Solvation and Dynamics of Sodium and Potassium in Ethylene

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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 J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06457 • Publication Date (Web): 18 Sep 2017 Downloaded from http://pubs.acs.org on September 23, 2017

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The Journal of Physical Chemistry

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: [email protected]; [email protected]; [email protected] 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 †

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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 differences 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 solvation 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 of the intrinsic properties of Na+ and K+ in organic electrolytes, which may ultimately influence the intercalation mechanism at the electrode-electrolyte interface and therefore battery performance, lifetime, and safety.

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Introduction Li-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. 1,2 This 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 been steady growing. In this regard, sodium 3–7 and potassium 8–10 ion 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 sodium 11–13 and potassium 14–16 ion 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 play a key role in the intercalation/deintercalation mechanism and therefore battery performance. 17,18 In 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+ . 19 This implies that Na+ generally exhibits a weaker interaction with the solvents considered compared to Li+ . Such a conclusion is consistent with a recent combined theoryexperimental study 20 and density functional theory (DFT)-based calculations of Na+ in various organic electrolytes. 21,22 Studies 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. 23 These theoretical studies of Na+ and K+ , however, were based on static gas phase models 20–23 that 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



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in organic electrolytes, have relied on classical force fields, which were derived based on specific model systems. 24 In this regard, first-principles simulations, which do not require a priori assumptions, 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 25,26 that 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, we describe 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/cm3 and 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

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− the cation and PF− 6 dissociated, and we verified that PF6 is 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, 27,28 where the electronic ground-state wave functions were optimized at each ionic step. The interatomic forces were computed using DFT with the projector augmented wave (PAW) method 29,30 and the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation functional. 31 The electronic wave-functions were expanded in a plane-wave basis set truncated at a cutoff energy of 450 eV, and the Brillouin zone was sampled at the Γ-point. We carried out the FPMD simulations in the NVT canonical ensemble using a Nose-Hoover thermostat 32,33 with a frequency of ∼1000 cm−1 , which corresponds to a period of ∼63 fs, and a time step of 0.5 fs. Following our previous work, 25 we 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), where X=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, the position of the gXO (r) first A, 2.34 ˚ A, and 1.95 ˚ A maximum follows the order rK+ > rNa+ > rLi+ , yielding values of 2.80 ˚ 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. 34 We also report in Fig. 1b the RDFs between the ions and either carbonyl oxygen 5



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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 for X=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 (OE , dashed line) of EC molecules. The corresponding results for Na+ and K+ are shown in the inset. (OC ) 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 that nXO increases with the size of the ion solvation shell, yielding average 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. 25 However, 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 bipyramidal and square pyramidal. In contrast 6


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(c)

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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 ion solvation 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 (OC ) 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 of the liquid, as indicated by a well-defined boundary located at the first gLi+ O (r) minimum (Fig. 1a). This is in contrast to Na+ and K+ , where gXO (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 probability distributions of the ion–oxygen 7



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Figure 3: Histograms of the oxygen coordination number in the first solvation shell around Li+ (black), Na+ (red) and K+ (blue) ions in EC. The first minima in the corresponding gXO (r) were used as distance cutoffs for determination of the first solvation shells. coordination numbers, shown in Fig. 3. We see that nLi+ O exhibits a sharp and narrow distribution, showing a nearly constant value (of four) for the duration of the simulation. On the other hand, Na+ and K+ prefer an oxygen coordination number of six and eight, respectively, but also exhibit much broader distributions of nXO (K+ broader than Na+ ). These broad nXO distributions 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 estimated τ by fitting an exponential of the form e−(t/τ )β to the time correlation function P (t) = hH(t) · H(0)i, where H(t) = 1 if a given EC oxygen atom is within the first solvation shell and 0 otherwise. 35,36 For 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


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Na+ , for which the ion solvation in carbonate-based electrolytes has been more extensively studied. 20 In 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+ 6 ions being associated, 25 by 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. 20 However, the ion solvation can be significantly different in linear and cyclic carbonate solvents, 25 making 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, 25 while accurate estimate of the kinetics of ion pairing requires extensive free-energy calculations, e.g., with respect to cation-anion separation; 37 however, 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 A is consistent with both previous FPMD 38,39 and Li+ in EC, the value of rLi+ = 1.95 ˚ classical simulations, 36,40 which 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 A simulation data for these ions in the liquid phase. Nevertheless, the calculated rNa+ = 2.34 ˚ is consistent with a previous DFT study of Na+ –EC clusters in the gas phase that reports a value of 2.36 ˚ A. 22 On the other hand, our conclusion on the solvation structure of Na+ differs significantly from a recent classical simulation that utilized the CHARMM General Force field. 24 Specifically, Ref. 24 yields a notably larger Na+ –EC carbonyl oxygen distance

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Figure 4: Solvation energies (∆Esol ) estimated from the binding energy of the X + (EC)n clusters, where n is the number of EC molecules in the first ion solvation shell, and X ≡ 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. A, while showing a clear boundary between the first and second solvation shells of rNa+ = 2.5 ˚ in the gNa+ 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 strength of 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. 17,18,41 Here, we rely on cluster calculations to estimate the ion solvation energies (∆Esol ). Specifically, ∆Esol was approximated from the binding energy of the X + (EC)n clusters, where X ≡ Li+ , Na+ or K+ , and n is the number of EC molecules in the first ion solvation shell. In particular,

∆Esol = EX + + E(EC)n − EX + (EC)n , 10


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where EX + (EC)n , E(EC)n , and EX + are the energies of the X + (EC)n and (EC)n clusters, and the ion X + in vacuum, respectively. In these calculations, configurations of the X + (EC)n clusters were extracted directly from the FPMD simulations, therefore temperature and dynamical effects are implicitly included. For each ion, we report in Fig. 4 the solvation energies computed for 100 configurations of X + (EC)n extracted 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 ∆Esol = 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. 42–44 More 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. 45,46 This 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 energy of 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 ∆Esol for Na+ and K+ compared to Li+ . Quantitatively, the standard deviation of ∆Esol is 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

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Figure 5: The location of Wannier centers (yellow spheres) is shown for representative snapshots 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 structures 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 solvations, we explore the differences in electronic structure of each of the solvated ions. We employ maximally localized Wannier function (MLWF) analysis 47,48 as 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 1s2 electrons is located at the center of the ion, in contrast to Na+ and K+ for which the four WCs associated with the 2s2 2p6 and 3s2 3p6 electrons 12


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(a): Li+ MLWFs

(b): K+ MLWFs

(c): MLWFs of an Oxygen lone pair near Li +

(d): MLWFs of an Oxygen lone pair near K +

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 pair of 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 1s2 electron 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, dbX + −W , computed from 100 configurations extracted from each FPMD trajectory. The results reveal that the WC of Li+ is located at the ion center (dbLi+ −W = 0.00 ˚ A), while dbNa+ −W = 0.30 ˚ A and dbK+ −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 dbX + −W values. We also observe that the solvating oxygen orbitals protrude closer to the Li+ center than to K+ (or 13



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Na+ , not shown), as discussed further below. The above analyses reflect the Coulombic attraction between the ion nucleus and its electrons, which is further related to the interaction strength between the ion and the valence electrons of the solvating EC molecules. This interaction strength was examined by considering the MLWFs associated with the carbonyl oxygen lone pair electrons of the solvating EC molecules of Li+ and K+ , as shown in Fig. 6c and Fig. 6d, respectively. These orbitals were analyzed due to the preferred interaction of the solvated ions with the EC oxygen lone pairs that are oriented toward the ions. We find that the WLWFs of the EC oxygen lone pair show a clear tendency to share electrons with Li+ , in contrast to K+ (and Na+ ). Accordingly, our analysis implies that the origin of the weaker solvation of Na+ and K+ by EC compared to Li+ can be traced to the delocalization of Na+ and K+ electrons that results in weaker interactions between the ions and EC oxygen lone pair electrons. This ordering in the delocalization is also consistent with the electron binding energies of Li, Na, and K. For example, the first ionization potentials of the species follow the ordering: Li (5.39 eV) > Na (5.14 eV) > K (4.34 eV). 49 We note that the strength of the ion solvation is determined not only by the intrinsic properties of the ion, but also the solvent types, as discussed in our previous study for Li+ . 25

Ion Dynamics The strength of the ion solvation shell discussed above is directly related to the transport properties of the ion. For example, our previous studies have shown that the strongly solvated Li+ diffuses much more slowly than the weakly solvated PF− 6 ion in carbonate solvents, including EC; 25,26 in particular, the dynamics of the former is limited by the caging effect, in contrast to the simpler Brownian-like motion of the latter. A similar observation was made in Ref. 38 when comparing propylene-carbonate (PC) and EC solvents, where it was shown that the weaker solvation of Li+ in PC results in a relatively faster ion diffusion. In addition, examination of Li+ in different solvents, including EC, ethyl methyl carbonate (EMC), and a 14


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Figure 7: Mean-square displacement (MSD) versus time computed for Li+ (black), Na+ (red) and K+ (blue) ions in EC. mixture of EC and EMC, revealed that the diffusivity of Li+ varies appreciably depending on the solvent interaction strength, i.e., the ion diffusion coefficient is smaller in solvents where Li+ is more tightly solvated. 25 Similarly, it has been demonstrated that mixing EC with solvents having lower dielectric constants, such as dimethyl carbonate (DMC), weakens the Li+ solvation shell and leads to faster diffusion compared to the pure solvent. 50 Collectively, these studies suggest that the transport of Li+ in EC (and other organic solvents) may be significantly different from that of Na+ and K+ , which exhibit significantly weaker solvation shells. The transport properties of Li+ , Na+ and K+ in EC were investigated by comparing their mean square displacements (MSD) versus time. As shown in Fig. 7, the calculated MSDs clearly indicate that Li+ diffuses much more slowly than Na+ and K+ . Specifically, the diffusion coefficients were estimated from the slopes of the MSD plots as 4.3 ± 0.7, 12.1 ± 2.0, and 11.2 ± 0.8 cm2 /µs for Li+ , Na+ and K+ , respectively. As a result, our simulations indicate that the diffusion coefficient of Li+ is about 3 times smaller than those of either Na+ or K+ , which can be directly related to a significantly stronger solvation shell of Li+ . On the other hand, although the K+ solvation is (slightly) weaker than Na+ , the computed diffusion coefficients are not significantly different, implying that the Na+ and K+ transport are more dictated by the bulk solvent properties, due to the lack of the strong ion–solvent

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6 4 2 0 0

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4

6

8

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Time (ps)

Figure 8: Mean-square displacement (MSD) computed for all EC molecules in the electrolyte with Li+ (black), Na+ (red) and K+ (blue) ions. The MSD computed for EC molecules only in the first solvation shell of Li+ is presented by the dashed line. interaction. (We also note the close quantitative similarity of the electron delocalization for Na+ and K+ discussed in the previous section.) The relatively large uncertainties in the estimated diffusion coefficients also implies that significantly more statistics are required for a better quantitative description of the ion diffusion coefficients; however, the distinction between Li+ and both Na+ and K+ is clear. Reducing these errors significantly further to allow more precise distinction between the diffusion coefficients of Na+ and K+ in FPMD simulations is nontrivial, since it would require many long (at least several tens of ps or more) and independent simulations. The ion dynamics is clearly governed by the nature of the ion–solvent interaction; conversely, the dynamics of EC molecules may also be affected by the presence of the ion. The effect of the ions on the solvent molecules is analyzed with MSDs computed for the EC molecules in the presence of the ions, as shown in Fig. 8. The results show a slight suppression of the EC diffusion in the electrolyte containing Li+ compared to Na+ and K+ . In particular, we obtained values of 14.4 ± 0.6, 16.0 ± 0.5, and 15.9 ± 0.2 cm2 /µs for the diffusion coefficients of EC molecules in electrolytes containing Li+ , Na+ and K+ , respectively. To understand the origin of these specific ion effects, we investigated the dynamics of EC molecules only in the first ion solvation shell, which are directly influenced by the ion, and we focus on Li+ that exhibits the strongest ion solvation. The result is shown by 16


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the dashed line in Fig. 8, indicating a much slower diffusion of EC molecules in the first solvation shell compared to bulk EC. The computed diffusion coefficient of the first solvation shell EC molecules is 4.9 ± 0.4 cm2 /µs, which is about three times smaller than the overall diffusion coefficients of bulk EC molecules. These results provide clear evidence that the low diffusivity of the EC molecules near Li+ is responsible for the slightly lower diffusivity of EC molecules in the electrolyte with Li+ compared to those with Na+ or K+ , and further highlights the specific ion effects in the organic electrolytes. We note that previous work 26,51 describes a diffusion mechanism for Li+ in EC that includes the four solvent molecules as a complex, which is reflected in the results presented here. The weaker, less-well-structured solvation of Na+ and K+ thus contributes to significantly higher diffusivity of those ions. Finally, we relate and compare the present findings with existing studies of these ions in aqueous solutions. For the latter, it is known that the dynamics of water molecules in salt solutions deviates from that of pure liquid water, and the concepts of structure-breaking and structure-making described by the empirical Jones-Dole viscosity coefficient, B, have been used for a qualitative explanation of the ion effects on the water dynamics. 52 Specifically, ions with B > 0 reflect a strong hydration and are classified as “structure-making”, while B < 0 denotes “structure-breaking.” In this context, Li+ is classified as a strong structure-maker (B=0.14), Na+ is a weak structure-maker (B=0.06), and K+ is a weak structure-breaker (B = −0.01) in water. Accordingly, the ordering of the solvation strength is the same for ions in water and EC, i.e., Li+ > Na+ > K+ . In addition, it has been shown experimentally that the water diffusion coefficient in aqueous solutions decreases with increasing LiCl or NaCl concentrations, with the strongest reduction observed for LiCl, whereas the variation is less significant for the KCl solution. 53,54 This implies that the diffusion of water molecules is slowest for solutions containing Li+ , indicating analagous ion dynamical behavior in the aqueous solution and EC. Finally, it is also worth pointing out that the oxygen coordination number in the ion first solvation shell is quite similar for water and EC, particularly for Li+ and Na+ , which yield values of 4.0 and 5.3 in water, respectively, 55,56 while K+ ex-

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hibits a slightly smaller oxygen coordination number (6.0-6.1) in water compared to EC (see Fig. 3). 56,57

Conclusions To conclude, we investigate the solvation and transport properties of Na+ and K+ in the EC solvent, compared to Li+ , using first-principles molecular dynamics simulations based on density functional theory. Our simulations reveal significant differences 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 solvation shell with a tetrahedral arrangement of carbonyl oxygen atoms of EC molecules, the larger Na+ and K+ ions show more disordered and flexible solvation structures. Specifically, Na+ and K+ exhibit increased average coordination numbers of 5.7 and 7.6, respectively, which are mostly comprised of carbonyl oxygens but also involve a non-negligible fraction of ether oxygens. The less-ordered solvation structures for the larger ions is reflected by weaker solvation energies; specifically, we obtain values of 5.85, 4.72, and 4.12 eV for Li+ , Na+ , and K+ , respectively. Using the analysis based on maximally localized Wannier functions, we trace the origin of this behavior to the increased delocalization of Na+ and K+ electrons that results in weaker interactions between the ions and EC oxygen lone-pair electrons. Our simulations imply a complex interplay between the ion dynamics and ion solvation strength in the EC solvent. Specifically, we find that weaker-solvated Na+ and K+ ions show a much faster diffusion than Li+ , yielding a diffusion coefficient about three times higher than that of Li+ . On the other hand, although Na+ exhibits a slightly stronger solvation structure than K+ , the dynamics of Na+ and K+ are not significantly different, indicating that the inhibited diffusivity of Li+ stems from its strong interaction with the solvent EC molecules, whereas the Na+ and K+ transport is more likely indicative of the bulk solvent due to the lack of strong ion–solvent interactions. Our study also reveals specific ion effects

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on the dynamics of the solvent; particularly, we demonstrate that EC molecules diffuse slower in the Li+ first solvation shell, which is in turn dictated by the strong ion–solvent interaction. Furthermore, the strong ion–solvent interactions of Li+ reflects the “structure-maker” nature of Li+ in the EC solvent, indicating an analog to the behavior of solvated ions in aqueous electrolytes. Finally, our results indicate that the use of K+ or Na+ instead of Li+ in an organic electrolyte may benefit the charge/discharge rates in energy storage devices, due to their fast transport. In the context of energetics for ion intercalation, the smaller solvation energy of K+ and Na+ compared to that of Li+ implies easier migration to the electrode from the electrolyte. We note that ion solvation and dynamics, and the energy barrier for ion intercalation/de-intercalation, also depend on the solvent types as well as chemistry of the electrode/electrolyte interface, which are topics of future study. Work is also in progress to compute the kinetics of ion pairings, and to understand the dynamics of the ion pairs in different solvents.

Acknowledgement This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Support for this work was provided through Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences. T.A.P acknowledges the support from the Lawrence Fellowship Program. Computational resources were from the Lawrence Livermore National Laboratory Institutional Computing Grand Challenge Program.

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Graphical TOC Entry

Na+ Li+

K+

Increasing Ion Coordination Number

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Solvation and Dynamics of Sodium and Potassium in Ethylene

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