Ion Solvation and Dynamics at Solid Electrolyte ... - ACS Publications

Article Cite This: J. Phys. Chem. C 2018, 122, 3219−3232

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Ion Solvation and Dynamics at Solid Electrolyte Interphases: A Long Way from Bulk? Lauren Raguette and Ryan Jorn* Department of Chemistry, Villanova University, Villanova, Pennsylvania 19085, United States S Supporting Information *

ABSTRACT: Rechargeable lithium-ion battery technology has revolutionized energy storage for small electronic devices. However, a deeper understanding is required of the interfaces present in such devices for this technology to continue to advance. While many insights into the solid electrolyte interphase (SEI) for lithium-ion systems have been collected from decades of study, many questions also remain. In particular, this work is interested in exploring SEI composition and its impact on electrolyte structure and dynamics. By using a previously tested classical molecular dynamics approach, the impact of the crystallinity of the SEI interface as well as its content of organic and inorganic species is assessed. It is found that the presence of an amorphous SEI results in the accumulation of ions at the interface, ordering of solvent molecules, and a slowing down of solvation dynamics. These behaviors are intensified when crystal surfaces from LiF and Li2CO3 are considered. In addition to these general observations, the changes in lithium and PF6− solvation structure are also considered as they approach the SEI interface. In both cases, the drive to aggregate arising from greater ion accumulation is shielded in part from interaction with the charged groups in the SEI interface. This competition is tilted toward salt aggregation in the case of crystalline SEI, suggesting a significantly different solvation environment than typically seen in bulk for adsorbed species.

I. INTRODUCTION The search for “better” electrodes and electrolytes for energy storage technology is complicated by the reality that the interface between the two acts as a third component to the system and plays a critical role in battery performance.1,2 Since the 1980s it has been known that the typical organic electrolyte solvents used in metal-ion batteries, namely linear and cyclic carbonates, are chemically unstable during charge cycling at both lithium metal and lithiated graphite anodes.3,4 In addition to the solvent molecules, the salt anions likewise can decompose during battery operation and remove lithium from active transport by absorbing ions in new compounds. These byproducts nucleate into surface films on the order of tens of nanometers thick5,6 and may undergo continual dissolution/precipitation during battery operation.7,8 Ideally the films formed by the electrochemical reactions are electron insulating and ion conducting, resulting in their description as a solid electrolyte interphase (SEI) connecting the electrode to the electrolyte.8,9 While depending on a variety of experimental conditions, including choice of electrode material,10,11 temperature,12 composition of the electrolyte,13 and salt concentration,14 typical species detected at the anode surface include lithium fluoride, lithium oxide, lithium carbonate, and larger organic oligomers.15 For the prototypical lithium-ion electrolyte composed of ethylene carbonate (EC) mixed with LiPF6 salt at a graphite surface, the predominate products are LiF and lithium ethylene dicarbonate Li2EDC.16−18 © 2018 American Chemical Society

Voluminous studies have probed the structure, growth mechanism, and transport behavior of the SEI formed in lithium-ion devices. Regarding structure, general agreement can be found on the reaction products adopting a roughly layered distribution.19−22 Depth profiling experiments have shown that close to the anode surface, inorganic species are present in greater concentrations, including LiF, Li2O, and Li2CO3, while farther away from the electrode a mixture of dicarbonates and organic molecules is produced.20,23 Concerning the growth mechanism for the SEI, insights into the initial reactions occurring at the interface have been gleaned from investigating the impact of changes to the electrode surface and electrolyte composition.9,14,24 Beyond the first few charge cycles, it has been demonstrated that the SEI continues to grow in thickness and evolve in composition over time;25−28 however, the mechanisms for these processes remain an active area of investigation. Theoretical methods have been applied as a complementary tool to map the reaction pathway for electrolytes and the initial stages of SEI formation at idealized interfaces. Wang et al. were among the first to study the one- and two-electron reductions of EC to form Li2EDC and lithium carbonate using a density functional theory (DFT) approach.9,24 Since Wang et al. Received: November 21, 2017 Revised: January 29, 2018 Published: January 31, 2018 3219

DOI: 10.1021/acs.jpcc.7b11472 J. Phys. Chem. C 2018, 122, 3219−3232

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The Journal of Physical Chemistry C

to ion migration at the electrolyte boundary warrants further investigation. Given the importance of the electrolyte interface to the rate performance of the battery and the uncertain role of SEI structure and composition on observed transport, this work focuses on the SEI|electrolyte interface. Since experiments capable of probing molecular structure at the interface and in situ are rare,53,54 computational modeling can play a critical role in establishing connections between SEI structure and properties.55−57 Previous work by Jorn et al. considered the impact of SEI composition and applied voltage on electrolyte structure. They demonstrated the tendency for ion accumulation at the SEI interface for a limited range of amorphous compositions and at very thin film thicknesses close to the electrode surface.58 This work is an expansion of those efforts in which we focus on the later stages of SEI development farther removed from the electrode surface and expand the study to include crystalline LiF and Li2CO3. We shall show that the composition of the amorphous SEI plays a less important role than the crystallinity of idealized SEI films in altering the electrolyte structure and for the first time quantify changes in transport behavior as lithium ions approach the interface.

showed the importance of including ion solvation structure in the reduction of EC, explicit solvent models within ab initio molecular dynamics (AIMD) have become increasingly prevalent.11,29 By including all of the electrolyte components in a fully atomistic representation, the free energy for reactions between EC and other additives has been explored30,31 in addition to the impact of the electrode surface on the solvent reduction mechanism.32 Leung and Budzein investigated the breakdown of EC at graphite surfaces using AIMD and found the two-electron reduction to lithium carbonate to be the favored product.33,34 Ganesh, Kent, and Jiang captured the effect of different surface functionalizations at graphite and suggested that the presence of oxygen termination may favor the formation of Li2EDC.35 The continued reduction of SEI components during charge cycling, often overlooked, has likewise been modeled using AIMD and provides a window into the complex evolution of the SEI.36 Looking beyond the nanoscale, kinetic Monte Carlo37 and variations of ReaxFF38 have been adapted to capture mesoscale film growth. These studies have loosely confirmed the layered structure of the SEI reported previously and indicate morphological differences to the film arising from the choice of carbonate solvent. Informed by these studies of the reactive dynamics for carbonate solvents, this work will focus on the effect of an SEI consisting of known reaction products on charge transport. While questions on SEI structure and evolution remain, it is clear that both impact the ion transport process during charge cycling. Electrochemical impedance spectra of the graphite/ electrolyte interface have indicated the significant role of the SEI resistance to overall battery charging rate.39,40 The total ion resistance of the electrode|electrolyte interface has been decomposed into three contributions: (1) resistance to ion migration in the electrode, (2) resistance from ion diffusion through the SEI, and (3) lithium ion desolvation at the SEI| electrolyte interface.41 By using combinations of electrodes and electrolytes with and without an SEI, Xu et al. attempted to separate out the contributions from ion desolvation and SEI diffusion. The consensus of their work, in addition to the others referenced, was to ascribe most of the energy barrier for lithium transport to the process of ion desolvation at the electrode surface. Surprisingly, recent theoretical modeling of lithium transport at the SEI interface has shown the opposite to be true.42−44 Borodin and Bedrov reported that lithium ions can readily exchange at the electrolyte surface in their polarizable model but that the diffusion into the bulk SEI is rate-limiting. The findings from their simulations were further validated by agreement with experimental measurements of conductivity for bulk Li2EDC and Li2BDC morphologies.45 Apart from a few additional reports,46,47 modeling transport internal to the SEI has generated more interest than its interface with the electrolyte. Ab initio calculations have been used to map energy barriers to migration for both lithium vacancies and excess lithium ions added to interstitial spaces in crystalline SEI materials.48 By introducing a thermodynamic model for crystal defects, the dependence of the charge migration mechanism on the applied voltage, prevalence of various charge carriers, and space charging effects at mixture boundaries have likewise been considered.49,50 Beyond charge migration pathways from vacancies and interstitials, a Grotthuslike mechanism for lithium transport has also been connected to the results from isotopic labeling experiments.51,52 While providing insight into the mechanism of ion migration within the SEI, a deeper understanding of the desolvation contribution

II. METHODS Investigation of the electrolyte/SEI boundary is performed using classical molecular dynamics (CMD) in order to balance accuracy of ion solvation structure with increased sampling of the heterogeneity of the interface and computational expediency. Both the electrolyte and SEI are represented using a modified COMPASS force field discussed in a previous publication.59 On the one hand, the advantage of Class 2 force fields is their history of success in describing the structure and thermodynamic properties of carbonates and ethers,49 molecules of great relevance to electrolytes for energy storage technology. However, on the other hand, the disadvantage of these models lies in their tendency to overstructure the solvation shell of the metal cation as a result of relying on simple pairwise nonbonded interactions, as seen in both lithium and sodium ion electrolytes when compared with ab initio results.60 The van der Waals parameters for the lithium salt dissolved in ethylene carbonate were previously derived to reproduce the forces present in an ab initio molecular dynamics (AIMD) simulation and were implemented to improve the pairwise model.60 The result of this force-matching process was to noticeably increase agreement with radial distribution functions (RDFs) from AIMD in comparison to an “off-theshelf” Class 2 parametrization. However, in comparison to AIMD simulations and fully polarizable CMD models, stronger coordination of the Li+ by carbonate oxygens persists for the force-matched model. The over coordination results total solvation number closer to 4.5, in contrast to the 4.0 often quoted in the literature.61,62 It is assumed that the tighter binding of the metal cation is a result of adopting a pairwise nonbonding interaction between point charges on the atoms and neglecting explicit polarization in the electrostatics.60,63 This conclusion is supported by the extensive work of Borodin and Smith whose polarizable description showed better agreement with quantum calculations on the solvation structure and the limited experimental data available.60 Suggestions that the solvation number for lithium may actually be closer to 4.2 based on recent Raman spectroscopy would represent a fortuitous agreement with nonpolarizable models7,64,65 and may imply a need to revisit the 3220


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definitive crystal structure is not available, and there are minimal suggestions from experiments that the carbonates exist in a crystalline phase during battery operation.50 In contrast, crystalline regions of smaller inorganic components, such as LiF, have been identified in the SEI67 and will be considered subsequently. The electrolyte was taken to be composed of EC and 1.3 M LiPF6 with the SEI films composed of combinations of Li2EDC, Li2CO3, and LiF reported in mass percentages (see Supporting Information Table S1 for simulation details). A slightly higher concentration of LiPF6 than the normally quoted 1.0 M was used to account for the rapid accumulation of ions at the SEI interface that lowered the final bulk region concentration to approximately 1.0 M. In order to construct a Class 2 pairwise force field for the combined SEI/electrolyte system, the bonding parameters for the individual molecules were obtained directly from CFF91 force field files included in the LAMMPS distribution.48 The nonbonded parameters were obtained by charge fitting to quantum calculations, force-matching dispersion terms, and applying mixing rules. The electrostatic charges from a previous study were used for LiPF6, Li2EDC, and EC, while a new fit was performed for Li2CO3 via electrostatic potential fitting within CP2K.18 The dispersion parameters for interactions between species in the electrolyte were taken from the previous forcematching of Jorn et al.55 while parameters for interactions between SEI atoms were taken directly from the CFF91 force field file. In the case of lithium carbonate, the oxygens were given the same van der Waals parameters as the equivalent Li2EDC oxygens. The mixing of van der Waals parameters between the electrolyte and SEI atoms was performed by mapping the electrolyte atoms into CFF91 atom types and applying the Class 2 rules. The only exception to the previous practice was made for the lithium ions, which were given the same interaction parameters whether the lithium was originally in the SEI or in the electrolyte. In all cases, the long-ranged nonbonded interactions were included via PPPM for the electrostatics and a truncated 9−6 van der Waals function for the dispersion interaction. In order to mimic the electrolyte/SEI interface, simulation cells were initially constructed by dividing the box into two adjacent blocks: one for the SEI material and one for the electrolyte (see Figure 1). The electrolyte was added to the designated region via random packing with Packmol to initialize the cell.68 The same approach was used for the seven amorphous SEI compositions involving Li2EDC to randomly pack the SEI-designated box in each simulation cell. For the LiF and Li2CO3 film simulations, known crystal structures for the inorganic SEIs were used to fill the appropriate blocks of the cell. The number of EC molecules included in the electrolyte were chosen to reproduce 105% of the EC density determined from bulk simulations to ensure good contact between the SEI films and the electrolyte. The length of the electrolyte region was set to be at least twice the length of the SEI film to guarantee that the middle of the simulation cell corresponded to a bulklike reference region with minimal surface effects. After merging the electrolyte and SEI, the system was equilibrated via a multistep process. The entire system was heated to 453 K and allowed to propagate for 6 ns under constant pressure conditions at 1.0 atm. Next, the electrolyte was frozen, and the SEI film alone was relaxed with a single round of simulated annealing. While keeping the simulation cell volume fixed, the film was heated to 900 K over 2 ns, propagated at 900 K for 3 ns, and subsequently cooled back to 453 K over 3 ns. Following

tuning of metal ion−carbonate oxygen interactions. Comparison of the averaged structure for amorphous Li2EDC as a result of using a Class 2 force field and a polarizable model also yielded encouraging agreement. The similarity between the radial distribution functions of the lithium ion and the Li2EDC oxygens suggests that a reasonable representation of the lithium environment in the electrolyte can also be replicated in the SEI film.60 While the slight overbinding of the metal ions does not seem to greatly effect average electrolyte structure, the stronger coordination does affect the transport properties of the Li+ in a manner that is hard to predict. Surprisingly, a previous study using the same force field as the simulations presented herein showed reasonable agreement with the polarizable model of Smith and Borodin for the lithium diffusion coefficient in ethylene carbonate, and compared well with AIMD results.65 However, the same study also demonstrated that agreement did not carry over to the description of lithium diffusion in the SEI layer of Li2EDC. At room temperature, Li2EDC is a solid, and on the time scales of tens of nanoseconds, the lithium ions do not reach a diffusive regime. Using a polarizable model, Borodin et al. demonstrated that at temperatures above 500 K diffusive motion of lithium can be measured during a 200 ns simulation, allowing for estimation of the diffusion coefficient at lower temperatures by extrapolation.66 They also pointed out the tremendous effect of polarization on the observed dynamics, with a strictly pairwise nonbonded model at 600 K differing by an order of magnitude in the diffusion coefficient from polarizable simulations! We have confirmed their findings of slower lithium dynamics by measuring the lithium diffusion coefficient to be 2.0 × 10−12 m2/s at 600 K for a melt of Li2EDC with the model used in the current study. Given the previous success in capturing the structure of bulk Li2EDC and EC electrolytes, this work remains dedicated to the CFF91 model with the caveat that the lithium motion may be artificially slowed down within the SEI and potentially at the electrolyte interface as well. In order to explore the impact of SEI composition and structure on electrolyte properties, simulations were performed on a total of nine different SEI compositions ranging from pure amorphous Li2EDC to pure crystals of Li2CO3 and LiF (see Figure 1 for simulation cell and the Supporting Information for individual molecular structures). An ordered phase of Li2EDC was not considered since a

Figure 1. Example snapshots of the simulation cells used for the SEI films (represented with ball-and-stick figures) composed of (a) amorphous Li2EDC, (b) crystalline LiF, and (c) crystalline Li2CO3 immersed in electrolyte (represented as sticks). Atom coloration matches that of the insets in Figure S1. 3221


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The Journal of Physical Chemistry C the simulated annealing of the SEI film, the entire simulation cell was equilibrated for an additional 2.0 ns at 453 K and 1 atm before collecting production data over 35 ns. It was discovered that performing a simulated annealing on the SEI film was critical to correctly describing the structure and distribution of additives in the Li2EDC, as described subsequently. In the case of the crystalline SEI films, the impact of the interface was felt farther from the interface region, resulting in selection of a larger electrolyte box for the simulation cell and additional annealing of the electrolyte. The electrolyte region was constructed to be 3 times as long as the SEI film, and instead of annealing the crystalline film, which was kept fixed throughout the simulation, the electrolyte region was annealed to accelerate equilibration. In the case of the LiF crystal, a clean [100] face was exposed to the electrolyte, while in the case of Li2CO3, the truncated [010] face was selected resulting in a slightly corrugated surface (see Figure 1). The annealing protocol for the electrolyte was similar to that used for the amorphous SEI films discussed previously, with the exception that the volume of the simulation cell remained fixed throughout the heating and cooling steps. After annealing the electrolyte, 70 ns of production data was recorded at both 453 and 553 K in order to compare observed electrolyte residence times between crystalline and amorphous SEI film simulations.

the carbonyl group pointing away. The overall solvent coordination of the anion is estimated to be 8.5 EC molecules. Overall, the RDFs for phosphorus indicate a much weaker structuring of the electrolyte in response to the anion in comparison with the impact of lithium. The different behavior of the ions can be attributed to both the smaller charge to size ratio of the anion in comparison to lithium and its greater charge delocalization among the six symmetric fluorine atoms. Having demonstrated reasonable agreement with previous reports on solvent structure in the electrolyte, attention turns to both qualitative and quantitative assessments of the representation of the SEI materials. Since the pure LiF and Li2CO3 SEI simulations use unaltered crystal structures with bulk lattice constants and unit cells, the focus of comparison lies with the SEI materials consisting of amorphous films. As shown in the RDFs for Li2EDC (see Supporting Information), the structure postannealing agrees well with the results from Jorn et al. and indicate that each lithium is shared between two EDC2− moieties in its nearest-neighbor shell. Aggregation of carbonate heads groups and lithium ions in dicarbonates has been emphasized previously60 and relies on multicarbonate binding of lithiums to form bridged structures. It is of interest to note that in spite of differing values of atomic charge and dispersion parameters, the first “solvation” shell of lithium ions in the bulk electrolyte and in the bulk dicarbonate SEI both consist of 4−5 carbonate oxygens. Hence, the transport from electrolyte to an amorphous SEI more closely resembles a “resolvation” rather than a desolvation of lithium ions in order to conform to a significantly different environment. Apart from quantitative measures of structure, the trends in phase separation and distribution of mixed SEI materials provide a qualitative comparison with experiment. While experimental confirmation of the SEI structure remains challenging, it has been accepted for some time that the film tends to separate into a predominantly inorganic layer (lithium fluoride and lithium oxides) close to the electrode surface, followed by a majority organic layer as one reaches the electrolyte interface (lithium carbonate and dicarbonate oligomers). The behavior of inorganic components mixed with Li2EDC in the present simulations can be seen in Figure 2 by snapshots taken postannealing. At smaller mass percentages, the LiF tends to cluster and in general does not favor direct exposure to the electrolyte surface. As the amount of LiF

III. RESULTS AND DISCUSSION a. Bulk Electrolyte and SEI Structure. Before discussing the structure at the SEI/electrolyte interface, it is important to affirm confidence in the model for describing the bulk properties of the components. The coordination of the lithium ions and PF6− anions were considered in both the electrolyte and the SEI far from the interface to compare with structures from prior bulk environment studies (see Supporting Information). The EC coordination of lithium in the center of the simulation box was seen to agree well with previous reports of the electrolyte structure in terms of the shape of the RDF’s, location of the first solvation shell peak and the total number of EC molecules coordinating lithium (around 4.20). Similar agreement holds for the coordination of lithium by the counteranion PF6−, with the average phosphorus coordination being 0.34, implying significant ion dissociation in the electrolyte and the formation of solvent-separated ion pairs. Taken together, the total coordination number for the lithium ions in the bulk region of the electrolyte is 4.54. As discussed previously (see Methods section), the lack of explicit polarization likely accounts for stronger binding in the solvation sphere and a higher amount of coordinating EC than reported by Borodin and Smith.60 Though rarely discussed in the literature, the solvation structure of the counteranion PF6− was also considered, and the RDFs between the phosphorus and EC atom types are shown in Figure S2. Recently, a combination of ion spray mass spec, NMR, and molecular modeling demonstrated that the interaction between the hexafluorophophate and carbonate solvents is much weaker than that of Li+, resulting in less structure in the RDFs associated with anion solvation.69 The average solvation structure seen for PF6− agrees with that expectation and shows smaller and broader maxima in the RDFs for both EC hydrogens and carbonyl carbons as compared to the distributions for lithium ions. The location of the anion solvation peak associated with EC-hydrogen as well as carbonyl carbon implies that the EC mostly orient themselves with their hydrogens pointing toward the anion and

Figure 2. Snapshots of the equilibrated and postannealed SEI films where the region consisting of SEI components is outlined in purple and the presence of added fluoride (green spheres) and carbonate anion (connected red and black spheres) are indicated. The mass percent of the added fluoride or carbonate anion are indicated and increase from left to right. 3222


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The changes at the interface are not exclusively the result of adsorption on the surface, as implied by the presence of ions and EC molecules at negative z values. Ion density within the SEI region suggests that the accumulation also includes absorption of electrolyte species from the electrolyte into the SEI layer. Indeed, previous studies have demonstrated the accumulation and exchange of electrolyte species at the SEI interface occurring even more rapidly when explicit polarization is included.70 However, caution must be exercised in placing too much emphasis on density plotted from an arbitrarily drawn boundary. Ultimately, the true nature of the solvation environment at the SEI interface requires considering solvation structures as a function of distance from the interface. Radial distribution functions for lithium, phosphorus, and EC were considered as a function of distance from the interface, and coordination numbers for the ions by their counterion and solvent molecules were examined as they approached the SEI from the bulk electrolyte (see Figure 4). As the ion accumulation in the density profile indicates from Figure 3, the increased concentration of ions does result in higher numbers of ions present in the first solvation shell as one nears the SEI. In the case of lithium, the amount of coordinating anion reaches 2 times the bulk coordination at the interface. However, given the bulk electrolyte value of PF6− coordination of lithium is 0.34, the coordination at the interface is around 0.70. Therefore, the change in coordination number does not imply significant condensation of aggregates or even complete formation of contact ion pairs at the interface on average, in spite of these higher overall concentrations. The reason for this difference likely arises from the increased coordination between charge groups in the SEI with the electrolyte ions at the interface, weakening their drive to form aggregates in spite of their higher densities. The competition between electrostatic interactions is seen in Figure 4, where at the peak of lithium coordination by PF6− there is also an increase in EDC2−. While Figure 4 presents normalized results, the unscaled coordination numbers for both lithium and hexafluorophosphate ions demonstrate their strong interactions with the SEI material. The average coordination of PF6− at the interface by lithium ions from the SEI is 2.5, while the coordination of lithium ions by EDC2− from the SEI is close to the bulk value of 5.2 carbonate oxygen atoms per lithium. It seems reasonable to conclude that the added interaction with the electrolyte-exposed SEI charge groups at the interface is integral to the accumulation of the ions; however, this interaction simultaneously prevents further aggregation of the electrolyte charges into salt pairs. In considering the behavior of ion pairs at the SEI interface with different amorphous compositions of LiF and Li2CO3, deviations from the results of the pure Li2EDC film are surprisingly insignificant (see Supporting Information). The changes in Li+ solvation as the ions approach the SEI with 10% LiF added to the SEI film emphasize the minimal role played by the additional fluoride regarding electrolyte structure. As discussed in association with Figure 2, the fluoride does not make a significant contribution at the surface where EDC2− coordination remains over 3 times larger. On average, the electrolyte ions see less than half of a fluoride anion, even at several angstroms deep into the interface. This behavior is also evident when substantially more LiF is added to the SEI region, and yet insignificant changes occur to the fluoride coordination of lithium ions in the electrolyte. By 50 mass % LiF, the coordination numbers remain similar to those seen for 10%

increases, the individual clusters eventually join to form a contiguous layer of the fluoride that remains shielded from the electrolyte by a thin layer of Li2EDC. The pronounced phase separation implies that the LiF does not occupy a significant portion of the immediate SEI/electrolyte boundary and hence would not play an important role in determining solvation structure and dynamics directly at the interface. The observed phase separation has been seen in images taken from mixtures of LiF and lithium carbonate, showing qualitative agreement with the trend seen here.65 In contrast to the behavior of LiF, Figure 2 clearly shows that lithium carbonate mixes more evenly with the Li2EDC with less specificity for avoiding the electrolyte interface. Incidentally, the greater homogeneity may in part contribute to the difficulty of determining the nature of the organic layer from experiments since it may consist of many carbonate-containing moieties. Clearly, the differences in structure from the mixing of these components could have important effects on the properties of the film, but these will not be considered further in this work since interest is focused on the electrolyte/SEI interface itself. b. Ion Solvation Structure at the SEI Interface. Having established the manner in which ions are solvated far from the SEI surface, the remainder of this work is devoted to whether and how electrolyte structure changes as one approaches the interface. The short answer to this question is provided by plotting the density of electrolyte species as a function of location in the z-direction (see Figure 3) where the axis used to

Figure 3. Location of the electrolyte/SEI “interface” for the simulation with an amorphous film containing only Li2EDC is determined by the point at which the center-of-mass density of EC (upper panel black dashed) and EDC2− (upper panel purple solid) are equivalent. The densities of Li+ from the electrolyte (blue dashed), PF6− (red solid), and Li+ from the SEI film (green dot-dashed, scaled by a factor of 0.15 for graphing) are shown as a function of distance from this interface.

define the initial SEI and electrolyte regions of the simulation cell is shown in Figure 1. For the amorphous films, the process of annealing and equilibration tends to blur the initially sharp boundaries between the SEI and the electrolyte. As a result, the location of the “interface” between the two phases cannot be strictly identified based on position in the simulation cell alone. For the sake of clarity, the subsequent discussion relies on defining “the interface” by the crossing point of the densities of their major components: the EDC2− center-of-mass in the SEI and the EC center-of-mass in the electrolyte. The densities of the ions in the system were then averaged as a function of distance from this interface and show a significant accumulation at the film surface with local densities reaching 4 times their bulk value within the first 5 Å of the interface (see Figure 3). 3223


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Figure 4. Average coordination is shown for a lithium cation (left panel) and a phosphorus atom from the PF6− anion (right panel) as a function of distance from an amorphous Li2EDC SEI film. Coordination of lithium by phosphorus (red ×), EC carbonyl oxygens (black +), and EDC2− carbonate oxygens (blue ○) are shown in the left panel with the corresponding designations for each region (absorbed, etc.). In the right panel, coordination of phosphorus by lithium cations (red ×), EC hydrogens (black +), and lithium from Li2EDC (blue ○) are shown. In all cases, values are normalized by the coordination in bulk electrolyte or SEI film.

LiF, with electrolyte ions seeing less than half a fluoride on average even 3 Å into the SEI region. The impact of adding Li2CO3 to the behavior of ions at the SEI interface is likewise minimal, but not as a result of their absence from the electrolyte-exposed surface. Figure S3 clearly shows that the carbonate competes equally with EDC2− to coordinate lithium ions from the electrolyte; however, the similarities in interactions between the electrolyte species and both the carbonates result in no major changes to ion pairing. While the nature of the lithium ion−counterion contact does not change significantly for any of the amorphous films considered, a corresponding change to the EC solvation shell around the ions does take place at the film interface. The nature of the desolvation process as ions transition from the electrolyte to the electrode environment has been at the center of discussions of the charge transfer barriers for battery operation for some time. Emphasis has been placed on the high energy barrier associated with lithium transfer arising from having to strip away the EC solvation shell.55 In the simulations presented here, the lithium cations lose their EC solvation shell within a width of 5 Å of the SEI interface, as seen in Figures 4. The loss of EC follows a roughly inverse relationship with binding to SEI components. This behavior is very different from previous conclusions from modeling bare graphite electrode surfaces in which high voltages were required to begin peeling off the EC solvation shell from lithium48,60 and lends credence to the concept of a “resolvation” to describe lithium ion transport rather than desolvation. As shown by Borodin and Bedrov,47 and supported by the simulations reported here, the barrier associated with this resolvation can actually be much smaller than migration barriers through the SEI material itself. While the lithium achieves structures devoid of EC in Figure 4, the PF6− never completely severs interaction with the EC in its first solvation shell as a result of its larger size preventing its entry further into the film. The observed changes in the average EC coordination of both the lithium and hexafluorophospate ions in Figure 4 were used to loosely categorize the nature of the solvation environment experienced by the ions as a function of distance from the interface. When the average EC coordination corresponded to less than one molecule, the ion in question was labeled “absorbed” into the SEI film by loss of contact with the electrolyte solvent. When the amount of coordinating EC

was between 1 molecule and half the bulk electrolyte solvation shell (about 2.0 EC molecules on average for lithium and 4.0 molecules for PF6−), the ions were categorized as “adsorbed”. Finally, when the solvation was between half a solvation shell and the bulk value, the corresponding region was referred to as “diffuse”. The latter category is reminiscent of double-layer models in which the diffuse layer connects the Stern surface layer to the bulk electrolyte.60 Using these categories, distinctions can be made between the ions accumulating at the interface based on EC solvation environment. The widths of the designated regions (absorbed, adsorbed, and diffuse) are indicated in Table 1 for each type of Table 1. Total Widths of the Assigned Solvation Regions in angstroms (Absorbed, Adsorbed, and Diffuse) and Total Integrated Densities across the Three Regions for Each Type of SEIa SEI film

ΔZabs

ΔZads

ΔZdiff

Li+

PF6−

Li2EDC + 10% LiF + 25% LiF + 50% LiF + 10% Li2CO3 + 25% Li2CO3 + 50% Li2CO3 LiF crystal Li2CO3 crystal

6.0 4.5 8.5 8.5 7.0 6.0 7.0

3.5 3.5 1.75 1.75 3.5 4.5 1.5 2.0 5.0

7.0 10.0 9.75 5.75 9.5 7.5 7.5 7.0 8.0

1.17 1.16 1.20 0.79 1.18 1.04 1.22 1.67 2.21

1.26 1.21 1.12 0.76 1.25 1.06 1.18 1.49 2.25

a

The number of accumulated ions is reported scaled with respect to the corresponding value in the bulk electrolyte, i.e., how many ions would be found in a region of the same thickness at the center of the simulation cell far from the SEI interface.

SEI film along with the total ion density integrated across all three regions. From the widths of each region, it is clear that the effect of the SEI on solvation structure persists for 1−2 nm from the amorphous film surface, beyond which the bulk electrolyte structure is recovered. In comparing Figures 3 and 4, it can be seen that the “adsorbed” lithium ions correspond to the region of greatest ion accumulation and also the thinnest layer at the interface according to Table 1. Comparison between the different types of amorphous SEI shows that on the average the adsorbed region is around 4 Å wide while the 3224


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lithium accumulation. The impact of changing the SEI composition is to shift more lithium ions into the absorbed region but does not greatly affect the net amount of accumulated ions. Up to this point only amorphous SEI films have been considered since crystal structures and more detailed information are lacking from experiments for carbonate oligomers. When considering SEI’s comprised predominantly of LiF and Li2CO3, crystalline surfaces provide a significant contrast to the ethylenedicarbonate systems. In Figure 5, the changes in lithium ion solvation are shown as one approaches pure crystals of LiF and Li2CO3, respectively. In both cases, the interface is defined as the location of the outermost layer of surface atoms and therefore lacks the ambiguity associated with the amorphous films. However, it was found that as a result of the ordered surface layer, the changes to the EC coordination of lithium do not readily lend themselves to the same categories as before. In specific, at the LiF surface the coordination of lithium never drops below half of the bulk value and hence would never be described as “adsorbed” using the previous definition, even when the lithium atoms are clearly in physical contact with the crystal surface. As seen by the circled portion of Figure 6, the origin of this behavior lies in the way EC molecules orient themselves close to the LiF surface. Their preference to coordinate to lithium ions in the LiF surface via their ester oxygens favors their retention of a high coordination number to lithium at the surface even though the actual solvation structure is distorted from the bulk electrolyte. In the case of LiF, the location of the adsorbed layer was determined based on the clear peak in the ion density and corresponds to roughly the size of one layer of lithium ions. In the case of the carbonate crystal, the surface was corrugated and did not show the same persistence of EC coordination, allowing for use of the same definition for adsorbed as used previously. For the Li2CO3 crystal, partial removal of the EC shell can be seen for the lithium ions inserted into the troughs between the crystal layers in the side view of Figure 6. Clearly, in neither case do absorbed lithiums appear. The inability to absorb extra lithiums is by design since the crystals are fixed; however, the solvation changes induced by the jagged interface indicate the important role of surface structure in encouraging lithium desolvation. For both crystal films, the changes to the EC solvation shell are minimal outside of the adsorbed layers, indicating a more rapid return to bulk solvation structures than seen for the amorphous films. The change in the interaction between the lithium salt pair is more dramatic than for the crystalline SEI than those reported for the amorphous films as one approaches the interface. The number of PF6− present in the first solvation shell of lithium increases to over 1.0 in the diffuse region for LiF and nears 1.5 in the diffuse region of Li2CO3. The much larger increase in anion coordination implies greater formation of contact ion pairs and aggregates between the lithium salt ions than previously seen for the amorphous SEI. The large drop in the coordination of anions in the adsorbed region is balanced by the increased interaction between lithium and countercharges present in the SEI crystal. In addition to driving a greater pairing of the electrolyte salt, substantially more ions are also seen to accumulate at the interface of LiF and Li2CO3 than Li2EDC. While the ion accumulation among the ethylene dicarbonate SEI tended to average out across the regions of differing solvation structures, it persists in the case of SEI crystals with somewhere between 1.7 and 2.2 times as many

diffuse region spans nearly 1 nm in length across all amorphous SEI films considered. Surprisingly, there also exists a significant region of absorbed structures in which lithium ions either have completely exchanged with the SEI during equilibration or have lost the majority of their EC solvation shell to stabilize the interface. It is interesting to note that for pure Li2EDC and low mass % LiF and Li2CO3 films the adsorbed regions are larger and the absorbed regions smaller. In the case of larger amounts of added LiF and Li2CO3, the absorbed region expands at the cost of the adsorbed region. This effect could arise from the Li2EDC at the interface having more flexibility to coordinate electrolyte species when its own network is significantly disrupted by added inorganic compounds, as in the case of 50% LiF, or as a result of the prevalence of added carbonate at the electrolyte interface, as in the case of Li2CO3. Lithium carbonate provides a more localized charge density than Li2EDC that attracts electrolyte ions to a greater extent. The fact that the total ion density integrated across all three regions of solvation structures remains close to 1.0 (1.0 corresponding to the same as bulk electrolyte) indicates that the three regions must alternate between ion accumulation and depletion in order to agree with Figure 3. Table 2 further breaks down the distribution of the ions in each category based on average solvation structure and Table 2. Integrated Ion Densities at the SEI/Electrolyte Interface for Each of the Assigned Regions (Absorbed, Adsorbed, and Diffuse) and for Each Type of SEIa PF6−

Li+ SEI film

nabs

nads

ndiff

nabs

nads

ndiff


0.81 0.99 1.53 0.56 1.03 1.04 1.78

2.28 2.37 1.01 1.89 1.66 1.06 0.61 6.30 3.37

0.72 0.72 0.87 0.78 1.11 0.98 0.72 0.34 1.48

0.32 0.00 0.57 0.00 0.61 0.00 0.00

1.86 0.37 2.43 0.00 2.55 0.01 0.96 3.85 2.00

1.67 1.65 1.92 1.56 1.27 1.91 1.85 1.99 2.93

a

The number of accumulated ions is reported scaled with respect to the corresponding value in the bulk electrolyte, i.e., how many ions would be found in a region of the same thickness at the center of the simulation cell farthest from the SEI interface.

compares the integrated total to bulk values for layers of the same size. As is clear from the amorphous Li2EDC film, there is a significant accumulation of adsorbed lithium ions with a total number about twice what would be expected for a comparable region in the bulk. The accumulation of lithium in the adsorbed region is followed by a similar increase in the number of phosphorus found in the diffuse layer, reminiscent of a doublelayer structure at the interface. In the diffuse region there is a slight depletion of lithium ions, again fitting with a doublelayer-type model for the SEI interface. Examining the behavior of the ion accumulation as a function of the SEI composition reveals only slight changes to the amount of ion accumulation in each region with 10% LiF and Li2CO3 present, with some shifting of the accumulated anions from the diffuse to the adsorbed region for the carbonate mixture. In summary, the data on ion accumulation points to the general trend of lithium adsorbing at the amorphous SEI interface at roughly 1.5−2.0 times the bulk concentration and the PF6− anion following the 3225


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Figure 5. Change in average coordination is shown for lithium cations as a function of distance from the LiF crystalline [100] surface (left panel) as well as the Li2CO3 [010] surface (right panel). As in Figure 4, coordination of lithium by phosphorus (red ×) and EC carbonyl oxygens (black +) is shown along with fluoride (left panel, blue ○) and carbonate oxygens (right panel, blue ○). The phosphorus result was additionally scaled by a factor of 1.25 on the right for graphing purposes. Coordination by EC was also scaled with respect to bulk electrolyte, while the SEI species was scaled by the final value at the surface. Assignment of regions is indicated with “ads” being adsorbed.

defined z-axis normal to the SEI interface (see Figure 7 for definitions). Beginning with EC, the probability distribution for

Figure 6. Snapshots of the species adsorbed to the LiF crystal surface (left) and the Li2CO3 surface (right). The color scheme follows previous convention (see Supporting Information); however, the atoms of the crystal surface are drawn as larger spheres to distinguish them from electrolyte atoms.

Figure 7. Diagrams of the orientation angles for (a) the carbonyl carbon bond of EC and (b) the plane containing the EDC2− carbonate group with respect to the surface normal of the SEI.

ions within 1 nm of the crystal surfaces compared to bulk. Looking closer at the ions as characterized by their solvation environment, one can see from Table 2 that the accumulation of adsorbed lithium and PF6− is far greater than seen for the EDC2−-based films. The greater prevalence of PF6− is attributed to the stronger electrostatic interaction between the anion and the lithium ions present in the crystal surface layer. Overall the LiF and Li2CO3 surfaces provide a much saltier environment than Li2EDC: more ions accumulate at their interfaces, and this accumulation drives greater interaction between the lithium salt pair. However, these effects are tightly confined to the surface and decay rapidly away from the crystal. c. Solvent/SEI Orientation at the Interface. The observed changes to the solvation environment of the ions in the electrolyte have been discussed in terms of competition between coordination by SEI groups and the solvent. One expects that in order to facilitate these interactions, charge groups in the amorphous SEI may reorient to gain greater access to the electrolyte during the simulation. Similarly, the attraction between the EC carbonyl groups and surface SEI charges may also result in net structuring of the solvent in the vicinity of the surface similar to that seen for bare graphite electrodes.60,71,72 Investigation of these ordering effects was carried out by calculating the angles between vectors attached to the framework of the EC and EDC molecules and the

the angle between the carbonyl bond dipole and the z-axis (θEC) was considered as a function of distance from the SEI interface. Representative plots of the distribution for EC molecules are shown in Figure 8 for two of the amorphous films in comparison with the pure LiF and Li2CO3 crystals. For an entirely randomly oriented dipole (equal probability of any projection onto the z-axis), one would expect a sin(θEC) probability distribution in the angle. Far enough into the electrolyte, this form is recovered as shown in panel b of Figure 8. In all four cases shown, this simple distribution is distorted as the SEI is approached and greater order is imposed on the solvent molecules. At 6−7 Å from the defined interface, the distributions for the two amorphous SEI are only slightly modified from the isotropic distribution, while moving 4 Å closer shifts the distribution to favor EC with θEC greater than 90°. By comparing with Figure 7, one can see that at these angles the EC are oriented with their carbonyl bond dipoles on the average pointing toward the SEI. Moving another 4 Å toward the SEI, the EC orientation splits into several peaks at around 90°, 120°, and 150° for the 50% Li2CO3 SEI, indicating a variety of favorable orientations pointing toward the interface. Surprisingly, for the 10% LiF SEI the distribution at the same location only consists of two major populations centered at 60°and 135° corresponding to both pointing away from the SEI 3226


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Figure 9. Orientation of the EDC2− carbonate group (see Figure 7) in the SEI film composed of (a) Li2EDC with 10% LiF, (b) Li2EDC with 10% Li2CO3, (c) Li2EDC with 50% LiF, and (d) Li2EDC with 50% Li2CO3. In panel a, the distribution of angles is reported at z = −6.52 Å (red solid), −2.52 Å (green dot-dashed), and 1.48 Å (blue dotted) with respect to the SEI/electrolyte interface. In panel b, the distribution of angles is reported at z = −4.16 Å (red solid), −0.16 Å (green dot-dashed), and 3.84 Å (blue dotted) with respect to the SEI/electrolyte interface. In panel c, the distribution of angles is reported at z = −6.51 Å (red solid and scaled by 0.5 for graphing), −2.51 Å (green dot-dashed), and 1.49 Å (blue dotted) with respect to the SEI/electrolyte interface. In panel d, the distribution of angles is reported at z = −5.51 Å (red solid and scaled by 0.5 for graphing), −1.51 Å (green dot-dashed), and 2.49 Å (blue dotted) with respect to the SEI/electrolyte interface.

Figure 8. Orientation of the EC carbonyl bond (see Figure 7) when approaching an SEI composed of (a) Li2EDC with 10% LiF, (b) Li2EDC with 50% Li2CO3, (c) LiF crystal, and (d) Li2CO3 crystal. In panel a, the distribution is reported at z = −0.52 Å (red solid), 3.48 Å (green dot-dashed), and 7.48 Å (blue dotted) with respect to the SEI/ electrolyte interface. In panel b, the distribution is reported at z = −1.51 Å (red solid), 2.49 Å (green dot-dashed), and 6.49 Å (blue dotted) with respect to the SEI/electrolyte interface. In panel c, the distribution is reported at z = 1.9 Å (red solid and scaled by 2 for graphing), 3.9 Å (green dot-dashed), and 5.9 Å (blue dotted) with respect to the SEI/electrolyte interface. In panel d, the distribution is reported at z = 0.9 Å (red solid and scaled by 1.5 for graphing), 2.9 Å (green dot-dashed and scaled by 1.5 for graphing), and 4.9 Å (blue dotted) with respective to the SEI/electrolyte interface.

and pointing toward it, respectively. The differences in distributions between the 10% LiF SEI and the 50% Li2CO3 film can be correlated to the presence of more localized charges at the carbonate-enriched interface that eliminates the low angle population seen for the LiF-containing film. The results from panels a and b are in contrast to a previous assumption that the random nature of the SEI would not impose a net ordering on the solvent.48 The angular distributions for the crystal surfaces demonstrate several changes in θEC when compared with the amorphous films. First, the peaks at the interface are much sharper (note the scaling used in Figure 8), which is consistent with the EC being more strongly coordinated by the charged groups on the surface of the crystal. Second, the impacts of solvent structuring are felt further into the electrolyte as a result of the regular ordering of the crystal surface. In both cases, even at distances of 6 Å from the surface, the EC have still not obtained a completely isotropic distribution. Finally, the maxima in the distributions for the pure LiF and Li2CO3 crystals differ at the interface by about 25°. The origin of this shift can be seen in Figure 6 where a snapshot of the first solvent layers at the crystal surfaces is shown to consist of EC flattened to the surface of LiF, while in the case of lithium carbonate the EC are pointed more perpendicular to the surface. Overall, the changes to EC orientation as they approach the SEI correlate well with the loss of EC in the electrolyte ion solvation shells, indicating that the EC are swapping from electrolyte ion solvation to SEI ion coordination. The flexibility of the solvent molecules allows them to reorient to solvate the SEI interface, but what about the configurations of the EDC2− at the boundary of the electrolyte? The process of annealing in the presence of the electrolyte does not dramatically affect the orientation of the EDC2− groups in the case of Li2EDC with 10% LiF added, as seen in Figure 9.

Whether looking at the angular probabilities 6.5 Å into the SEI domain or 1.5 Å into the electrolyte domain, the deviations from the isotropic distribution are minimal and present a small wiggle superimposed on the ideal sine curve for θEDC. With the addition of Li2CO3, the bulk structure also does not show great deviations until the interface. Interestingly, at the interface there is a large peak at around 165° followed by a smaller peak at 15° that corresponds to the EDC2− carbonate groups being oriented nearly parallel to the electrolyte surface. A smaller peak also exists at 120°, indicating some population of carbonate groups oriented more toward the electrolyte; however, these remain minor contributors. When the amount of added fluoride and carbonate are increased to 50 mass %, panels c and d in Figure 9, significant changes are seen to the orientation at the interface. It has already been shown that with the added LiF the strongly phaseseparated SEI film favors a thin layer of Li2EDC at the interface to shield the LiF. A thin shielding layer of EDC2− correlates with favoring smaller angles (parallel to the SEI surface). In contrast, probability distribution found between 60° and 120° refer to configurations in which the EDC2− carbonate groups are pointed toward the electrolyte surface and presumably favor interaction with the electrolyte ions. This slight change may correlate with the shift seen in the accumulation of PF6− to the diffuse region of the 50% LiF SEI compared to the 10% LiF SEI (see Table 2) as a result of increased binding of EDC2− to lithium ions. Finally, in the case of 50% carbonate there are two clear peaks that emerge close to the interface corresponding to 60° and 150°. The former in particular represents configurations with the EDC2− group oriented toward the electrolyte and capable of coordinating electrolyte lithium. Comparison of Table 2 suggests that this difference in EDC2− orientation correlates with a greater amount of absorbed lithium. Apart 3227


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Table 3. Solvation Residence Times in nanoseconds for EC and PF6− in the First Solvation Shell of Li+ for the Indicated Interface Regions Defined in Figure 5a PF6−

EC SEI film

τads

τdif

τbulk

τads

τdif

τbulk


4.23 11.00 2.18 9.28 4.54 1.86 4.07 7.63 × 108 7.55 × 104

0.37 0.27 0.22 0.32 0.19 0.17 0.21 3.02 1.12

0.11 0.11 0.12 0.11 0.11 0.11 0.11 0.28 0.34

95.44 48.03 102.74 1.51 33.23 6728.9 259.07 7.98 × 108 374.30

2.16 0.94 1.02 1.94

0.23 0.23 0.23 0.18 0.20 0.24 0.22 1.10 0.84

0.47 0.64 6.00

In this case, τads is the residence time for a species solvating a Li+ in the adsorbed region, τdif is for the diffuse region, and finally τbulk is the residence time in the bulk region of the simulation. Missing numbers were excluded based on poor statistics.

a

from this final example, it seems that the majority of the amorphous films investigated kept their EDC2− groups oriented parallel to the electrolyte interface and potentially indicates a limitation on the annealing process used to equilibrate the simulations. Further study using a more flexible methodology for enhanced sampling may allow better exploration of surface structures and could impact the distributions reported here. Even so, it is interesting to note that the added inorganic components may impact the orientation of Li2EDC at the interface, even when the additives are buried beneath the surface and do not directly interact with the electrolyte, as is the case when adding LiF. d. Electrolyte Dynamics. Up to this point, the information reported on the SEI/electrolyte interface has focused on changes to averaged structure of the ion solvation shell and ion densities. However, in the course of performing simulations, it was evident that there were also changes to the dynamics of adsorbed species compared to molecules far from the SEI. Hence, the influence of the interface on the dynamics in the electrolyte is also considered by calculating average residence times between species. To characterize the evolution of the solvation structures, the solvation residence time of the lithium ions by the electrolyte components was investigated using a simple step function Hsolv(t). For each EC molecule in the simulation, for example, the value of this function was taken to be 1 if the EC was within the first solvation shell of the lithium ion in question and zero otherwise. By evaluating this function from an initial snapshot, taken to be t = 0, the correlation function at later times could be calculated for each EC molecule to obtain ⟨Hsolv(0)Hsolv(t )⟩

t

e −( α )

β

(2)

where, for simplicity, the value of α was taken to be the average residence time for the electrolyte species around a given lithium ion. The values for the solvation residence times for both species were considered for all of the SEI films studied and are compiled in Table 3. A radical difference is seen in the average residence times for both EC and the electrolyte anion around a given lithium ion as one approaches the SEI. Starting with EC, one can see that the residence times for the solvent molecules when the lithium ions are in the adsorbed region of the cell differ by over an order of magnitude from the residence times in the bulk. Hence, the EC remain coordinated to a single Li+ for much longer at the SEI surface with clear implications for studies of the reactivity of the solvation shell of the solvated lithium ion during charge and discharge. For example, the persistence of a single EC coordinating a lithium for nanoseconds at the interface might provide an additional factor favoring multielectron events. The solvent exchange speeds up in the diffuse layer but still remains a factor of 2 slower than the average of 110 ps seen in bulk. In comparing the different amorphous SEI films, there is not a clear trend in the behavior with SEI composition and residence times fluctuate within a factor of 3 from each other at the interface. In contrast to the changes in amorphous composition, the residence times change dramatically at the crystalline surfaces where the EC are essentially frozen in place during the simulation. The slower solvent dynamics once again persist to the diffuse and bulk regions of the crystal simulations, suggesting that even in the middle of the simulation cell there remains a slight slowing down as a result of the surface. Studies conducted on smaller simulation cells and at different temperatures indicate that this is an effect arising from the strong coordination of the solvent by the crystal surface and could be eliminated by considering even larger electrolyte box sizes. Once again since the interest here is in qualitative trends, larger simulations were not considered. The impact of the interface on lithium−anion coordination is even more pronounced. For most of the amorphous films, the PF6− remains stuck to the lithium ion over the duration of the simulation. Given that the lithium ions on average do not form contact ion pairs, the implication is that the coordination discussed previously accounts for an average over several solvation environments at the interface rather than an average over exchanges between solvation spheres. Basically, lithium

(1)

As indicated by the brackets, the resulting correlation function was averaged over the number of EC molecules present in the simulation, the number of lithium ions within a restricted region of the simulation, and across different snapshots serving as time origins. Naturally, one must be cautious in studying time correlation functions in the presence of a thermal bath; however, since the focus here is on the trends in behavior rather than absolute numbers, this caveat is assumed to not significantly impact the discussion. Example solvation correlation functions are shown in the Supporting Information for EC and PF6− coordinating to lithium ions in the electrolyte. Clearly, each follows an exponential decay and can be fit well using a stretched exponential: 3228


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Table 4. Normalized Surface Residence Times for EC, PF6−, and Li+ Initially Located in Each Interface Region Defined in Figures 4 and 5a PF6−

EC SEI film Li2EDC + 10% LiF + 25% LiF + 50% LiF + 10% Li2CO3 + 25% Li2CO3 + 50% Li2CO3 LiF crystal Li2CO3 crystal

τabs 3.32 5.46 72.6 3.77 1.77 1.49 4.78

× 105 × 104 × × × ×

103 104 104 103

Li+

τads

τdiff

τads

τdif

τads

τdif

20.7 12.8 4.18 15.6 22.7 14.1 13.5 6.08 × 104 6.69 × 107

2.89 2.41 1.86 2.51 2.92 2.46 2.41 2.31 28.2

648 86.4 13.4 124 481 170 137 3.56 77.8

3.18 3.00 1.61 3.06 3.48 1.92 2.42 1.90 3.35

70.9 91.9 6.55 25.3 746 55.8 12.7 7.61 3.56 × 103

4.03 3.77 1.99 3.40 5.61 2.47 2.39 1.00 10.9

In contrast to solvation residence times, the time constants, τads and τdiff, refer to residence times for species in the regions defined in Figures 4 and 5, regardless of their association with lithium cations. Each value has been divided by the bulk decay constant τbulk (see Table S3). a

ions with a PF6− coordinating at the interface keep their anion while a second population must irreversibly (on the time scales of tens of nanoseconds) swap the anion from their first solvation shell to coordinate with SEI components. As in the case of EC, the slow exchange persists in the diffuse region as compared to bulk but is more distinct. The additional slowing likely arises from the PF6− being attracted to the surface as well as the adsorbed layer formed by the accumulated lithium ions at the interface. It is interesting to note that the estimated residence times for the anion are much higher at the amorphous SEI with added carbonate than the LiF, possibly as a result of more lithium density at the SEI interface for the anion to coordinate. Behavior at the crystal interfaces follows that seen for EC, with the exception of the residence time at the troughs on the surface of the carbonate crystal. In this case, the size exclusion of the PF6− prevents it from interacting as strongly as the EC with the corrugated surface. If proximity to the interface slows down the solvent and anion exchange with coordinating lithium ions, it is also of interest to investigate whether the overall dynamics of the electrolyte at the interface may be slowed by coordination to the relatively immobile SEI film. While one could measure diffusion coefficients as a function of distance from an interface, an alternative approach to elucidating the general behavior is to consider a surface residence time calculation in the same spirit of the solvation residence times calculated above. A surface residence function, Hsurf(t), is calculated at a given time origin for every particle in the simulation box within a fixed distance from an interface parallel to the SEI in each of the relevant solvation regions (absorbed, adsorbed, diffuse, and bulk, discussed previously). The correlation function based on this measurement is then built by monitoring how long a given molecule stays within the cutoff from the interface before it leaves (see the Supporting Information for examples of surface residence correlation functions for lithium ions and EC solvent molecules at varying distances from a pure Li2EDC SEI). Once again, these were fit with a stretched exponential in the same manner discussed for the solvation residence time calculation and tabulated for each SEI film investigated (see Table 4). As a result of challenges with sampling an adequate number of species to obtain accurate statistics, the ranges of z coordinates used to describe the regions in Tables 3 and 4 are not identical. The unfortunate result is that comparison of the raw numbers from the two tables is not straightforward. As indicated by Table 4, there do exist some EC molecules within the absorbed region of the simulation for the amorphous

films that remain stuck in this region throughout the simulation. These EC molecules are not coordinated to a Li+ from the electrolyte and were partially inserted into the SEI layer during equilibration. The ratio of the surface residence times for the EC molecules in the adsorbed and diffuse regions are very similar to the ratio of solvation residence times to bulk for EC coordinated to lithium. This similarity suggests that it is the slowing down of dynamics in general at the interface that results in the changes to solvation residence times. Once again, the EC remain practically frozen in place at the crystal interfaces, in agreement with the large solvation residence times estimated for the EC at LiF and Li2CO3 surfaces. In considering the residence times of the ions, the differences in observed time scales at the interface indicate a decoupling of their motion as a result of the interface groups. For example, in the diffuse regions the ions escape at about the same average rate while in the adsorbed region their residence times may differ by an order of magnitude. Limitations on the time scales explored by the simulations make definitive statements in the adsorbed region inappropriate but are indicative of differences in ion dynamics.

IV. CONCLUSIONS Computational modeling with classical molecular dynamics (CMD) was used to explore the interface between the SEI and the electrolyte in lithium-ion batteries at the molecular level. The validity of the model was tested by quantitative and qualitative comparison with previous experiments and modeling efforts. By considering the distribution of ions spatially in tandem with their averaged solvation environment, greater insight was provided to the structure of ions at the interface. It was shown, based on the changes in solvation structure, that for amorphous SEI films consisting of Li2EDC the transition of lithium ions from electrolyte to the film more accurately resembles a “resolvation” rather than the strict desolvation often discussed for lithium transport. Based on the observed changes in solvation structure at the interface, this work supports the notion that for amorphous SEI the energy barrier to lithium insertion may be lower than that of subsequent migration. It was found that changes to the composition of the amorphous film, i.e., adding more LiF and Li2CO3, produced minimal impact on structural changes such as ion accumulation. However, a connection may exist between these changes and the orientation of the surface EDC2− groups and lithium absorption. In the case of crystalline inorganic SEI components at the interface, it is clear that ion accumulation is substantial 3229


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and strongly impacts the environment seen by lithium ions at the surface with potential implications for the desolvation mechanism. Clearly, the interfaces with the fluoride and carbonate crystals are also saltier, encouraging greater pairing and aggregation of the electrolyte ions. Finally, the changes to electrolyte dynamics as the SEI is approached were quantified, showing significant slowing compared to bulk residence times. In the case of the LiF and Li2CO3 crystals, the slowing down of the ion and solvent motion was attributed to the substantial adsorbed layer formed at the interface. Beyond the detailed findings from this study, a larger message conveyed by this work is the significant changes to solvation structure and dynamics as one approaches the SEI interface. It is anticipated that understanding the energy barriers to lithium transport from a molecular level will require continued efforts to account for these changes and efforts toward this end are ongoing.

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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.jpcc.7b11472. The number of each species used in each simulation (Table S1), radial distribution plots of the bulk solvation environments for electrolyte species (Figures S1 and S2), changes in coordination for Li+ when approaching SEI composed of 10% LiF and 50% Li2CO3 (Figure S3), example correlation function plots for solvation and surface residence times (Figures S4 and S5), table of integrated ion densities for different solvation environments (Table S2), and table of surface residence times for electrolyte species without normalization to bulk values (Table S3) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (R.J.). ORCID

Ryan Jorn: 0000-0002-0192-9298 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant ACI-154862. Both authors thank XSEDE for computing time granted on Comet at SDSC through startup allocation TG-CHE150044. L.R. thanks Villanova University for funding in support of this research, and R.J. thanks Villanova University for start-up funding for purchasing computer resources used in this work and summer support.

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REFERENCES

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