]+ complex seems more energetically favorable with respect to the [Li(G4)1]+ complex at a low concentration of LiTFSA salt. Our finding is opposite to a recent study focusing on 0.5 mol/L LiTFSA-glyme electrolytes,42 where it was shown that the [Li(G4)1]+ complex is prevalent. The conflicting results could be due to the difference in simulation settings (e.g., time duration, supercell size, and Li salt concentrations). -9.4 -9.5

1mol/L-Conf1 1mol/L-Conf2 1mol/L-Conf3

-9.6

Eb (eV/Li)

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

-9.7 -9.8 -9.9

-10.0 -10.1 -10.2

0

1

2

3

4

5

6

7

8

9

10


Figure 5. The binding energies of 1mol/L LiTFSA-G4 electrolyte as a function of simulation time after the equilibration. 3.3 Tetraglyme electrolyte with high (equimolar) LiTFSA concentration. Equimolar electrolyte models are constructed with 11 [Li(G4)1]+ complexes and 11 TFSA− anions (Equimolar-Conf1 and Equimolar-Conf2), and with 11 [Li(G4)1]+TFSA− contact ion pairs (Equimolar-Conf3). The energetically favorable (c5) and unfavorable (c1) [Li(G4)1]+ complexes in the gas phase are used in Equimolar-Conf1 and Equimolar-Conf2, respectively. For the Equimolar-Conf3 model, we directly use the most stable contact ion pair c5[Li(G4)1]+TFSA− in gas phase calculations. The Equimolar-Conf1 system reaches almost equilibrium after 15 ps (Figure 6a). The c5 conformations of [Li(G4)1]+ complexes are basically preserved (Figure 6b). The Li+ ions are predominantly coordinated by four or five O atoms from one G4 molecule and one O atom from one TFSA− anion, the same as the second most stable contact ion pair c5’-[Li(G4)1]+ TFSA− as shown in Figure 1b. From the RDFs shown in Figure 6c, we may see that the probability of Li-OTFSA bonding is much higher compared with the aforementioned low concentration electrolytes. The total CN of Li+ ions is approximately 5.3 (Figure 6d), also higher than that of 1mol/L electrolytes. The CN attributed to Li-OG4 and Li-OTFSA bonds is 4.30


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and 0.98, respectively, consistent with the dominant c5’-[Li(G4)1]+ TFSA− conformation mentioned above.

(a)

-2734

(b)

Avg. over 1.5 ps

-2735

Li C O H F S N

Energy (eV)

-2736 -2737 -2738 -2739 -2740 -2741 -2742

0

5

10

15

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30

35


(d)

(c) 30

5

Li-OG4 Li-OTFSA

25

NC (r)

15 10

4.30

3 2 1

5 0 0.0

Li-OG4 Li-OTFSA

4

20

g (r)

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


0.98 0.5

1.0

1.5

2.0

r (Å)

2.5

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4.0

0 0.0

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r (Å)

Figure 6. MD simulation of the equimolar-Conf1 electrolyte. (a) The total energy as a function of the simulation time. (b) A snapshot of the system at 34 ps. Magnified view shows the representative [Li(G4)1]+ TFSA− pair. (c) Average radial distribution function g(r) of Li centers over the simulation time from 24 to 34 ps. (d) Coordination number of Li+ ions NC(r) as a function of distance averaged over the simulation time from 24 to 34 ps.

The total energy of Equimolar-Conf2 model with initially under-coordinated Li+ ions requires a longer simulation time (~20 ps) to reach the equilibrium (Figure 7a). In contrast to the uniformly distributed [Li(G4)1]+TFSA− pairs in the case of Equimolar-Conf1, the equilibrated structure of Equimolar-Conf2 is aggregated: some Li+ ions are coordinated by two G4 molecules forming [Li(G4)2]+ complexes, others are coordinated by one G4 molecule, and then paired with two TFSA− anions. The resulting RDF of Li+ ions is very different from the Equimolar-Conf1 (Figure 7c). The peak of Li-OTFSA is much higher, contributing to a CN of 1.72 (Figure 7d). Simultaneously, the CN arising from Li-OG4 bonds decrease to 2.83. The total CN is only 4.55, indicative of under-coordinated Li+ ions in the Equimolar-Conf2.



(a)

(b)

-2730 Avg. over 1.5 ps

Energy (eV)

-2732

Li C O H F S N

-2734 -2736 -2738 -2740 0

5

10

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25

30


(d)

(c)

5

20

Li-OG4 Li-OTFSA

10

2.83

3 2

1.72

5

0 0.0

Li-OG4 Li-OTFSA

4

Nc (r)

15

g (r)

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

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1

0.5

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r (Å)

Figure 7. MD simulation of the equimolar-Conf2 electrolyte. (a) The total energy as a function of the simulation time. (b) A snapshot of the system at 32 ps. Magnified views provide details of typical solvation structure. (c) Average radial distribution function g(r) of Li centers over the simulation time from 22 to 32 ps. (d) Coordination number of Li+ ions NC(r) as a function of distance averaged over the simulation time from 22 to 32 ps.

The Equimolar-Conf3 model was constructed by using the most stable c5-[Li(G4)1]+TFSA−. The MD simulation almost reaches equilibrium at about 20 ps (Figure 8a). The equilibrated structure, however, is very different from the initial contact ion pairs. As shown in Figure 8b, Li+ ions are coordinated by three/four O atoms from the G4 molecule and two/one O atoms from the TFSA− anion. The calculated RDFs of Li-OTFSA and Li-OG4 are an intermediate between the Equimolar-Conf1 and the Equimolar-Conf2 (Figure 8c). The CNs from Li-OG4 and Li-OTFSA bonding are 3.72 and 1.25, respectively, suggesting that most Li+ ions are coordinated by four OG4 atoms and one OTFSA atom. The total CN of Li+ ions is ca. 5.0, also between the Equimolar-Conf1 and the Equimolar-Conf2.


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(b)

(a) Avg. over 1.5 ps

Energy (eV)

-2732

Li C O H F S N

-2734 -2736 -2738 -2740 0

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(c)

(d)

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5

Li-OG4 Li-OTFSA

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3.72 12

NC (r)

g (r)

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3

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Figure 8. MD simulation of the equimolar-Conf3 electrolyte. (a) The total energy as a function of the simulation time. (b) A snapshot of the system at 31 ps. Magnified views provide details of typical solvation structures. (c) Average radial distribution function g(r) of Li centers over the simulation time from 21 to 31 ps. (d) Coordination number of Li+ ions NC(r) as a function of distance averaged over the simulation time from 21 to 31 ps. Comparing the binding energies of above three equimolar models (Figure 9), we see that the Equimolar-Conf1 with the highest total CN (highest Li-OG4 CN and lowest Li-OTFSA CN) is the most energetically favorable. The Equimolar-Conf2, which has the lowest Li-OG4 CN and highest Li-OTFSA CN, exhibits the highest binding energy (on average, +0.19 eV/Li vs. Equimolar-Conf1) among all three models examined, indicating the instability of undercoordinated Li+ ions in equimolar LiTFSA-G4 electrolytes. Interestingly, the Equimolar-Conf3 model, constructed by the most stable contact ion pair in gas phase calculation, leads to an unexpectedly high binding energy (on average, +0.14 eV/Li vs. Equimolar-Conf1). The significant change in lithium solvation structures, before and after being equilibrated, suggests the huge impact of inter-pair interactions on the geometry of contact ion pairs in equimolar LiTFSA-G4 electrolytes.



-10.6 Equimolar-Conf1 Equimolar-Conf2 Equimolar-Conf3

-10.7

Eb (eV/Li)

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

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Figure 9. The binding energies of equimolar LiTFSA-G4 electrolyte as a function of simulation time after the equilibration. The predominant geometry of contact ion pairs in the most stable Equimolar-Conf1 agrees well with the neutron scattering characterizations of the equimolar Li-tetraglyme electrolyte:43 the Li+ ions are not coordinated to all five O atoms but only to four of them, and then the [Li(G4)1]+ complex forms pair with the TFSA− anion. The pairing between [Li(G4)1]+ complexes and TFSA− anions reflects an ionic-liquid-like nature, consistent with experimental reports.7, 44 By contrast, Li+ ions prefer not to be in direct contact with TFSA− anions at a low concentration of Li salt. The tendency of increased contact ion pairs with Li salt concentration has been observed in a previous study by Raman spectroscopy.45 Compared with the case of low Li salt concentration (1mol/L), the MD simulation results of equimolar LiTFSA-G4 electrolytes are more dependent of initial model constructions. The three 1mol/L models lead to very close RDFs and CNs, despite the fact that the detailed solvation structures of Li+ ions are different and thereby cause differences in the binding energy. By contrast, we may see a clear difference in the equilibrated RDFs and CNs among the three equimolar models. The positive correlation between the total CN of Li+ ions and the phase stability is evident. Our results also suggest that an unreasonable initial model of equimolar electrolytes would lead to aggregated solvation structures, which corresponds to undercoordinated Li+ ions and high binding energies. Therefore, it is important to construct reasonable initial structures for obtaining meaningful simulation results. Despite that all above MD simulations achieved the convergence in terms of both total energies and solvation structures, however, the converged results depend on the initial model construction and therefore are not the absolute convergence, probably due to the weak ion


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diffusivity at room-temperature and insufficient simulation time. To achieve the absolute convergence independent from initial model constructions, a longer simulation time up to nanoseconds may be required. For this purpose, we need a computationally more efficient method with high accuracy comparable to DFT-level calculations, e.g., MD simulations with the artificial neural network potential.46-49 3 SUMMARY Employing FPMD simulations, we have studied the solvation structure of lithium ions in LiTFSA-G4 electrolyte at both low (1mol/L) and equimolar concentrations. In the case of 1mol/L LiTFSA, different initial models lead to very close coordination numbers of Li+ ions after reaching the equilibrium. The total CN is approximately 5.0, mainly contributed by O atoms from G4 molecules. The difference in binding energies suggests that the [Li(G4)2]+ complex is more stable than the [Li(G4)1]+ complex at a low concentration of Li salt. For the equimolar LiTFSA-G4 electrolyte, the equilibrated solvation structure of Li+ ions are highly dependent on the initial model construction. The Equimolar-Conf1 starting from a uniform distribution of ground-state [Li(G4)1]+ complexes and TFSA− anions, results in the most stable solvation structure and highest CN of 5.3 among all three models examined. The predominant geometry of contact ion pairs in the equilibrated Equimolar-Conf1 is however not c5[Li(G4)1]+TFSA−, the most stable one in gas phase calculations. Instead, most of the contact ion pairs adopt the geometry of the second most stable c5’-[Li(G4)1]+TFSA−, in which Li+ ion is solvated by four O atoms from G4 and one from TFSA, highlighting the difference between isolated clusters and real electrolytes. Simulation results also suggest that the aggregation of G4 molecules or TFSA− anions will lead to under-coordinated Li+ ions and phase instabilities, which is different from LiTFA-G3, suggesting different Li+ ion diffusion mechanism. The [Li(G4)1]+TFSA− contact ion pair, which is prevalent in the equimolar LiTFSA-G4 electrolyte, is rarely seen in the 1mol/L electrolyte. Therefore, the probability of pairing between the LiG4 complexes and TFSA− anions is significantly increased by the increased concentration of Li salt, rationalizing the ionic-liquid-like properties of the equimolar LiTFSA-G4 electrolyte. Our results reveal the solvation structure of tetraglyme based electrolytes at the DFT level and can be a solid step toward unraveling the complex diffusion behavior based on the advanced sampling and machine-learning techniques.

■ ASSOCIATED CONTENT



* Supporting Information is available.

■ AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest. ■ ACKNOWLEDGMENTS This work was supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan through the “Development of Environmental Technology using Nanotechnology” program and by ALCA-SPRING of Japan Science and Technology Agency. The numerical calculations were performed using the Numerical Materials simulator of National Institute for Materials Science. We would like to thank Dr. Ashu Choudhary for helpful discussions.


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Insight into the Solvation Structure of Tetraglyme-Based Electrolytes

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