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LLNL-JRNL-734121

Solvationand DynamicsofSodium and

Potassiumin EthyleneCarbonatefrom

AbInitio MolecularDynamicsSimulations

T.A. Pham,K.Kweon, A.Samanta,V. Lordi,J.

Pask

July1, 2017

Journalof PhysicalChemistryC

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Solvation and Dynamics of Sodium and

Potassium in Ethylene Carbonate from Ab Initio

Molecular Dynamics Simulations

Tuan Anh Pham,

?,†Kyoung E. Kweon,†Amit Samanta,‡Vincenzo Lordi,?,†and

John E. Pask

Quantum Simulations Group, Materials Science Division, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA, and Physics Division, Lawrence Livermore

National Laboratory, Livermore, CA 94550, USA

E-mail: pham16@llnl.gov; lordi2@llnl.gov; pask1@llnl.gov Phone: 925-423-6501. Fax: 925-423-5733?To whom correspondence should be addressed †Quantum Simulations Group, Materials Science Division, Lawrence Livermore National Laboratory,

Livermore, CA 94550, USA

‡Physics Division, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 1

Abstract

The development of sodium and potassium batteries offers a promising way to meet the scaling and cost challenges of energy storage. However,compared to Li+, several intrinsic properties of Na +and K+, including their solvation and dynamics in typical organic electrolytes utilized in battery applications, are less well-understood. Here, we report a systematic investigation of Na +and K+in ethylene carbonate (EC) using first-principles molecular dynamics simulations. Our simulations reveal significant dif- ferences in the solvation structure and dynamical properties of Na+and K+compared to Li +. We find that, in contrast to Li+which exhibits a well-defined first solva- tion shell, the larger Na +and K+ions show more disordered and flexible solvation structures. These differences in solvation were found to significantly influence the ion dynamics, leading to larger diffusion coefficients of Na +and K+compared to Li+. Our simulations also reveal a clear and interesting analog in the behavior of the ions in EC and aqueous environments, particularly in the specific ion effects on the solvent dynamics. This work provides fundamental understanding ofthe intrinsic properties of Na +and K+in organic electrolytes, which may ultimately influence theintercalation mechanism at the electrode-electrolyte interface and therefore battery performance, lifetime, and safety. 2

IntroductionLi-ion secondary batteries (LIBs) remain the most popular rechargeable batteries utilized

in electronic devices due to their high energy and power densities. However, to meet the scaling and cost challenges of energy storage, the development of alternative energy storage technologies beyond traditional LIBs is necessary.

1,2This is partly due to the limited lithium

reserves in the Earth"s crust, that could lead to LIBs technological unsustainability as the demand of lithium usage in LIBs for new technologies has beensteady growing. In this regard, sodium

3-7and potassium8-10ion batteries have been considered as a promising way

to mitigate the potential shortage of lithium due to their greater abundance and low cost. While significant efforts are ongoing to optimize host materials for both sodium11-13 and potassium

14-16ion batteries, several fundamental properties of Na+and K+in battery

electrolytes remain less well-understood than those of Li +. Of particular importance are the ion solvation structure and transport properties that playa key role in the intercalation/de- intercalation mechanism and therefore battery performance.17,18In this regard, some aspects of the ion"s solvation have been recently addressed by both experimental and theoretical studies. Specifically, electrochemical impedance spectroscopy experiments show that Na+ insertion and desolvation processes in propylene carbonate and tetraglyme are much faster than Li +, while yielding an activation for Na+desolvation more than two times smaller than that of Li +.19This implies that Na+generally exhibits a weaker interaction with the solvents considered compared to Li +. Such a conclusion is consistent with a recent combined theory- experimental study

20and density functional theory (DFT)-based calculations ofNa+in

various organic electrolytes.

21,22Studies of solvation properties of K+in organic electrolytes

are rather rare. The most recent DFT calculations using gas phase models indicate that compared to Li +and Na+, K+displays the lowest interaction energy with the solvents considered.

23These theoretical studies of Na+and K+, however, were based on static gas

phase models

20-23that neither account for temperature effects nor yield dynamical properties

of the ions. On the other hand, existing molecular dynamics (MD) simulations of,e.g., Na+ 3 in organic electrolytes, have relied on classical force fields, which were derived based on specific model systems.

24In this regard, first-principles simulations, which do not requirea

prioriassumptions, are particularly valuable for providing a microscopic description of the solvation and dynamics of Na +and K+in organic electrolytes. Here, we present a detailed investigation of the solvation and transport properties of Na +and K+in ethylene carbonate (EC) using first-principles molecular dynamics (FPMD) simulations based on DFT. Our simulations show significant differences in the solvation structure and dynamical properties of Na +and K+compared to Li+, which are directly related to the variations in their intrinsic electronic properties. In addition, our results reveal analogous behavior of these ions in EC solvent compared to aqueous environments, particularly regarding specific ion effects on solvent dynamics. The current study builds on our previous work

25,26that examined the relationship between the structural and dynamical

properties of Li +in organic electrolytes, which is critical for optimizing the charge/discharge process in LIBs. The remainder of the paper is organized as follows. First, wedescribe our computational methods, including the construction of the electrolyte model. Then, we discuss our results regarding the solvation structures, dynamics, and electronic structures of Na+and K+in EC solvent, along with comparisons to corresponding results for Li+. Finally, we discuss our main conclusions.

Methods

The electrolytes were modeled by cubic supercells consisting of one cation (Li+, Na+, and K +), a counter anion (PF-6), and 63 EC molecules. The simulation models consist of 638 total atoms in a supercell 19.283 A on a side, yielding a density of 1.32 g/cm3and an ion concentration of 0.23 M. A low ion concentration was chosen in order to investigate the solvation structure of single ions. For the same reason, configurations were generated with 4 the cation and PF-6dissociated, and we verified that PF-6is never associated with the cation during the course of our simulations. 25
The FPMD simulations were carried out using the Born-Oppenheimer approximation with the VASP code,

27,28where the electronic ground-state wave functions were optimized

at each ionic step. The interatomic forces were computed using DFT with the projector aug- mented wave (PAW) method

29,30and the Perdew-Burke-Ernzerhof (PBE) generalized gradi-

ent approximation for the exchange-correlation functional.31The electronic wave-functions were expanded in a plane-wave basis set truncated at a cutoff energy of 450 eV, and the Bril- louin zone was sampled at the Γ-point. We carried out the FPMDsimulations in the NVT canonical ensemble using a Nose-Hoover thermostat

32,33with a frequency of≂1000 cm-1,

which corresponds to a period of≂63 fs, and a time step of 0.5 fs. Following our previ- ous work,

25we used a simulation temperature of 330 K to mimic an intermediate battery

operating temperature and to ensure EC was not frozen (Tmelt= 310 K). For each system, equilibration runs were carried out for 7 ps, and we collected statistics over 25 ps production runs.

Results and Discussion

Conformation of the First Ion Solvation Shell

Our initial examination of the ion solvation structures is based on the radial distribution functions (RDF) between the solvated ions and oxygen atoms of the EC molecules,gXO(r), whereX=Li+, Na+, or K+. We focus on the average ion-oxygen distance,rX, that is relevant for characterizing the ion solvation. As shown in Fig. 1a, theposition of thegXO(r) first maximum follows the orderrK+> rNa+> rLi+, yielding values of 2.80°A, 2.34°A, and 1.95° A for K +, Na+, and Li+, respectively. This ordering indicates an increase in the size of the first solvation shell from Li +to K+and reflects the trend in the ion radius among the three ions.

34We also report in Fig. 1b the RDFs between the ions and either carbonyl oxygen

5

12 34 5678

r (Å)

0246810

gXO (r) (a) Li+ Na+ K+

12 34 5678

r (Å)051015202530 gXO (r) (b)Li-OCLi-OE

12 34 5678

r (Å)051015 gXO (r) Na+ K+ Figure 1: (a) Ion-oxygen radial distribution functions,gXO(r), for solvated ions in EC, obtained from first-principles molecular dynamics simulations. Black, red, and blue lines indicate results forX=Li+, Na+, and K+, respectively. (b) Radial distribution functions between Li +and either the carbonyl oxygen atoms (OC, solid line) or the ether oxygen atoms (O E, dashed line) of EC molecules. The corresponding results for Na+and K+are shown in the inset. (O C) or ether oxygen (OE) atoms of EC molecules, which are discussed in more detail below. We then examine the distributions of the oxygen coordination number,nXO, in the first ion solvation shell to further describe the solvation geometries. Specifically, we find thatnXO increases with the size of the ion solvation shell, yieldingaverage values of 4.0, 5.7, and 7.6 for Li +, Na+, and K+, respectively. Typical solvation structures of the three ions are depicted in

Fig. 2. For Li

+(Fig. 2a), the solvation exhibits the well-known tetrahedral arrangement, as discussed in more detail in our previous study.

25However, the result is significantly different

for Na +and K+(Figs. 2b and Figs. 2c, respectively). For Na+, we find the geometrical arrangement is intermediate between trigonal bipyramidaland square pyramidal. In contrast 6 (a)(b)(c) +Na K+Li+ Figure 2: Typical solvation structures of (a) Li+, (b) Na+, and (c) K+in EC. The solvation structures of Li +and Na+, respectively, can be described as tetrahedral and distorted trigonal bipyramid (or square pyramidal), while the solvation structure of K+is less well-defined. Thick solid and transparent lines denote bonds to carbonyl and ether EC oxygen atoms, respectively. to Li +and Na+, the solvation structure of K+is not as well characterized by a definite geometry, due to a large number of coordinating oxygen atoms. The representative snapshots presented in Fig. 2 for the ionsolvation also hint at the notable differences between the solvation structure of Na +and K+compared to that of Li+, namely, that the first solvation shell of Li +involves only carbonyl oxygens of EC molecules, whereas those of Na +and K+consist of both carbonyl and ether oxygens. We quantified this feature by decomposing the RDFs for the carbonyl (O

C) and ether (OE) oxygen atoms

of the EC solvent separately, as shown in Fig. 1b. The calculated partial RDFs provide clear evidence that the first solvation shell of Li +consists only of carbonyl oxygens, and moreover that these carbonyl oxygens rarely exchange with the rest ofthe liquid, as indicated by a well-defined boundary located at the firstgLi+O(r) minimum (Fig. 1a). This is in contrast to Na +and K+, wheregXO(r) (X=Na+or K+) shows a much less well-defined boundary between the first and second solvation shells, while also having notable contributions of the ether oxygens of EC molecules to the first solvation shells (inset, Fig. 1b). Together, these results suggest a much more fluid interface between the first and second solvation shells of Na +and K+compared to that of Li+. We notice a general trend of increased coordination number from Li+to Na+to K+, with further insight provided by examining the probabilitydistributions of the ion-oxygen 7

246 8 10Coordination number (n)020406080100

P(n) Li+ Na+K+ Figure 3: Histograms of the oxygen coordination number in thefirst solvation shell around Li +(black), Na+(red) and K+(blue) ions in EC. The first minima in the corresponding g XO(r) were used as distance cutoffs for determination of the first solvation shells. coordination numbers, shown in Fig. 3. We see thatnLi+Oexhibits a sharp and narrow dis- tribution, showing a nearly constant value (of four) for theduration of the simulation. On the other hand, Na +and K+prefer an oxygen coordination number of six and eight, respec- tively, but also exhibit much broader distributions ofnXO(K+broader than Na+). These broadnXOdistributions imply that the solvation shells of Na+and K+are rather flexible and are characterized by frequent exchange of individual oxygen atoms of the EC molecules between the first and second ion solvation shells. This conclusion is further supported by the analysis of the residence time (τ) of oxygen atoms of EC molecules in the first ion solvation shell. We estimatedτby fitting an exponential of the forme-(t/τ)βto the time correlation functionP(t) =?H(t)·H(0)?, whereH(t) = 1 if a given EC oxygen atom is within the first solvation shell and 0 otherwise.

35,36For Li+, the residence time is well beyond the length of

the simulations (≂130 ps), whereas for Na+or K+,τ≂22-23 ps. Collectively, analyses of the time evolution of the ion first solvation shell support the interpretation of a more rigid, well-defined solvation structure of Li +, in contrast to more flexible solvation of Na+and K+. This difference is directly related to the variation in the solvation energy and transport of the ions, as discussed below. We also examine the variation in the ion solvation shell due to the formation of a contact ion pair, which is particularly relevant in the high salt concentration regime. We focused on 8 Na+, for which the ion solvation in carbonate-based electrolytes has been more extensively studied.

20In particular, we carried out a relatively short FPMD simulation of 5 ps, starting

from an initial configuration with the cation and anion associated. This configuration was generated based on the final snapshot of a 30 ps simulation of Li+and PF+6ions being associated,

25by replacing Li+with Na+. Analyses of the trajectory show that the ion

pair remains associated for the entire simulation. In addition, we find that the Na+ion first solvation shell is coordinated by≂4.5 oxygen atoms and the anion, simply showing a reduction of≂1 oxygen atom compared to Na+dissociated from the counter-ion. To the best of our knowledge, the only experimental study of the Na +solvation number in the literature was performed for linear carbonate solvents.

20However, the ion solvation can be

significantly different in linear and cyclic carbonate solvents,25making direct comparison with experiment difficult presently. We also compared the thermodynamic stabilities of electrolytes with associated and dissociated ion pairs by computing the average relative energies over the trajectories. Our simulations show that configurations with an associated ion pair are slightly favorable by≂0.1 eV compared to those with a dissociated ion pair. We note that the stability of the ion pair depends on the solvent,25while accurate estimate of the kinetics of ion pairing requires extensive free-energycalculations, e.g., with respect to cation-anion separation;

37however, these topics are beyond the scope of the present study.

Finally, it is of interest to compare the present results with the existing literature. For Li +in EC, the value ofrLi+= 1.95°A is consistent with both previous FPMD38,39and classical simulations,

36,40which report a range between 1.96 and 2.0°A. Comparison of Na+

and K +results with the existing literature is less straightforward due to a lack of available simulation data for these ions in the liquid phase. Nevertheless, the calculatedrNa+= 2.34° A is consistent with a previous DFT study of Na +-EC clusters in the gas phase that reports a value of 2.36 A.22On the other hand, our conclusion on the solvation structureof Na+ differs significantly from a recent classical simulation that utilized the CHARMM General

Force field.

24Specifically, Ref. 24 yields a notably larger Na+-EC carbonyl oxygen distance

9

0 20 40 60 80 100Configuration

3456

ΔEsol (eV)

Li+ Na+ K+ Figure 4: Solvation energies (ΔEsol) estimated from the binding energy of theX+(EC)n clusters, wherenis the number of EC molecules in the first ion solvation shell,andX≡ Li +(circle), Na+(square) or K+(triangle). The results were obtained for 100 structural configurations extracted at equal time intervals from FPMD simulations of each electrolyte. ofrNa+= 2.5°A, while showing a clear boundary between the first and second solvation shells in thegNa+O(r). These results indicate that, unlike simulations of Li+, larger discrepancy between classical and DFT-based simulations remains to be addressed for Na+in EC. We also note that, to the best of our knowledge, the current study presents the first investigation of the solvation of K +in organic cabonate-based electrolytes, which can also be utilized for benchmarking classical simulations.

Solvation Energy

The ion solvation energy is directly related to the strengthof the ion-EC interaction that governs the solvation structure. In addition, it plays an important role in determining the energetics of ion intercalation from the liquid electrolyte into the battery electrodes, since desolvation is required for intercalation.

17,18,41Here, we rely on cluster calculations to

estimate the ion solvation energies (ΔEsol). Specifically, ΔEsolwas approximated from the binding energy of theX+(EC)nclusters, whereX≡Li+, Na+or K+, andnis the number of EC molecules in the first ion solvation shell. In particular,

ΔEsol=EX++E(EC)n-EX+(EC)n,(1)

10 whereEX+(EC)n,E(EC)n, andEX+are the energies of theX+(EC)nand (EC)nclusters, and the ionX+in vacuum, respectively. In these calculations, configurations of theX+(EC)n clusters were extracted directly from the FPMD simulations, therefore temperature and dy- namical effects are implicitly included. For each ion, we report in Fig. 4 the solvation energies computed for 100 configurations ofX+(EC)nextracted at equal time intervals (250 fs) from the corresponding FPMD simulations.

Focusing first on Li

+for which the solvation energy has been widely discussed in the literature, we obtained an average value of ΔEsol= 5.85 eV at the PBE level of theory, which is in good agreement with results of 5.5-6.2 eV reported in previous studies using similar gas phase calculations.

42-44More interestingly, our result is also in reasonable agreement with a

value of 5.2 eV obtained from more computationally intensive free energy calculations using MD simulations performed at the same level of theory.

45,46This observation suggests that

the ion solvation energy is largely determined by the Coulombic interactions between the ion and the EC molecules that constitute the first ion solvation shell, and thus that cluster calculations provide a good estimate for the ion solvation energy in EC.

When compared to Li

+, the solvation energies of Na+and K+are notably smaller. We obtain values of 4.76 eV and 4.12 eV for Na +and K+, respectively, which are 19% and 30% smaller than the solvation energy estimated for Li +. In addition, we find that K+yields a smaller solvation energy than Na +; however, the difference (about 0.5 eV) is much less significant than the variation between the solvation energyof K+or Na+with respect to that of Li +, indicating only a slightly weaker K+solvation compared to Na+. These results are consistent with the generally less rigid solvation structures of Na+and K+, compared to the strongly tetrahedral solvation of Li +, discussed above. The results in Fig. 4 also show significantly larger fluctuations of ΔEsolfor Na+and K+ compared to Li +. Quantitatively, the standard deviation of ΔEsolis 0.43 eV and 0.37 eV for Na +and K+, respectively, as compared to the corresponding value of 0.28 eV for Li+. The larger standard deviations are associated with greater variations of the oxygen coordination 11

Lone pair

++LiNaK(a)(b) (c) Figure 5: The location of Wannier centers (yellow spheres) is shown for representative snap- shots of the first solvation shell of (a) Li +, (b) Na+, and (c) K+. Carbon, oxygen and hydrogen atoms are represented by blue, red and white spheres, respectively, whereas the cations are represented by transparent gray spheres. number of Na +and K+, which stems from the intrinsic flexibility of the ion solvation struc- tures discussed above. Thus, both the structural analysis and solvation energy calculations collectively show that Li +yields a rigid solvation structure, whereas those of Na+and K+ are much more flexible, with K +having the most flexible ion solvation of the three ions. We note that, in the context of energetics for ion intercalation, smaller desolvation energies of Na +and K+compared to Li+indicate that these ions can move more easily into electrodes from the electrolyte.

Electronic Structure

To further understand the origin of the intrinsic rigidity/flexibility of the different ion sol- vations, we explore the differences in electronic structureof each of the solvated ions. We employ maximally localized Wannier function (MLWF) analysis47,48as a convenient way to examine the ion-solvent interaction. With this analysis, the ground-state charge density is transformed into a local-orbital basis so that the associated positions of Wannier centers (WCs) can provide an intuitive picture of the ion polarization and bonding character. The positions of WCs around each ion, relative to the ion center, is related to the degree of localization of the ion"s electrons around the nucleus. Figure 5 shows the WCs computed for representative configurations of the ion solvation shells of Li+, Na+, and K+. For Li+, we observe that the WC of the 1s2electrons is located at the center of the ion, in contrast to Na +and K+for which the four WCs associated with the 2s22p6and 3s23p6electrons 12 (b): K MLWFs +(a): Li MLWFs + (d): MLWFs of an Oxygen lone pair near K lone pair near Li+(c): MLWFs of an Oxygen Figure 6: Isosurfaces of the maximally-localized Wannier functions (MLWFs) associated with semicore electrons of solvated (a) Li +and (b) K+ions in EC. Also shown are isosurfaces of the MLWFs associated with a representative oxygen lone pairof a solvating EC molecule in each case: (c) for Li +and (d) for K+. Positive and negative values are indicated by the yellow and blue surfaces, respectively. An identical isosurface value of 3.0 au was used in all cases. We observe in the case of Li +that both the Li 1s2electron and the EC oxygen lone pair electrons are drawn close to the Li +ion, while for K+(and Na+, not shown) more delocalization around the ion is apparent. for Na +and K+, respectively, are offset from and less tightly bound to the ion center. The delocalization of the ion electrons is quantified by the ensemble-averaged scalar distance between the WCs and the ion center, ?dX+-W, computed from 100 configurations extracted from each FPMD trajectory. The results reveal that the WC of Li+is located at the ion center ( ?dLi+-W= 0.00°A), while?dNa+-W= 0.30°A and?dK+-W= 0.35°A. The offset WCs for Na +and K+indicate weaker electron localization, with K+being the weakest, while Li+ shows strong localization. This difference in the electron localization is also reflected in the shape and extent of the MLWFs for these electrons, as shown representatively in Fig. 6a and

Fig. 6b for Li

+and K+, respectively. Specifically, we observe that the MLWF of Li+is much more tightly bound than those of K +, consistent with the computed?dX+-Wvalues. We also observe that the solvating oxygen orbitals protrude closerto the Li+center than to K+(or 13

Na+, not shown), as discussed further below.

The above analyses reflect the Coulombic attraction betweenthe ion nucleus and its elec-quotesdbs_dbs29.pdfusesText_35

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