Atomistic Description of Ionic Diffusion in PEO–LiTFSI: Effect of

Article Cite This: Macromolecules 2018, 51, 8987−8995

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Atomistic Description of Ionic Diffusion in PEO−LiTFSI: Effect of Temperature, Molecular Weight, and Ionic Concentration Daniel J. Brooks,† Boris V. Merinov,*,† William A. Goddard, III,† Boris Kozinsky,‡,§ and Jonathan Mailoa‡ †

Materials and Process Simulation Center, MC 139-74, California Institute of Technology, Pasadena, California 91125, United States ‡ Research and Technology Center, Robert Bosch LLC, Cambridge, Massachusetts 02139, United States § Harvard School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, United States Macromolecules 2018.51:8987-8995. Downloaded from pubs.acs.org by DURHAM UNIV on 11/19/18. For personal use only.

S Supporting Information *

ABSTRACT: Understanding the ionic diffusion mechanism in polymer electrolytes is critical to the development of advanced lithium-ion batteries. We report here molecular dynamics-based characterization of structures and diffusion in poly(ethylene oxide) (PEO) with lithium and bis(trifluoromethysulfonyl)imide (TFSI) ions imbedded into the PEO structure. We consider a range of temperatures (360−480 K), molecular weights (43, 22, 10, and 2 chains with 23, 45, 100, and 450 EO monomers, respectively), and ion concentrations (r = 0.02, 0.04, 0.06, and 0.08 Li:EO) for which there is experimental data. The found dependence of the diffusion coefficients on these variables is in good agreement with experimental measurements. We then analyze how the diffusion performance depends on details of the atomistic diffusion mechanism, the motion of the Li and TFSI along the polymer chains and hopping between them, the role of polymer motion, the temperature dependence of the intrachain and interchain diffusion contributions to the total ionic diffusion coefficients, and how these depend on ionic concentration and molecular weight. The most diffusive Li atoms exhibit frequent interchain hopping, whereas the least diffusive Li atoms oscillate or “shift” between two or more polymer chains. These shifts may affect the segmental motion of the PEO−LiTFSI polymer that is expected to be important for fast lithium-ion diffusion. The excellent agreement between experiment and theory validates the approach and methodology used in this study, setting the stage for applying this methodology to predicting how to modify the polymer structure to increase ionic conductivity for a new generation of electrochemical materials.

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cycling, and the propagation of lithium dendrites6−8 can cause short circuits and, potentially, combustion of the battery cell. Solid polymer electrolytes mitigate the effects of these problematic reactions by guiding lithium diffusion along a series of coordination sites along the polymer chains, slowing side reactions and greatly increasing the potential life span and range of safe operating conditions of the battery cell.9 Although a range of polymer backbones have been studied, poly(ethylene oxide) (PEO)-based structures are currently the leading candidates for application in lithium-ion batteries due to the flexibility of the polymer chains and presence of strong ether coordination sites.10 Improvements in ionic conductivity, however, are needed for the widespread use of solid polymer electrolytes. Thus, large research efforts are underway to increase the ionic conductivity of PEO-based polymers while

INTRODUCTION

Polymer electrolytes are promising materials for development of the next generation of energy storage devices, including lithium-ion polymer batteries, due to their exceptional chemical and mechanical stability, high energy density, and long lifetimes.1 Originally designed for use in portable electronic devices,2 lithium-ion batteries now show promise as energy storage devices for renewable energy sources that produce intermittent power, such as solar and wind power, as well as for electric vehicles. Recently, the availability of lithiumion batteries for residential use has increased with the release of home batteries like the Tesla Powerwall. The typical, commercially available, lithium-ion battery consists of an organic liquid electrolyte paired with a graphite anode and intercalated transition metal oxide cathode.3 Although high ionic conductivities can be obtained from liquid electrolytes, undesirable side reactions4 limit both the lifetime and safety of these systems. Specifically, the formation of dead lithium crystals5 can lead to capacity loss over repeated © 2018 American Chemical Society

Received: August 14, 2018 Revised: October 18, 2018 Published: October 31, 2018 8987

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maintaining the mechanical strength of the PEO backbone.1,11,12 The properties of PEO-based structures depend strongly on the molecular weight of each chain.10,13,14 Lower molecular weight structures tend to be more flexible and enable larger ionic diffusion coefficients, albeit with reduced mechanical stability. To address this issue, a number of modifications to the PEO structure have attempted to improve the stability of the backbone, including the creation of block copolymers15,16 as well as comb-like17,18 and cross-linked19,20 polymer structures. For sufficiently large molecular weights, the diffusion coefficient and diffusion mechanism are independent of chain length as well as the nature of polymer end groups.10 The crystallization of lithium salts in polymer electrolytes can limit the effective number of charge carriers, and thus the conductivity, within polymer electrolytes. Although a number of salts such as LiPF6,21 LiClO4,22,23 and LiBF424,25 have been studied, LiTFSI remains the leading candidate, in part, due to its diffuse charge distribution and resistance to clumping.1 An early description of the diffusion dynamics in polymer electrolytes was provided by the dynamic bond percolation (DBP) model developed by Ratner26,27 for describing diffusion through a disordered medium that contains a series of coordination sites. The key assumption of this model is the presence of a renewal time, τR, over which the neighboring coordination sites are updated due to motion of the polymer backbone. This model demonstrates that ionic motion is always diffusive for time scales longer than the renewal time (t ≫ τR). A Rouse-based model for ionic diffusion was developed by Maitra28 and later extended by Borodin and Diddens.29,30 This model builds upon the description of renewal events in DBP by introducing a time scale τ1 associated with intrachain motion along a chain, a relaxation time τ2 to describe the polymer chain segmental motion, and a waiting time τ3 between interchain hops. The overall ionic diffusion rate can be expressed as a combination of these three events.28 A growing body of experiments are being reported on PEOLiTFSI-based polymer systems. Timachova et al.14 used pulsed field gradient nuclear magnetic resonance (NMR) to measure Li+ and TFSI− diffusion over a range of molecular weights, Mw = 0.6−100 kg/mol, and ionic concentrations, r = 0.02−0.08. Pożyczka et al.31 recently performed impedance spectroscopy (IS) to study the bulk ionic conductivity and transference number, t+, of PEO−LiTFSI across a range of ionic concentrations. These experiments provide valuable data on how performance depends on molecular weights and ionic concentrations, but they do not provide the atomistic understanding needed to design improved systems. To gain this atomistic understanding, we report here a comprehensive computational investigation of ionic diffusion across the range of molecular weights, ion concentrations, and temperatures. We find that the predicted diffusion coefficients depend on these variables in the same way as in experiment. This allows us to interpret the dependence of the diffusion on these parameters in terms of atomistic concepts.11,14,31 Our analysis of chain coordination reveals that intrachain and interchain hoping and polymer backbone motions all contribute to lithium diffusion, in agreement with the Rouse model. We find polymer backbone motions suggesting that the presence of lithium reduces segmental chain motion, particularly when the lithium is coordinated to multiple chains.

Article

METHODS

Force field parameters were assigned using the Desmond32 system builder with the OPLS2005FF.33 Time steps were 1 fs for short-range interactions and 3 fs for long-range interactions, with the Desmond useries method applied to account for long-range Coulomb interactions beyond a 9 Å cutoff. We used fixed point charges of +0.7 to each Li cation and a total charge of −0.7 to a TFSI anion, in agreement with those obtained from the QM-based electrostatic potential (ESP) method (section 1 of the Supporting Information). A Berendsen thermostat with a time constant of τ = 1 ps was used for NVT diffusion simulations. We used the amorphous builder to create a series of polymer structures, each of which was equilibrated with a series of NVT and NPT minimizations applying scaled-effective solvent (SES)34 equilibration steps to fully relax the polymer chains. More details of this procedure are available in section 2 of the Supporting Information. PEO−LiTFSI structures were generated over a range of ionic concentrations, r = 0.02, 0.04, 0.06, and 0.08 Li:EO. For the r = 0.02 case, we also constructed structures with a range of chain lengths: N = 23, 45, 100, and 450 EO. To maintain a near-constant number of monomers (N = 1000) in these simulations, the cells were constructed with m = 43, 22, 10, and 2 chains, respectively. Simulations were performed at 360, 400, 440, and 480 K. Some experiments on PEO use methyl-terminated chains whereas others use hydroxyl-terminated chains (see, for instance, ref 31). The experiments suggest that the diffusion for both forms are essentially the same at higher molecular weights10 but may differ for PEO− LiTFSI polymers with lower molecular weights (N < 50). Our polymers are terminated with O−CH3 at one end and O−C2H5 at the other end, so our results can be compared to the CH3-terminated cases. Diffusion in polymers can exhibit more than one time scale. For shorter times, the particles may spend long periods in a local region that has higher free volume before hopping to a new such region. It is necessary to guarantee that the particles have made many hops between such regions, before we can relate mean-square displacement (MSD) traveled over the time period to a diffusion constant, MSD = 6Dt, the Fickian relationship. To ensure that sufficient time has elapsed, we plot the log(MSD) versus log(time) and look for a slope of 1. We find that to reach a regime characterized by Fickian diffusion, an MD time of 115 ns was required for 400, 440, and 480 K, while the simulations at 360 K were run for 400 ns. The polymer structure for r = 0.02 and N = 100 at the end of the 400 ns MD simulation is shown in Figure 1. The density of the structure, 1.125 g/cm3, is in the experimental range.1,10 At this ionic concentration (r = 0.02), the Li atoms are primarily coordinated to 4−6 oxygen atoms of the PEO chains. The ionic diffusion coefficient, Dion, was derived from the ionic mean-squared displacement (MSD) curve using the 3D diffusion relation: ÷÷÷÷÷÷÷◊ 2 MSDion (t ) ≡ r(t )ion = 6Diont (1) Because this relation only holds for Fickian diffusion,35 care was taken to identify the Fickian regime of the MSD curve. The largest domain, t, where the log−log slope is nearly unity (within a tolerance of ±0.1) is selected as the fitting region, with a minimum width of one-tenth of the total simulation time to ensure good statistics. An example fit is shown in Figure 2. The remainder of the MSD curves are shown in section 3 of the Supporting Information. To obtain insight into the atomistic nature of diffusion, we developed a model for lithium coordination. Each individual Li atom is described as coordinated to an oxygen, if it is within 2.5 Å, roughly the outer width of the first Li−O coordination shell.12 Similar to ref 28, we successively numerated the oxygen atoms of a polymer chain and define a Li position along a chain by the mean index n which is an average of the enumerated oxygen atoms involved in the coordination sphere of the Li atom. Correspondingly, Δn is a change in the Li atom coordination with time. The chain to which a Li atom is most 8988

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Figure 3. Schematic summarizing the three outcomes of the Li diffusion mechanism in PEO−LiTFSI: interchain diffusion (case a), shift (case b), and intrachain diffusion (case c). Li atom: green; O atoms: red. Note that the typical Li atom is coordinated to 4−5 oxygens. Therefore, changes in coordination can be fractional. These changes are tracked over 0.25 ns intervals of the MD trajectories. For intrachain diffusion (a Li atom remains coordinated to the same chain) we measure whether a Li atom remains fixed, Δn = 0, moves to the next oxygen site along the chain, Δn ≤ 1, to two oxygen sites along the chain, Δn ≤ 2, or moves farther than two oxygen sites, Δn > 2. For interchain diffusion (a Li atom’s most coordinated chain changes) the possible outcomes are an interchain hop, where Li is only coordinated to a single chain at the end, or a shift, where Li remains coordinated to at least two chains.

Figure 1. A typical PEO−LiTFSI structure consisting of 20 LiTFSI and 10 chains of PEO with 100 monomers in each chain after 400 ns of dynamics at 360 K. Li atoms: green; N: blue, S: yellow, O: red; H: white; CF3: teal

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RESULTS AND DISCUSSION To understand the nature of local sites in the polymer structure, we first analyze the coordination of lithium. The Li− O radial distribution function (RDF) is shown in Figure 4. It

Figure 2. Mean-squared displacement (MSD) versus time for lithium ions diffusing through a PEO polymer matrix (10 chains each with N = 100 monomers) at T = 480 K for a concentration of r = 0.08. The green line has a slope of 1, showing the time needed to attain the Fickian regime. The total time of this MD simulation is 115 ns. The diffusion coefficient is obtained by finding the region of the MSD curve (red) that is tangent to the 6Dt green line over the region where the log−log MSD slope is closest to 1. Similar pictures are provided in the Supporting Information for all other cases reported here.

Figure 4. Li−O radial distribution function (RDF) for the system containing 10 PEO chains of length 100 monomers and r = 0.02 Li:EO, averaged every 100 ps over a 400 ns trajectory at 360 K. This indicates an average of four O atoms within 2.5 Å of the Li.

coordinated is tracked as the chain with the greatest number of coordinated oxygen. In the event of a tie, the chain with the smallest Li−O distance is considered to be the most coordinated chain. We consider the three events of the Li diffusion in PEO−LiTFSI (Figure 3): (1) “interchain diffusion” occurs when a Li atom changes chain coordination and fully coordinates to a single new chain; (2) a “shift” is when a Li atom changes a multiple chain coordination for a single chain coordination but remains “stuck” between the chains; and (3) “intrachain diffusion” is when lithium’s most coordinated chain remains constant and is characterized by a change of the Li−O coordination site, Δn.

looks very similar to the Li−O RDF observed for PEO− LiTFSI in ref 36. The first coordination peak is at 2.12 Å, in good agreement with the 2.1 Å peak observed in a neutron scattering study.12 It corresponds to the Li−OPEO bonds, while the second broad peak at ∼6.2 Å represents the Li−OTFSI atom pairs. The integrated RDF up to 3 Å (near the first minimum in the RDF) shows that the average Li is coordinated by 4.5 oxygen atoms within a distance of 2.55 Å. An example of a Li site in the r = 0.02/N = 100 structure at 360 K is shown in 8989

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monomers is ∼1000). For both experiment and theory, the ionic diffusion coefficient decreases with increasing chain length, with a significant drop by a factor of 2−3 (depending on the temperature) between 23 and 100 monomers and a plateau between 100 and 450 monomers. This likely results from increased polymer motion of flexible chain length. In all cases, the anion diffusion is faster than the cation one. This result is in agreement with reported experimental and computational data11,14,37−40 and explained by the significantly stronger interaction of the Li ions with the oxygen atoms of the PEO polymer compared to the interaction of the TFSI anions with the surrounding atoms. As a result, the TFSI anions diffuse more freely than the Li cations. The lithium transference number calculated from our computationally predicted ionic diffusion coefficients ranges from 0.2 to 0.3 as r changes from 0.02 to 0.08, which is in very good agreement with the values obtained by Pożyczka et al.31 from the IS experimental study and reproduces the peak at r = 0.06 observed in the experiment (Figure 8). To examine the nature of segmental motion of the polymer chain, we analyzed the displacements of individual oxygen atoms. Table 1 shows the results of this analysis for the two extreme cases: oxygen atoms located at the center of the chain (n = 50, 51) and oxygen atoms located at the edges of the chain (n = 1, 100). Across all temperatures, we see that the oxygen atoms near the edge of the polymer chain displace ∼30% more than the oxygen atoms at the center of the chain. This suggests increased polymer flexibility at the edges of the chains, but this increased apparent diffusion may not represent true diffusion. Figure 9 shows the lithium displacements associated with each component of the total diffusion process: intrachain diffusion, shifts, and interchain hops (diffusion). When there is no change in coordination (Δn = 0), the lithium displacements are caused by the segmental motion of the polymer chains. We see that segmental motion is the dominant contributor to ionic diffusion over short time scales. Intrachain changes in coordination along a chain (Δn > 0) contribute to the overall lithium diffusion, but intrachain hops alone are not enough to reach the Fickian diffusion limit. On the other hand, interchain

Figure 5. The Li atom is coordinated by three polymer O atoms with Li−O interatomic distances of ∼2.1 Å, while the

Figure 5. Local coordination of lithium (green) to PEO oxygen atoms (red) at the end of the 400 ns, 360 K/20LiTFSI/N = 100 simulation.

fourth O is at 2.62 Å. These O atoms belong to two different polymer chains, and the Li position corresponds to a shift event in the hopping model. We analyzed the diffusion coefficients for Li and TFSI as a function of temperature, ionic concentration, and molecular weight (chain length) (Figures 6 and 7). The predicted diffusion coefficients at 360 K for Li are in excellent agreement with the more recent IS experiments,31 both in magnitude and in the factor of 2 decrease as ionic concentration increases from r = 0.02 to 0.08. In the literature, this drop decrease has been attributed partially as an increase in the number of salt clusters,31 which we do not observe in our simulations. As shown in Figure 6, the diffusion coefficients obtained from NMR14 are a factor of 5 higher than those from IS and from our computed values. We do not know the reason for this discrepancy; however, our calculations of diffusion are directly related to the IS experiments (for further discussion see Figure S3). Figure 7 shows the diffusion coefficients for Li and TFSI for r = 0.02 as a function of chain length for N = 23, 48, 100, and 450 monomers (in each case the total number of PEO

Figure 6. Li (a) and TFSI (b) diffusion coefficients over a range of ionic concentrations, r = 0.02, 0.04, 0.06, and 0.08 Li:EO for 10 PEO chains of length N = 100 and temperature of 360, 400, 440, and 480 K. The experimental values from NMR and IS are shown for T close to 360 K. The magnitude and ionic concentration dependence of the MD simulations are rather close to the IS values but significantly smaller than the NMR values. 8990

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Figure 7. Li (a) and TFSI (b) diffusion coefficients for r = 0.02 as a function of chain length N = 23, 48, 100, and 450 monomers for temperature of 360, 400, 440, and 480 K. In each case the total number of PEO monomers is ∼1000.

Figure 9. Average Li displacements associated with coordination change. The Δn = 0 displacement is related to the vehicular motion of the polymer backbone.

Figure 8. Values of the lithium transference number of PEO−LiTFSI electrolytes obtained from our MD simulations and reported in the literature published.31 Our predicted values (red open circles) are in very good agreement with the experimental values which were calculated using the formula proposed by Watanabe41 (open green circles). The original figure is taken from ref 31, and the numbers in square brackets correspond to the list of the references in ref 31.

associated with the vehicular diffusion of lithium ions. Frequent lithium intrachain hops and less frequent interchain hops contribute to the overall diffusion process. Comparing the mobility of the oxygen atoms of a polymer chain in Table 1 (3.0−3.8 Å in Δt = 0.25 ns at 360 K) to the motions of the Li atoms (2.1 Å) at their regular positions, Δn = 0 (Figure 9) (where the Li is at a fixed site in the chain), we see that the O atoms are significantly more mobile than the Li! This seems to suggest high flexibility of the polymer which may allow the polymer to tightly hold the Li ions, particularly when the lithium is coordinated to multiple chains, slowing down the Li-ion diffusion. To understand the atomistic nature of the ionic diffusion in PEO−LiTFSI, we use the coordination model to analyze the atoms with the largest and smallest MSD over the simulation time. These atoms are denoted as the most and least diffusive lithium. The chain coordination of the most diffusive Li atom in the MD simulation with r = 0.02 Li:EO and N = 100 at 360 K is plotted as a function of time in Figure 10a, while Figure 10b shows the real position of this single Li atom at points spaced every 1 ns in the MD trajectory. The lithium resides on the eighth chain for around 30 ns before hopping to the ninth chain and then the fifth. Over the 400 ns simulation time, the

Table 1. Displacement (Å) of Polymer Backbone Oxygen for the Case of 10 Chains with N = 100 at T = 360 K and r = 0.02a T (K)

center

edge

360 400 440 480

3.0 4.8 6.5 7.6

3.8 6.3 8.8 10.4

Here we examined the average displacements for time steps of Δt = 0.25 ns over the full 400 ns simulation. This was done for the two oxygen sites closest to center (n = 50, 51) and edge (n = 1, 100) of each polymer chain.

a

hops are correlated to the largest increases in lithium motion and contribute significantly to the diffusion process. Taken together, these results indicate that the atomistic nature of the lithium diffusion is consistent with the Rouse model29 formulationthe segmental motion of polymer chains is 8991

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Figure 10. Chain coordination (a) and displacement (b) behavior of the single most diffusive Li atom in the 360 K/20LiTFSI/N = 100 simulation as a function of time. Blue lines in (b) show the unit cell.

Figure 11. Chain coordination (a) and displacement (b) behavior of the single least diffusive Li atom in the 360 K/20LiTFSI/N = 100 simulation as a function of time.

Figure 12. Chain coordination (a) and displacement behavior (b) of the single most diffusive Li atom in the 480 K/20LiTFSI/N = 100 simulation as a function of time. In (b) we show multiple copies of the unit cell (each 43.44 Å on a side) to represent the total displacement.

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Figure 13. Chain coordination (a) and displacement (b) behavior of the single least diffusive Li atom in the 480 K/20LiTFSI/N = 100 simulation as a function of time.

most diffusive lithium moves a total of 59.3 Å and coordinates to seven different chains. For comparison, the coordination behavior of the least diffusive Li atom in this simulation is shown in Figure 11. This Li atom diffuses only a total of 12.2 Å and coordinates to chain 8 for most of the simulation time, occasionally shifting to chains 5 and 9. Thus, there is considerable variability in the diffusional behavior of individual ions. The more diffusive Li atoms hop more frequently between chains, whereas the less diffusive ones only temporarily shift between chains. We performed a similar analysis for the most and least diffusive Li atoms for the same structure (r = 0.02 Li:EO and N = 100) but at higher temperature, 480 K. Figure 12a shows the coordination of the most diffusive lithium as a function of time, while Figure 12b displays the real positions of the lithium at points spaced every 1 ns in the trajectory. At this temperature, we observe numerous interchain hops between all ten PEO chains over the 115 ns trajectories for both the most diffusive (Figure 12) and less diffusive lithium (Figure 13), and the total displacement of the lithium is 115.4 and 45.5 Å, respectively. The hopping model, shown in Figure 3, describes the lithium motion as intrachain and interchain diffusions, and as shifts, when lithium remains coordinated to multiple chains. The changes in the chain coordination of the most and least diffusive Li atoms assume a connection between the chain coordination and total lithium displacement. To examine this assumption, changes in lithium coordination are tracked every 0.25 ns in the trajectory. An analysis of the lithium coordination frequency is shown in Figure 14 as a function of temperature. We find that a small number of Li atoms undergo no change in coordination, Δn = 0. Short intrachain hops, Δn ≤ 1, correspond to slight changes in the Li−O coordination shell and are more frequent at lower temperatures. Increases in temperature are correlated to an increased frequency of larger intrachain hops, Δn > 2, and interchain hops, which means that an activation barrier is associated with these processes. This is also confirmed by the fact that the frequency of shifts or, in other words, the frequency of attempts to perform interchain hops is rather

Figure 14. Frequency of lithium coordination changes as a function of temperature.

independent of temperature, but the number of successful attempts increases with increasing temperature.

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CONCLUSIONS In our computational simulations, we built a number of PEO− LiTFSI polymer structures and predicted the ionic diffusion coefficients. We find very good agreement with the experimental data14,31 across a range of ion concentrations, temperatures, and molecular weights. Our results show that intrachain ionic diffusion is the most probable mode at 360 K, which is near the battery operating temperature, but the longrange ionic diffusion depends to great extent on the polymer backbone motion and interchain hopping diffusion. The comparisons of the MSD diffusion rates for Li ions and the polymer center and the polymer extremities seem to suggest that the PEO polymer is too flexible, maybe holding onto the Li ions too much. Thus, the Li ions tend to stay too long associated with a region of the PEO. This suggests that a less flexible polymer, perhaps using a blend with some poly(propylene oxide), might lead to faster diffusion of the Li ions relative to the polymer matrix. The excellent agreement achieved between experiment and theory validates the approach and methodology used in this study which can now be applied for predicting the polymer structure and ionic 8993

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molecular weight and end groups. Solid State Ionics 2012, 227, 119− 127. (11) Gorecki, W.; Jeannin, M.; Belorizky, E.; Roux, C.; Armand, M. Physical properties of solid polymer electrolyte PEO (LiTFSI) complexes. J. Phys.: Condens. Matter 1995, 7, 6823−6832. (12) Mao, G.; Saboungi, M.-L.; Price, D. L.; Armand, M. B.; Howells, W. Structure of liquid PEO-LiTFSI electrolyte. Phys. Rev. Lett. 2000, 84, 5536−5539. (13) Teran, A. A.; Tang, M. H.; Mullin, S. A.; Balsara, N. P. Effect of molecular weight on conductivity of polymer electrolytes. Solid State Ionics 2011, 203, 18−21. (14) Timachova, K.; Watanabe, H.; Balsara, N. P. Effect of molecular weight and salt concentration on ion transport and the transference number in polymer electrolytes. Macromolecules 2015, 48, 7882− 7888. (15) Panday, A.; Mullin, S.; Gomez, E. D.; Wanakule, N.; Chen, V. L.; Hexemer, A.; Pople, J.; Balsara, N. P. Effect of molecular weight and salt concentration on conductivity of block copolymer electrolytes. Macromolecules 2009, 42, 4632−4637. (16) Royston, E.; Ghosh, A.; Kofinas, P.; Harris, M. T.; Culver, J. N. Self-assembly of virus-structured high surface area nanomaterials and their application as battery electrodes. Langmuir 2008, 24, 906−912. (17) Hou, W.-H.; Chen, C.-Y.; Wang, C.-C.; Huang, Y.-H. The effect of different lithium salts on conductivity of comb-like polymer electrolyte with chelating functional group. Electrochim. Acta 2003, 48, 679−690. (18) Liang, Y.-H.; Wang, C.-C.; Chen, C.-Y. Synthesis and characterization of a new network polymer electrolyte containing polyether in the main chains and side chains. Eur. Polym. J. 2008, 44, 2376−2384. (19) Snyder, J. F.; Carter, R. H.; Wetzel, E. D. Electrochemical and mechanical behavior in mechanically robust solid polymer electrolytes for use in multifunctional structural batteries. Chem. Mater. 2007, 19, 3793−3801. (20) Hayamizu, K.; Aihara, Y.; Price, W. S. Correlating the NMR self-diffusion and relaxation measurements with ionic conductivity in polymer electrolytes composed of cross-linked poly (ethylene oxidepropylene oxide) doped with LiN(SO2CF3)2. J. Chem. Phys. 2000, 113, 4785−4793. (21) Chaurasia, S. K.; Singh, R. K.; Chandra, S. Ion−polymer and ion−ion interaction in PEO-based polymer electrolytes having complexing salt LiClO4 and/or ionic liquid, [BMIM][PF6]. J. Raman Spectrosc. 2011, 42, 2168−2172. (22) Newman, G.; Francis, R.; Gaines, L.; Rao, B. Hazard investigations of LiClO4/dioxolane electrolyte. J. Electrochem. Soc. 1980, 127, 2025−2027. (23) Fullerton-Shirey, S. K.; Maranas, J. K. Effect of LiClO4 on the structure and mobility of PEO-based solid polymer electrolytes. Macromolecules 2009, 42, 2142−2156. (24) Munshi, M.; Owens, B. Ionic transport in poly(ethylene oxide) (PEO)-LiX polymeric solid electrolyte. Polym. J. 1988, 20, 577−586. (25) Henderson, W. A. Crystallization kinetics of glyme− LiX and PEO− LiX polymer electrolytes. Macromolecules 2007, 40, 4963− 4971. (26) Nitzan, A.; Ratner, M. A. Conduction in polymers: dynamic disorder transport. J. Phys. Chem. 1994, 98, 1765−1775. (27) Druger, S. D.; Nitzan, A.; Ratner, M. A. Dynamic bond percolation theory: A microscopic model for diffusion in dynamically disordered systems. I. Definition and one-dimensional case. J. Chem. Phys. 1983, 79, 3133−3142. (28) Maitra, A.; Heuer, A. Cation transport in polymer electrolytes: a microscopic approach. Phys. Rev. Lett. 2007, 98, 227802. (29) Diddens, D.; Heuer, A.; Borodin, O. Understanding the lithium transport within a Rouse-based model for a PEO/LiTFSI polymer electrolyte. Macromolecules 2010, 43, 2028−2036. (30) Diddens, D.; Heuer, A. Lithium ion transport mechanism in ternary polymer electrolyte-ionic liquid mixtures: A molecular dynamics simulation study. ACS Macro Lett. 2013, 2, 322−326.

conductivity and for designing new advanced polymer materials for applications in electrochemical devices.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01753.

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A table of charges used in MD simulations, a description of the procedure applied for building polymer structures, MSD plots for Li and TFSI, diffusion coefficients obtained from MD simulations, NMR, and IS measurements at T = 360 K, predicted and experimental activation energies for Li and TFSI diffusions (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Boris V. Merinov: 0000-0002-2783-4262 William A. Goddard, III: 0000-0003-0097-5716 Boris Kozinsky: 0000-0002-0638-539X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Bosch Energy Research Network Grant 13.01.CC11. We thank Drs. Saber Naserifar, Andres Jaramillo-Botero, Francesco Faglioni, and Nicola Molinari for fruitful discussions and critical feedback on this work.

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DOI: 10.1021/acs.macromol.8b01753 Macromolecules 2018, 51, 8987−8995