Complex Ion Dynamics in Carbonate Lithium-Ion Battery Electrolytes

Mar 6, 2017 - Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah 84112, United States. ∥ Physics Division, Lawrenc...
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Complex Ion Dynamics in Carbonate Lithium-Ion Battery Electrolytes Mitchell T. Ong,*,† Harsh Bhatia,‡ Attila G. Gyulassy,§ Erik W. Draeger,‡ Valerio Pascucci,§ Peer-Timo Bremer,‡ Vincenzo Lordi,*,† and John E. Pask∥ †

Materials Science Division, Lawrence Livermore National Laboratory, Livermore, California 94550, United States Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California 94550, United States § Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah 84112, United States ∥ Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, United States ‡

S Supporting Information *

ABSTRACT: Li-ion battery performance is strongly influenced by ionic conductivity, which depends on the mobility of the Li ions in solution, and is related to their solvation structure. In this work, we have performed first-principles molecular dynamics (FPMD) simulations of a LiPF6 salt solvated in different Li-ion battery organic electrolytes. We employ an analytical method using relative angles from successive time intervals to characterize complex ionic motion in multiple dimensions from our FPMD simulations. We find different characteristics of ionic motion on different time scales. We find that the Li ion exhibits a strong caging effect due to its strong solvation structure, while the counterion, PF6− undergoes more Brownian-like motion. Our results show that ionic motion can be far from purely diffusive and provide a quantitative characterization of the microscopic motion of ions over different time scales.

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principles molecular dynamics.6−8 These calculated diffusion coefficients can successfully predict experimentally determined values with reasonable accuracy,9 as long as the ion dynamics follow this simple behavior. Even though the analysis of the MSD has been successful in describing simple diffusive motion, it assumes isotropic behavior and fractal dynamics with its onedimensional order parameter. Sometimes, the MSD can show nonlinear behavior with time such as in Figure 1, which is a plot of MSD versus time for Li+ in an ethylene carbonate (EC) solvent from a first-principles molecular dynamics simulations.

INTRODUCTION Lithium ion batteries are commonly used to power many portable electronic devices such as laptop computers, portable phones, and music players. Recently, their usage has also been extended to electric vehicles and aerospace applications.1 These batteries rely on the movement of Li ions between the anode and cathode in order to generate an electrical voltage.2 The speed at which the Li ions move in the organic solvent between the anode and cathode is often quantified by the diffusion coefficient, which is proportional to the ion mobility, and is a measure of the transport properties of a Li-ion battery electrolyte. The magnitude of the diffusion coefficient is important for determining the cycling rate performance of a battery. The diffusion coefficient is commonly evaluated from molecular dynamics simulations using the Einstein−Stokes relation:3 D=

⟨(X(t ) − X(t0))2 ⟩ 6t

(1)

In this expression, ⟨(X(t) − X(t0))2⟩ is the mean square displacement (MSD), where X(t) is the particle position at time t and ⟨⟩ denotes an ensemble average over all t. A linear relationship between the MSD and time is an indication of simple Brownian motion where the particle exhibits diffusive behavior, and its motion is uncorrelated in time. The MSD method has been used to compute the diffusion coefficient of Li+ in different organic electrolytes using classical4,5 and first© XXXX American Chemical Society

Figure 1. Mean-square displacement versus time for Li+ in a EC solvent showing deviations from linearity suggesting non-Brownian motion. Received: March 1, 2017 Published: March 6, 2017 A

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are able to quantify the correlated and uncorrelated directional motion of Li+ and its counterion (PF6−), using the full threedimensional trajectory information. We identify specific time scales over which the Li+ and PF6− ions deviate from simple Brownian motion and compare the dynamics across time scales of both ions in different solvents. Our results characterize the multiscale behavior of ions in Li-ion battery organic electrolytes, which can be used to predict how ions move through the electrolyte and clarify when standard analyses such as MSD should and should not necessarily apply.

The deviations from linearity in the MSD plots indicate time scales of the dynamics that are nonfractal (i.e., not simple Brownian motion). Therefore, the MSD analysis alone is not enough to characterize the complex nature of the ionic motion. Recently, a new statistical parameter was introduced by Burov et al.10 that considers the distribution of relative angles traversed by a particle over different time scales. This parameter measures correlated motions that deviate from Brownian motion, which are not captured in a MSD analysis. A schematic diagram defining the relevant vectors that comprise the relative angle analysis are given in Figure 2. In order to calculate the

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where X0, X1, and X2 are positions of the ion at times t, t + Δ, and t + 2Δ, respectively. The relative angle θ is then defined as the angle between vectors V1 and V2, as V ·V cos θ = 1 2 |V1||V2| (3)

COMPUTATIONAL METHODS We performed first-principles molecular dynamics using density functional theory (DFT) with the projector augmented wave (PAW) method12,13 and the PBE generalized gradient approximation exchange-correlation functional,14,15 as implemented in the VASP16,17 software package. The systems considered consisted of 63 EC molecules + 1 LiPF6, 42 EMC molecules + 1 LiPF6, and 35 EC molecules + 15 EMC molecules + 1 LiPF6. A 450 eV plane-wave cutoff was used, and Brillouin zone sampling was restricted to the Γ-point. All molecular dynamics simulations were performed in the NVT ensemble using a Nosé−Hoover thermostat,18,19 with the Nosé frequency of ∼1000 cm−1 corresponding to a period of ∼32 fs, and time step of 0.5 fs. Each system was equilibrated for 5−7.5 ps at 330 K, followed by 30 ps of simulation time to gather statistics. A temperature of 330 K was used to mimic an intermediate Li-ion battery operating temperature and to ensure that EC was not frozen (experimental TEC melt = 310 K). Histogram plots were created by combining several onedimensional (1D) cuts at different Δ values. These 1D cuts were generated by averaging the relative angles across different initial positions along the trajectory for a specific value of Δ. All 1D cuts were normalized such that the area under the histogram is unity for each Δ, producing probability densities along the θ axis. ReaxFF 2 0 − 2 2 simulations were performed in the LAMMPS23,24 molecular dynamics code under NVT conditions using a Nosé−Hoover chain thermostat with 3 Nosé−Hoover chains and time step of 0.25 fs. The Nosé frequency was set to ∼1333 cm−1 corresponding to a period of ∼25 fs. A system of 63 EC + 1 LiPF6 molecules was equilibrated for 125 ps at 330 K followed by 2 ns of simulation time.

For each time interval Δ, we calculate the relative angle across all times in the trajectory for a given particle. We use these values to construct a histogram, which is normalized as a probability density distribution. Details of the interpretation of different relative angle distributions have been given in ref 10.; briefly, a distribution centered at a relative angle near zero indicates forward ballistic motion, while a distribution centered near 180° indicates a caging effect. A uniform (flat) distribution indicates ideal Brownian motion, since motion in any direction is equally probable, and is a signature of diffusive behavior. A schematic of these representative distributions is shown in Figure S1 of the Supporting Information. Previously, this analysis has been applied to 2D experimental particle tracking data in colloidal suspensions10 and molecular dynamics simulations of proton transport in solution,11 where it was used to detect and quantify caging effects. In this work, we use this relative angle analysis to study ionic motion in carbonate organic-liquid battery electrolytes using first-principles molecular dynamics (FPMD) simulations. We

We have performed first-principles molecular dynamics simulations of a single LiPF6 molecule in three different organic solvents relevant for lithium-ion batteries: ethylene carbonate (EC), ethyl methyl carbonate (EMC), and a 3:7 (molar) mixture of EC:EMC. Determination of the solvation structures and diffusion coefficients from the mean square displacement were given in previous work.8 Here, we examine the directional motion of the Li+ and PF6− ions in these three organic solvents by considering the relative angle parameter defined by Burov et al.10 The trajectories of the Li+ and PF6− ions are shown in Figure 3a−c, with different representative Δ time intervals indicated. The colored line segments indicate the vectors used to calculate the relative angle for a single initial time t0. Statistics were averaged over all possible t0. We observe that Li+ changes direction much more frequently than PF6− resulting in more back and forth motion. This leads to faster net forward motion for PF6− compared to Li+.

Figure 2. Relative angle θ is defined between the vectors V1 and V2 as shown.

relative angle, three successive positions of a given particle in the trajectory separated by a constant time interval Δ are used to form two vectors: V1(t ) = X1 − X 0 V2(t ) = X 2 − X1

(2)

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RESULTS AND DISCUSSION

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underneath the histograms, which are representative of different characteristics of ionic motion. We observe that both ions have sharp peaks near (0,0) corresponding to forward ballistic motion at the shortest time scales, which transitions to structured motion over longer time scales. In general, we see that PF6− has a longer transition time scale to structured motion (longer ballistic regime, up to order 1 ps) compared to Li+, which transitions to structured motion at much shorter time scale (on order 0.1 ps). Distributions for both ions show time scales where there are clearly defined peaks and regions that are more broad. In general, longer time scale dynamics approach a more Brownian-type behavior (broad distribution). Clearly, however, the dynamics of neither ion is purely diffusive, but rather exhibit more complex behavior. In particular, we find that Li+ shows a clearly peaked distribution at θ ∼ 120° for a broad range of intermediate time scales; peaks centered at large relative angles in the histogram are indicative of caging, where the ion is trapped by its solvent molecules and reverses direction frequently.10,11 Even though some structure is evident in the relative angle distributions for PF6−, particularly at shorter times scales, the distributions for Δ ≳ 2 ps are generally broad and characteristic of more Brownianlike motion, where the ion exhibits random, diffusive behavior. The stronger caging effect in Li+ is consistent with tighter solvation of the EC molecules around Li+ compared to PF6−.8 More diffusive behavior observed in PF6− is consistent with weaker solvation compared to Li+. This observation is, in turn, consistent with the diffusion coefficients calculated previously where it was found that Li+ diffusivity is less than that of PF6−, due to strong solvent drag on Li+.8 The strong solvation of Li+ by 4 EC molecules in the first solvation shell, which persists for the duration of our simulations, creates a Li + 4EC complex

Figure 3. Trajectories for Li+ (top) and PF6− (bottom) at different Δ time intervals (50 fs, 2 ps, and 4 ps) for organic solvents (a) ethylene carbonate (EC), (b) ethyl methyl carbonate (EMC), and (c) 3:7 mixture of EC:EMC. Green circles indicate the initial position of the trajectory. Li and P trajectories are plotted on the same scale for each electrolyte.

We can visualize trends in the relative angle probability distribution across different time scales by combining 1D histograms for the range of Δ values into a 2D plot. New software has recently been developed in order to construct these relative angle distributions more efficiently and was used to construct the figures in the present work.25 Results for Li+ and PF6− in ethylene carbonate (EC) are shown in Figure 4. We also include one-dimensional cuts at specified Δ values

Figure 4. Histograms of the relative angle probability distribution at different time intervals Δ for (a) Li+ and (b) PF6− in EC. One-dimensional cuts at representative Δ values are shown below. Yellow dashed line indicates the trend of the relative angle at short time scales. Green dashed lines indicate Δ values for each 1D cut. The horizontal dashed line on each 1D cut shows the hypothetical distribution for Brownian motion for comparison. C

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Figure 5. Histograms of the relative angle probability distribution at different time intervals Δ for (a) Li+ and (b) PF6− in EMC. One-dimensional cuts at representative Δ values are shown below. Yellow dashed line indicates the trend of the relative angle at short time scales. Green dashed lines indicate Δ values for each 1D cut. The horizontal dashed line on each 1D cut shows the hypothetical distribution for Brownian motion for comparison.

Figure 6. Histograms of the relative angle probability distribution at different time intervals Δ for (a) Li+ and (b) PF6− in 3:7 EC:EMC mixture. One-dimensional cuts at representative Δ values are shown below. Yellow dashed line indicates the trend of the relative angle at short time scales. Green dashed lines indicate Δ values for each 1D cut. The horizontal dashed line on each 1D cut shows the hypothetical distribution for Brownian motion for comparison.

diffusing with an effectively heavier mass than PF6−, which is only weakly solvated. We now compare the histograms of the relative angle distribution at different time scales for EMC to EC in order to

determine the effect of solvent choice on ionic motion. In Figure 5, we show similar histograms as in Figure 4 for EMC. We observe similar short time scale behavior as in EC, where PF6− again shows a longer time scale for transition from D

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The Journal of Physical Chemistry C ballistic to structured dynamics than Li+. Peaks in the Li+ distribution are not as well-defined and intense in EMC compared to EC. PF6− also exhibits a greater spread in the angle distribution than Li+ in EMC which is similar to EC. Overall, we find a broader distribution at different time scales for both Li+ and PF6− in EMC compared to EC. This is because the strength of solvation of the ions is weaker than in EC, which allows for more diffusive behavior. Furthermore, this observation is consistent with the diffusion coefficients calculated in previous work where both ions were found to diffuse faster in EMC than in EC.8 We also compare the ion dynamics in a 3:7 mixture of EC:EMC to study the effects of mixed solvents. In Figure 6, we show the relative angle distribution at different time scales for both Li+ and PF6− in the EC:EMC mixture. Representative one-dimensional cuts at different time intervals are also included for Li+ and PF6−. Many observations are similar across the three different electrolytes. These include the longer initial ballistic transition regime at small Δ for PF6− compared to Li+ and PF6− exhibiting more Brownian-like motion than Li+. A notable difference in EC:EMC compared to the other electrolytes is that Li+ shows a much stronger caging effect than either pure EC or EMC alone. The increased interaction with and influence of the solvent molecules on the ion dynamics is also reflected in the smaller Li+ diffusion coefficient in the mixture compared to both pure EC and EMC as found in previous work.8 This suggests that Li+ is much less diffusive and more tightly solvated in the mixture than in the pure solvents at the short time scales probed in our FPMD simulations. In Figure 7, we compare the Li+ trajectories in EC and the 3:7 EC:EMC mixture to illustrate the stronger caging effect

observed it in EC:DMC mixtures using a combination of polarizable force-field and FPMD methods.26 An explanation for the observation of jump diffusion events in these simulations was given by Bhatia et al., who observed transient species during FPMD simulations consisting of Li+ solvated by either three or five EC molecules.27 The formation of these transient species allowed different EC molecules to rotate in and out of the first solvation shell, which provides a mechanism for the jump diffusion process even at short FPMD time scales. Since our quantum mechanical FPMD simulations are limited to time scales of tens of picoseconds, we used the ReaxFF classical reactive force field20−22 to further examine the effect of longer time scales on the relative angle distributions. We consider a 1 LiPF6 + 63 EC system and run molecular dynamics simulations for up to 2 ns. We show representative trajectories of Li+ over different time scales of the simulation in Figure 8. We see that at the time scales of the DFT simulations

Figure 8. Li+ trajectories of a molecular dynamics simulation using ReaxFF for a 63 EC + 1 LiPF6 system and scanning time scales between 30 ps and 2 ns. The first 150 ps is highlighted in gray on the 2 ns trajectory.

(0−30 ps), the Li+ remains locally confined, but at longer time scales, it begins to spread out and explore more regions/local basins in space. Trajectories for PF6− are shown in Figure S3 in the Supporting Information, where we notice that PF6− traverses larger displacements than Li+ overall. At the longer time scales and coarser time resolution of the ReaxFF simulations, the mean square displacements for both Li+ and PF6− appear linear, as shown in Figure S5 of the Supporting Information, indicative of ideal Brownian motion. We plot the relative angle probability distribution at different time scales from the ReaxFF MD simulations in Figure 9, where we examine gradually longer time frames to assess how increased sampling affects the distribution. We find that the intensity of the peaks at larger Δ values decreases as more sampling is included when considering longer time frames. A similar observation was made for PF6−, as shown in Figure S4. This observation is illustrated more clearly in Figure 10, where in plots (b) and (c) the sharp noisy peaks for Δ = 4 and 6 ps that exist for the 0−30 ps time frame are shown to decrease and smooth with additional time sampling. While the distributions become smoother, it appears that the general peak positions for Δ values up to ∼6 ps remain the same even with additional sampling. We conclude that the inclusion of more time samples broadens the peaks in the relative angle distributions and reduces their heights but does not change general locations and shapes, thus validating the corresponding observations from FPMD simulations at shorter time scales.

Figure 7. Comparison of the Li+ trajectory in pure EC and the 3:7 EC:EMC mixture showing stronger caging effects in the mixture.

observed in the mixture. For pure EC, we observe regions in time exhibiting tight clusters of spatial excursion separated by occasional large displacements. In contrast, for the 3:7 EC:EMC mixture, we observe only a single large tight cluster. The observation of these two regimes is indicative of two different types of ionic motion for Li+, either moving within its solvation structure or hopping to another adjacent solvation environment, and leads to nonlinear behavior in the MSD, as shown in Figure 1 for EC and Figure S2 in the Supporting Information for 3:7 EC:EMC. These two mechanisms were referred to as carrier-based diffusion (Li+ trapped within its solvation shell) and jump diffusion (Li+ jumping from one solvent configuration to another) by Borodin et al., who

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CONCLUSIONS We computed and analyzed the ionic motion of Li+ and PF6− in EC, EMC, and an EC:EMC mixture using first-principles E

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Figure 9. Histograms of the relative angle distribution as a function of time time interval Δ for simulation lengths from 30 ps to 2 ns for Li+ in 63 EC + 1 LiPF6 from ReaxFF molecular dynamics simulation.

Figure 10. 1D histogram cuts for Δ values of (a) 2 ps, (b) 4 ps, and (c) 6 ps for simulation lengths of 30 ps, 90 ps, and 2 ns from ReaxFF MD simulation of Li+ in 63 EC + 1 LiPF6.

of EC:DMC mixtures.26 The observation of the jump diffusion mechanism is attributed to short-lived transient solvation structures with either three or five EC molecules surrounding Li+,27 which allow other EC molecules to rotate into or out of the first solvation shell. Our results highlight the highly complex nature of ionic motion in these organic solvents, with different characteristics at different time scales, a phenomenon manifested in the nonlinear dependence of the mean square displacement with time,8 which further highlights the difficulty of characterizing ionic motion in these liquids based solely on standard 1D MSD analysis. 1D MSD analysis is ideal for longer time scale simulations where different types of ionic motions are averaged out when calculating diffusivity, but nonlinearities in the MSD often arise when considering short time scale simulations where correlated motion can dominate the analysis and become more apparent. The microscopic detail of the ionic

molecular dynamics and relative angle analysis. Analysis of the relative angle distribution for the different electrolytes showed that Li+ exhibits a caging effect at intermediate time scales, while PF6− undergoes simpler Brownian-like motion in all three solvents examined. The different dynamics of Li+ versus PF6− are related to Li+ being more strongly solvated than PF6−, with subtle differences among the solvents consistent with differences in solvation. We find that EMC shows the most uncorrelated (simple diffusive) behavior of the three solvents, consistent with calculated diffusion coefficients from our previous work that showed the largest diffusivity for both ions in EMC compared to EC or the EC:EMC mixture.8 We also observed a larger caging effect in the 3:7 EC:EMC mixture compared to pure EC. This is due to two different types of Li+ motion in pure EC, which correspond to carrier-based diffusion and jump diffusion as described by Borodin et al. in the context F

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(10) Burov, S.; Tabei, S. M. A.; Huynh, T.; Murrell, M. P.; Philipson, L. H.; Rice, S. A.; Gardel, M. L.; Scherer, N. F.; Dinner, A. R. Distribution of Directional Change as a Signature of Complex Dynamics. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 19689−19694. (11) Savage, J.; Voth, G. A. Persistent Subdiffusive Proton Transport in Perfluorosulfonic Acid Membranes. J. Phys. Chem. Lett. 2014, 5, 3037−3042. (12) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (13) Kresse, G.; Joubert, D. From Ultrasoft Pseudo Potentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775. (14) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (15) Perdew, J. P.; Burke, K.; Ernzerhof, M. Erratum: Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1997, 78, 1396. (16) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (17) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (18) Nose, S. A Unified Formulation of the Constant Temperature Molecular-Dynamics Methods. J. Chem. Phys. 1984, 81, 511. (19) Hoover, G. H. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31, 1695. (20) van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A., III ReaxFF: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A 2001, 105, 9396−9409. (21) Islam, M.; Bryantsev, V. S.; van Duin, A. C. T. ReaxFF Reactive Force Field Simulations on the Influence of Teflon on Electrolyte Decomposition During Li/SWCNT Anode Discharge in Lithium Sulfur Batteries. J. Electrochem. Soc. 2014, 161, E3009−E3014. (22) Bedrov, D.; Smith, G. D.; van Duin, A. C. T. Reactions of Singly-Reduced Ethylene Carbonate in Lithium Battery Electrolytes: A Molecular Dynamics Simulation Study Using the ReaxFF. J. Phys. Chem. A 2012, 116, 2978−2985. (23) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (24) Aktulga, H. M.; Fogarty, J. C.; Pandit, S. A.; Grama, A. Y. Parallel Reactive Molecular Dynamics: Numerical Methods and Algorithmic Techniques. Parallel Computing 2012, 38, 245−259. (25) Bhatia, H.; Gyulassy, A. G.; Pascucci, V.; Ong, M. T.; Lordi, V.; Draeger, E. W.; Pask, J. E.; Bremer, P. T. Interactive Exploration of Atomic Trajectories Through Relative Angle Distribution and Associated Uncertainties. Proceedings of the 9th IEEE Pacific Visualization Symposium 2016, DOI: 10.2172/1331475. (26) Borodin, O.; Olguin, M.; Ganesh, P.; Kent, P. R. C.; Allen, J. L.; Henderson, W. A. Competitive lithium solvation of linear and cyclic carbonates from quantum chemistry. Phys. Chem. Chem. Phys. 2016, 18, 164−175. (27) Bhatia, H.; Gyulassy, A.; Ong, M.; Lordi, V.; Draeger, E.; Pask, J.; Pascucci, V.; Bremer, P. T. Technical Report LLNL-TR-704318: Understanding Lithium Solvation and Diffusion through Topological Analysis of First-Principles Molecular Dynamics 2016, DOI: 10.2172/ 1331475.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b02006. Examples of MSD plots for the 3:7 EC:EMC mixture and for the EC ReaxFF trajectory; a diagram illustrating ideal ballistic, caging, and Brownian motion; and figures showing the PF6− trajectory and relative angle distributions from ReaxFF simulations (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Vincenzo Lordi: 0000-0003-2415-4656 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. Support for this work was provided through Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences.

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