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Research Papers

# Computational Studies of Interfacial Reactions at Anode Materials: Initial Stages of the Solid-Electrolyte-Interphase Layer FormationOPEN ACCESS

[+] Author and Article Information
G. Ramos-Sanchez

Departamento de Quimica,
Iztapalapa 09340, CDMX, Mexico

F. A. Soto, J. M. Seminario

Department of Chemical Engineering,
Texas A&M University,
College Station, TX 77843

J. M. Martinez de la Hoz

The Dow Chemical Company,
2301 N. Brazosport Boulevard,
Freeport, TX 77541

Z. Liu, P. P. Mukherjee

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843

F. El-Mellouhi

Qatar Environment and Energy Research Institute,
Doha, Qatar

P. B. Balbuena

Department of Chemical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: balbuena@tamu.edu

1Corresponding author.

Manuscript received April 14, 2016; final manuscript received July 13, 2016; published online October 20, 2016. Assoc. Editor: George Nelson.

J. Electrochem. En. Conv. Stor. 13(3), 031002 (Oct 20, 2016) (10 pages) Paper No: JEECS-16-1049; doi: 10.1115/1.4034412 History: Received April 14, 2016; Revised July 13, 2016

## Abstract

Understanding interfacial phenomena such as ion and electron transport at dynamic interfaces is crucial for revolutionizing the development of materials and devices for energy-related applications. Moreover, advances in this field would enhance the progress of related electrochemical interfacial problems in biology, medicine, electronics, and photonics, among others. Although significant progress is taking place through in situ experimentation, modeling has emerged as the ideal complement to investigate details at the electronic and atomistic levels, which are more difficult or impossible to be captured with current experimental techniques. Among the most important interfacial phenomena, side reactions occurring at the surface of the negative electrodes of Li-ion batteries, due to the electrochemical instability of the electrolyte, result in the formation of a solid-electrolyte interphase layer (SEI). In this work, we briefly review the main mechanisms associated with SEI reduction reactions of aprotic organic solvents studied by quantum mechanical methods. We then report the results of a Kinetic Monte Carlo method to understand the initial stages of SEI growth.

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## Introduction

Electron and ion transfer occurring at interfaces affect many processes of high significance in everyday life. Transport and reactions at dynamic interfaces define electrochemical phenomena taking place in energy storage and other power-source devices, which are key ingredients for the practical use of renewables. Recent emphasis on the development of renewables requires parallel progress in energy storage [1]. Rechargeable batteries and supercapacitors are among the most promising electrochemical energy storage devices [2]. Li-ion batteries (LIBs) are the main portable power sources for popular electronic devices, such as cell phones and laptops. However, uses of LIBs in electric vehicles require further development not only in materials for electrodes and electrolytes but also in the understanding and control of properties derived from the complex interactions existent in this ultracorrelated system. In particular, their storage efficiency is largely limited by the occurrence of side reactions that take place via electron transfer at the solid–electrolyte interface and lead to irreversible charge loss [3]. Among the constituent cell materials, the electrolyte is the essential key component of a battery or supercapacitor. No matter how much time and resources are invested into the development of electrode materials, most of the effort will be wasted if the interfacial electrode/electrolyte properties are ignored. That is because the electrolyte is a nexus between the two electrodes, having the function of transporting ions from one electrode to another during charge or discharge of the battery [410], but more importantly, the electrolyte has the potential to control the chemistry of the reactions taking place at the electrode surfaces [11].

This control depends on one essential condition: the chemical properties of the electrolyte need to be such that it must remain stable within a certain electrochemical stability window (Fig. 1) defined by the electronic properties (electrochemical potentials) of the two electrodes and those of the electrolyte [12,13]. To ensure electrochemical stability, the energy gap (Eg) characterizing the electronic properties of the electrolyte must be larger than the energy difference of electrochemical potentials (μ) between the two electrodes (eVoc) at open circuit voltage (Voc). Otherwise, electron transfer reactions (see arrows in Fig. 1) may happen due to chemical instability of the electrolyte, which is reduced (oxidized) at the negative (positive) electrode [14]. Products of the reduction (at anode) or oxidation reactions (at cathode) including inorganic compounds such as Li2CO3 and organic compounds such as Li ethylene dicarbonate (Li2EDC) aggregate forming blocks and developing a heterogeneous film (Fig. 2) that in the best scenario could provide a protective role to the electrode, facilitating ionic conduction and blocking further electron transfer, i.e., self-controlling film growth [15]. Unfortunately, this is not always the case, and the formed film, known as the solid-electrolyte interphase (SEI) layer [16], has physicochemical properties that can result in an irreversible capacity loss, electrode mechanical fracture, and an overall decrease in the efficiency of the electrochemical cell. The formation of an effective SEI layer is one of the greatest challenges of current electrochemical energy storage devices [17,18].

To achieve this goal, a proper understanding of the film nucleation and growth is crucial. This understanding may start from a fundamental analysis of the interfacial reactions to determine the factors affecting the SEI formation. Even more essential is to identify how the SEI properties influence the overall battery performance: capacity and lifetime. SEI layers are formed at both the anode and the cathode. In this paper, we concentrate in the anode reactions.

Three key materials for LIBs are: allotropes of carbon; Li metal, and Silicon-based anodes. Furthermore, Li metal is an ideal anode material to advance the next generation of energy storage systems due to its high theoretical specific capacity (3860 mAh/g), low density (0.59 g cm−3) and having the lowest negative electrochemical potential (−3.040 V versus the standard hydrogen electrode) [19]. Carbon is by far the most widely used anode material (i.e., graphite). There is no absolute parameter or formulas that may define all the SEI, instead is the combination of factors which produces its specific properties, quality, and efficiency. Among the main factors, the most investigated are the type of carbon, pretreatment, electrolyte composition, cycling mode, temperature, and storage [15]. Similarly, among the promising anode materials, Si is an attractive choice due to its high gravimetric capacity (4200 mAh/g, equivalent to a lithiation of Li4.4Si) and volumetric capacity (9786 mAh/cm3) [20]. Here, we review the multiscale modeling approaches used to develop a better understanding of the interactions of the electrolyte with graphite and Li metal anode surfaces. Although there has been recently a great deal of modeling SEI reactions on lithiated Si anodes, we defer their review to a future report. We also report our study using a coarse-grained kinetic Monte Carlo (CG-KMC) approach of the growth on an anode surface of one of the main SEI components derived from the decomposition of ethylene carbonate (EC): the oligomer species known as lithium ethylene dicarbonate (Li2EDC).

## Initial Stages of the SEI Layer Formation: Electrolyte Decomposition

###### Electrolyte Reduction on Lithium Electrodes.

Although the Li metal is extremely reactive, models of Li metal electrodes are relatively simple in comparison to that on the more complex graphitic or Si-based anodes; therefore, the first attempts for more complex simulations of electrolyte reduction were made at the interface of the electrolyte with Li electrodes.

###### Gas Phase Reactions of Electrolyte at the Li Surface.

Tasaki et al. [21] were among the first studying the effect of a metallic Li cluster on the reduction of a set of solvents commonly used in LIBs. The model is fundamentally different to all previous solvent reduction simulations, focusing on the direct decomposition of the solvent on the surface of the electrode. A cluster model of 15 Li atoms and one solvent molecule was fully optimized using the Hartree–Fock (HF) method. The initial orientation of the molecule on the Li cluster was such that the carbonyl oxygen of the molecule faced the Li cluster while the hydrocarbon moiety was away from it.

The solvent and additive molecules examined included EC, propylene carbonate (PC), vinyl ethylene carbonate (VEC), vinyl carbonate (VC), vinyl vinylene carbonate (VVC), ethylene sulfite (ES), and tetrahydrofuran (THF). It is important to note that for VEC, two ring-opening reactions are possible: one with butadiene released and the other with no butadiene released upon reduction. Thus, the label VECa is used when butadiene is released and VECb when no butadiene is released upon reduction. Results for direct ring opening activation and reaction energy were reported. The full set of solvents was grouped into two subsets: those with higher reaction energies (more stable products) including EC, PC, and VECa with activation energies for ring opening ∼25 kcal/mol. On the other hand, solvent/additive molecules VC, VECb, and VVC decompose with a lower activation energy ∼10 kcal/mol. The THF molecule is a special case as the activation energy is very high and the reaction energy is the smallest. For all the molecules having low activation energy, the C-O scission (CE-O2) of the ring was followed by the direct adsorption of the product molecule on the cluster surface without fragmentation. This direct adsorption suggests that Li-organic compounds may be generated on the Li surface; thus, this group of molecules may be relatively superior to PC and EC regarding the formation of an appropriate SEI layer. Despite the limitations of the theoretical model due to the relatively small size of the cluster, the lack of co-solvent molecules and the relatively low level of theory used, the results were important to elucidate the differences occurring when more than one Li atom is used during the solvent reduction simulations. Thus, the results of these simulations were compared to those of the molecular clusters illustrated in Figs. 3(a) and 3(b) [22,23].

Another approach to the direct interaction of isolated molecules with Li metal atoms was made by Leung et al. [24]. It was shown that direct EC decomposition into CO3−2 and C2H4 (mechanism Fig. 3(c)) is thermodynamically more favorable than cleaving the Cc-O2 bond to form O(C2H4)OCO2− by 35.3 kcal/mol, with a negligible activation barrier for both processes using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation (XC) functional. A slightly higher barrier for the Cc-O2 breaking of 3.7 kcal/mol was obtained with the more accurate HSE06 XC functional. Based on the magnitude of the calculated barriers, it may be concluded that both processes are possible on picosecond timescales at explicit EC/Li-electrode interfaces. The next question is how the kinetic prefactors could lead to the preference of either route, which may be addressed by methods able to model the dynamics of the process.

###### Dynamics of Solvent Reduction at the Li Surface.

The inclusion of more than a single molecule of solvent on the surface of Li metal accounts for the interaction between molecules and also between molecules and the electrode, which may provide a better picture of the reduction process. Yu et al. [25] reported ab initio molecular dynamics (AIMD) simulations with the PBE functional. EC molecules pre-optimized with empirical classical force fields were allowed to interact with the Li (100) surface in the AIMD simulations. The EC molecules closer to the electrode undergo a drastic change from the planarity (imposed by some classical force fields) within 50 fs, then within 200 fs the Cc-O2 breaks leading to the precursor O(C2H4)OCO2− and CO, while two electrons are being transferred to the molecule. Using a hybrid functional HSE06 [26] to follow the same trajectory, it was found that the bond breaking occurred at the same timescales, therefore confirming that in direct contact with electrodes the direct CO formation mechanism (Fig. 3(d)) is more robust at electrode surfaces than inside the bulk EC liquid regions. Following the decomposition trajectory, it was found that within 15 ps, all the EC molecules adjacent to the Li metal were reduced ending in ring opening reactions. It is important to note that 90% of the EC molecules followed the CO formation reduction route (Fig. 3(d)) while only 10% resulted in the formation of ethylene and CO3 [24]. Therefore, the preference for the CO route should be inherent to kinetic factors owed to similar activation energies [27]. Neither CO nor OC2H4OCO2− radical anions are final products, in this simulation CO was adsorbed into the Li metal while the OC2H4OCO2− group remained reactive.

Classical molecular dynamics (MD) simulations using reactive force fields were employed to analyze the reaction products of Li in contact with EC or di-methylcarbonate (DMc) solvents. In contrast with traditional nonreactive force fields, reactive force fields allow bonds to break and form [28]. The SEI thickness and its components are found to be dependent on the type of solvent/salt/additives used. For Li metal interacting with EC, the main SEI components are Li2O and Li2CO3 along with trapped gas molecules of C2H4. Even though Li ethylene dicarbonate (Li2EDC) is formed during the initial stages of SEI growth, these simulations showed that it may decompose by interacting with Li atoms on the Li metal surface; however, the scenario may change at different Li concentrations on the surface of other electrodes. Actually, much work on the stability of the SEI products have been reported recently [29,30]. In contrast, when DMC is used, the SEI was found to be mainly composed of Li2O, LiOCO2CH3, Li2CO3, LiCH3, and LiOCH3. Therefore, during the formation of LiOCH3, one CO molecule could be released and indeed it was found to be one of the major components trapped closer to the Li metal. Another important difference according to this study is the extent of the SEI formed during the 40 ps of simulation, the SEI is thicker when only EC is used and thinner with DMC, having intermediate values for solvent mixtures. The analysis of the distribution of formed species confirmed a multilayer arrangement with the first layer (closer to the electrode) composed of gasses trapped during SEI formation, then inorganic salts, and finally organic salts (in contact with the electrolyte). These reactive MD simulations have proved to be fairly accurate in describing competing reactions in different regions, leading to a very reasonable preliminary description of the SEI growth stages, although more details about the inorganic products resulting from salt decomposition and other reactions were not included.

###### Electrolyte Reduction on Carbon Electrodes.

Graphite continues being the most popular negative electrode material in LIBs due to its relatively low cost and moderately long cycle life. During the initial lithiation cycles, a passivating SEI layer is formed on the graphite surface due to the reduction of unstable electrolyte components. Although the SEI layer prevents further consumption of the electrolyte solution, its formation results in an irreversible capacity loss of the working electrode, and consumption of Li-ions that would otherwise participate in the charging/discharging cycles [31]. The chemical structure and morphology of the SEI layer have been found to influence long-term electrochemical properties of the anode, including capacity retention, cycling efficiency, and resistivity for charge transport. Therefore, investigating the formation mechanisms of SEI layers on graphite anodes is important as it may improve the understanding of the role played by this film in the battery operation. Different types of theoretical models describing the SEI formation have been proposed for addressing this problem. Here, we review a few representative cases to illustrate the role and need of multiscale modeling approaches to address complex problems involving a variety of length and timescales.

###### Molecular/Atomistic Models.

These models include more detailed physicochemical characteristics of the battery materials, and can be used to study different features of the SEI, such as structural properties and chemical composition across the surface of the electrode particles. These types of models include kinetic Monte Carlo (KMC), classical MD, AIMD, and density functional theory (DFT). AIMD simulations are based on a quantum mechanical description and can provide valuable information on reaction pathways, rates, and reduction products resulting from electrolyte decomposition. These types of simulation offer an advantage over cluster-based DFT calculations because electrodes and liquid electrolytes can be explicitly included in the model systems. Moreover, Leung et al. demonstrated that electrode–electrolyte interfaces can be simulated within timescales accessible to AIMD [24,3234]. Leung and coworkers performed AIMD simulations of the fully charged anode by “immersing” an SEI-free LiC6 electrode into liquid EC [34]. Four layers of LiC6 graphite were periodically replicated, and 32 EC molecules were confined between the exposed edges, representing the liquid electrolyte solution in contact with the electrode. Besides the intercalated Li, an extra Li+ resided in the liquid region. Dangling orbitals on edge carbon atoms were terminated with hydroxyl (C–OH), quinone (C = O), carboxylic acid (COOH), and/or protons (C–H). No reactions were observed on the anode with proton-terminated edges during the 7 ps of simulation. However, in the system with oxygen-terminated edges, transferences of 2e from the electrode to EC molecules were observed, resulting in their reduction to C2H4/CO3−2, CO/O(C2H4)O2−, or O(C2H4)OCO2−. These reactions took place on the electrode surface, with the electron flowing directly to the decomposing EC molecules coordinated to Li+, and without the electron first becoming delocalized in the liquid region. In the case of hydroxyl-terminated edges, two different reduction reactions were observed, resulting in the formation of a CO3−2/C2H4 pair and a CO/OC2H4O2− pair. Subsequently, the OC2H4O2− anion extracted a proton from the electrode and formed ethylene glycol. Leung's work shed light on the mechanism of solvent decomposition near the graphite electrode, a process that represents the initial stages of the SEI formation. In summary, reduction of EC initiates at graphite edge regions rich in oxidized sites and it may result in either formation of CO/OC2H4O2− or CO/OC2H4CO22− pairs. Initial reduction stages are expected to be fast 2e transfer processes, and subsequently, as the SEI thickens slower 1e transfer processes are expected to become dominant [33].

Ganesh et al. extended Leung's work by evaluating the influence of different salt and solvent molecules on solvent reduction processes [35]. The model system was analogous to that used by Leung, with four layers of fully lithiated graphite in contact with liquid EC. Hydrogen-terminated anodes led to no reduction processes after 11 ps of AIMD simulation, in agreement with the previous results [34]. When the termination of graphite corresponded to a mixture of O/OH, a set of rapid reactions were found to take place. Some of them had been previously observed in Leung's simulations (carbonate formation), but other not very common reactions resulted in the formation of C2H3O, H2, and O*. The different reactivity of the anode calculated in Ganesh and Leung's work could be attributed to a more deficient plane wave cut-off used in Ganesh work (300 eV compared to 400 eV employed by Leung), which could result in different forces during the simulation, therefore, promoting other reactions. A critical observation from Ganesh's work is that different edge terminations determine the likelihood of a given reaction to take place. In the H-terminated anodes, no reaction took place owing to the inherent confinement of Li ions in the interior of the electrode, which results in no Li+ at the interface. In the case of O/OH-terminated anodes, Li ions were mainly located near the oxygen atoms, leading to a high percentage of Li+ at the interface. Moreover, more reactions occurred near O terminations than near OH terminations because the electron transfer is more easily done through oxygen than through hydrogen. When adding LiPF6 salt to the electrolyte, the mobility of the cations was enhanced. This mobility may be due to the dissolved salt not being sufficiently screened by the solvent, leading to attractive interactions with Li+ in the anode, but keeping the structural integrity of the (PF6). On the other hand, when the salt was present with the O/OH terminations, the (PF6) rapidly decomposed into LiF and PF5 forming LiF chains at the interface with the electrode. The specific solvent used was found to affect the reduction products. When PC was used instead of EC, the solvent easily decomposed, which may be related to the higher mobility of Li+ cations. These fast reduction reactions caused significant graphite deformation (probably exfoliation). When DMC was used as a solvent, no reduction processes were observed. It is important to recall that no other AIMD simulation had ever reported species like C2H3O and LiCH3, even though they had been experimentally detected through X-ray photoelectron spectroscopy (XPS) experiments [36]. However, as mentioned earlier, using low cut-off energy (300 eV) could be responsible for the observation of these very reactive species.

Although Leung and Ganesh demonstrated that AIMD simulations are useful in the determination of initial stages of solvent reduction on graphite anodes, longer timescales (impossible to be achieved with AIMD methods) are needed to investigate the continuous SEI formation, up to a few hundred nanometers, as observed in experiments. Tasaki performed classical MD simulations to examine bulk properties of the main reduction products of EC and PC, and their interaction with a graphite surface in gas and liquid phase [37]. The model compounds corresponded to Li2-EDC and dilithium 1,2-propylene dicarbonate (Li2-PDC), which have been identified as major components in SEI layers formed in the presence of EC and PC, respectively. Bulk properties of Li2-EDC and Li2-PDC, such as density and cohesive energy, were calculated at 300 K using a box with 40 molecules under fixed number of molecules, pressure, and temperature (NPT) conditions, using the COMPASS force field [38]. Li2-EDC was found to have a higher density and cohesive energy than Li2-PDC. This result suggests that SEI films formed in the presence of EC are denser and more brittle, which constitute favorable characteristics in the SEI. Subsequently, Tasaki investigated the solubility of Li2-EDC and Li2-PDC in EC and PC, respectively. Findings suggested that Li2-PDC is more soluble in PC than Li2-EDC in EC. Dissimilarities observed between the bulk properties of these reduction compounds are expected to cause contrasting physical properties in EC- and PC-based SEI films. Furthermore, adhesion of the decomposition products to graphite was explored. For this analysis, the simulation box consisted of one molecule of the decomposition product in contact with the (100) plane of five graphite layers. Then, quenched dynamics simulations were used to determine the global minimum for the system. A similar simulation box was employed to examine interactions between graphite and the decomposition product as a condensed material, using 40 molecules of the decomposition product instead (Li2-EDC or Li2-PDC) in contact with the (100) plane of graphite. Simulations showed that the adsorption energy of one Li2-EDC molecule to graphite is stronger than that of one Li2-PDC. Additionally, Li2-EDC in condensed phase also showed a more favorable interaction with graphite, which implies a better adhesion of the EC-based SEI layer to graphite, compared to that formed from PC. These findings were in agreement with the DFT studies reported by Wang and Balbuena [39]. Results from Tasaki's MD simulations are a good starting point for understanding marked differences in the cycling behavior of PC- and EC-based electrolytes, focusing on the bulk properties of the products forming the SEI layer, and the interaction of the SEI with both the electrolyte solution and the graphite anode. However, during the simulations, the graphite carbons were neutral, and the voltage in the anode was not taken into account.

Vatamanu et al. performed MD simulations of an electrolyte composed of EC, DMC, and LiPF6 near the basal plane of graphite as a function of the electrode potential [40]. Polarizable force fields that allow controlling the potential between the electrodes were employed, and the polarization of the electrolyte was represented using induced dipoles applied through isotropic atomic polarizabilities. Charges in the electrode and induced dipoles were calculated as to minimize the total electrostatic energy of the system. Induced dipoles were updated every 3 fs and electrode charges every 0.3 ps. The temperature was maintained at 453 K under NPT conditions, using a Nose-Hoover thermostat. The electrode model consisted of three layers of graphite whose basal plane was in contact with the electrolyte. The distance between the electrodes in the simulation box corresponded to 91.6 Å. The electrolyte consisted of 114 EC molecules, 256 DMC molecules, 31 PF6 ions, and 31 Li+ ions. Equilibration runs were at least 4 ns long, followed by production-run trajectories at potentials between 0 and 7 V. Results showed that the composition of the interfacial layer of electrolyte near graphite is significantly influenced by the electrode potential. The amount of EC near the interface noticeably increased with increasing electrode charge, relative to the amount of DMC. Increasing negative potentials increased the amount of Li+ on the graphite surface, thereby involving more EC molecules in Li+ coordination. The tendency for formation of either Li2CO3 or (LiCO3CH2)2 from EC reduction was suggested to depend on the concentration of Li+ near the graphite/electrolyte interface, with the formation of Li2CO3 being favored at low Li+ concentrations, and the formation of (LiCO3CH2)2 favored at high Li+ concentrations, in agreement with earlier quantum-mechanical analysis [41] and experimental observations [42].

More recently, Jorn et al. performed MD simulations of the graphite/electrolyte interface in the presence and absence of SEI, under applied voltages [43]. Their work aims to help to elucidate the connection between composition, structure, and ion transport characteristics of the SEI, with the overall performance of the battery. The modeling approach included the development of a force field for the electrolyte (EC with LiPF6 dissolved at 1M concentration), through the implementation of a force-matching algorithm developed from AIMD simulations of EC, Li+, and PF6-. The components of the SEI were chosen to be Li2EDC and lithium fluoride (LiF). The SEI components were described using the standard CFF91 model implemented in LAMMPS. Electrostatic interactions between the SEI components and the electrolyte were given by their partial charges, and long-range electrostatics interactions were incorporated using the P3M method. Simulations were carried out by placing the electrolyte in between two graphite electrodes. Both the basal and edge planes of graphite were evaluated. Simulations studying the effect of the SEI layer incorporated a randomly generated film built from Li2EDC and LiF of varying thickness and composition ranging from 0.5 to 2 nm and 0 to 50% of LiF. Applied voltages of 0, 3, 6, and 7 V were considered. The temperature was maintained at 450 K under NVT conditions, using a Nose-Hoover thermostat. Jorn and coworkers observed phase separation when LiF and Li2EDC were combined to form a solid phase. When the LiF concentration increased up to 50% wt., LiF adopted a layered structure. This concentration could explain the layered SEI structure formed in aged battery cells due to thermodynamically favorable relaxation of components over time [44]. Analysis of electrolyte molecules was carried out applying a potential difference of 0 or 3 V between the electrodes. The potential was divided equally between the two electrodes, so individual potential drops of 0 and ±1.5 V were obtained. When the electrodes were represented by graphite basal planes, the preferred orientation of EC molecules at 0 V was entirely parallel to the electrode. In the case of graphite edges, the molecules adopted a broader range of positions. When the applied potential was 3 V, the molecules adopted mainly two configurations, one parallel, and another one perpendicular to the anode, with the carbonyl part of the EC pointing away from the electrode. The EC density peak distribution was sharper and closer to the electrode in the case of the positively charged electrode. When there was an applied potential (3 V), the PF6 anions tended to populate the positive electrode at around 4 Å of separation. In the case of Li+, there were two peaks in the distribution close to the negative electrode, one at 4 Å, which does not change significantly with the application of voltage, and the other centered at 8 Å due to the reluctance of Li ions to lose their solvation shell. After increasing the applied potential to 7 V, the Li+ began to distribute nearer the basal plane of negative electrodes (about 2 Å). Therefore, it was concluded that edge terminations of graphite allow a higher degree of solvent disorder compared to basal planes.

After incorporating the SEI layer onto the graphite electrode, it was found that the electrolyte near the SEI interface lacks the structuring observed on bare electrodes. Random orientations seen in these cases were similar to those observed in the bulk of the electrolyte. The SEI thickness was found to influence the degree of interaction of EC molecules with the interface. Thinner SEI films undergo deformation, allowing EC molecules to interact directly with the electrode. As the SEI grows thicker, its deformation becomes more difficult, and EC molecules are not able to go through. The inclusion of LiF favors the formation of a sharper interface owed to the net unfavorable interaction of EC with the ionic LiF compounds. The SEI is expected to be formed by a bilayer structure, with a dense inorganic film closer to the anode; such layer was observed in these simulations as a concentrated region of fluorine within 4 Å of the SEI. A thicker porous organic layer, located at the interface with the electrolyte, is supposed to be covering the inorganic film. However, in these simulations, the porous behavior of the organic layer was not observed. Li+ and PF6- ions were found to be present inside the SEI region. Some ions were very close to the electrode (less than 2.4 Å) due to losing their solvation shell, and the ones retaining their solvation shell were further away (2.4 to 3.2 Å from the electrode). Increasing the LiF content resulted in Li ions from the electrolyte getting closer to the surface while PF6 anions were confined to the electrolyte region close to the SEI.

Methekar et al. used KMC simulations to explore the formation and growth of a passivating SEI layer on a graphite anode, especially in the area tangential to the surface of the anode during charging/discharging cycles (Fig. 4) [45]. The model explicitly considered phenomena such as adsorption of Li+ in the anode (intercalation), desorption of Li+ from the electrode surface (deintercalation), surface diffusion of ions and molecules on the surface, and reduction of particles on the electrode surface to form material products contributing to the thickness of the SEI layer. The rate of diffusion of molecules on the surface was modeled using a cubic lattice, and the formation of the SEI layer was assumed to follow Butler-Volmer (B-V) kinetics. The kinetic parameters used in the model were obtained from continuum models and experimental data [4648]. Upon calculation of transition rates for each possible process, a given transition was randomly selected following a probability proportional to its kinetic rate. Once the selected transition took place, the process was repeated until the electrode was fully charged. The active surface coverage was found to remain constant for the initial charging cycles, and then decreased with increasing cycle number due to the formation of a passive SEI layer on the surface tangential to the lithium ion intercalation. This coverage also resulted in shorter times required for charging due to the reduced surface area available for electrodeposition of active atoms (reduced electrode capacity). Besides reproducing the capacity fade phenomenon observed experimentally, Methekar et al. also investigated the effect of temperature on the active surface area of the anode during cycling, and found that the temperature that optimizes the active surface area during the first cycle may not be optimal for the long-run performance of the battery.

###### Macroscopic Models.

Continuum mechanics models are usually employed to predict SEI film growth rates, and electrode capacity loss, using kinetic and transport properties of electrolyte species involved in the film formation. Species and charge conservation equations are derived and solved, resulting in the prediction of concentration and electric potential profiles [4953]. Christensen and Newman developed a continuum mathematical model of the SEI as a mixed conductor, including details of the chemistry of SEI formation to simulate the growth of a 1D film of Li2CO3 on a planar graphite surface [53]. The electrolyte solution was assumed to be 1 M LiPF6 in an idealized solution of reactive EC and inert DMC. The elementary steps considered for the SEI formation mechanism included Li+ intercalation, EC adsorption, and EC reduction to Li2CO3. B-V kinetic equations were used to describe all charge-transfer reactions, and nonequilibrium interfacial kinetic expressions were used in the film boundary conditions. Other factors, such as diffusion of Li+ in graphite and variations of potential with the state of charge, were also taken into account. Calculated film growth rate at open circuit (zero current) was found to be proportional to the rate of electron transfer, and faster film growth rates were observed for charged batteries compared to uncharged batteries. The model showed that film growth directly affects both, irreversible capacity loss and film resistance. Colclasure and Kee extended Christensen and Newman's work by incorporating detailed electrolyte reduction mechanisms describing the charge transfer kinetics [51,52]. All microscopically reversible reactions were evaluated in elementary form, providing an alternative to the B-V formalism for charge transfer chemistry. Some limitations of the B-V formalism include the assumption of a single rate limiting step, making difficult to model simultaneous competitive reactions. Therefore, Colclasure and Kee's approach allowed the incorporation of multiple parallel pathways. Additionally, the semitheoretical Redlich-Kister expansion was used to represent nonideal effects of lithiated graphite. As a result, the model can predict SEI growth during charge and discharge cycles, which was not possible with Christensen and Newman's model. Results showed a weak dependence of growth rate on cycling rates, and a proportionality of film thickness and capacity loss with the square root of time. This results suggested that film growth during cycling was mainly limited by slow electron diffusion.

Incorporating detailed SEI chemistry into battery models can sometimes be difficult due to a large number of model parameters needed. Physical and chemical properties of reaction intermediates and rate expressions have to be estimated or derived from the literature. A different, simpler approach is to represent the SEI chemistry as a constant resistance. Ploehn et al. developed a 1D continuum mechanics model in which the SEI growth is described by a reactive solvent component diffusing through the SEI layer and undergoing a two-electron reduction at the graphite/SEI interface [50]. It is assumed that reduction of the solvent produces an insoluble product that increases the SEI thickness. The model simplifies the bilayer structure observed in SEI films (a compact inorganic phase close to the electrode, covered by a porous organic phase closer to the electrolyte) and represents it as a single layer with continuously varying properties, such as composition and porosity. Linear correlation was found between SEI growth at open-circuit conditions and the square root of time. Using reasonable assumptions about the SEI composition, an SEI thickness of several tens of nanometers was estimated. The irreversible capacity loss was also found to increase linearly with the square root of time, which agreed with experimental data and demonstrated that solvent diffusion models can be useful alternatives for the modeling of SEI growth and capacity loss behavior in Li-ion batteries. A similar result was found by Pinson and Bazant [54] using a single rate determining transport mechanism to describe SEI growth on a graphite anode. By treating the SEI layer as a homogeneous structure, their model calculated the Li diffusion coefficient at 60 °C to be 3 × 10−6 cm2/s.

Although the continuum models described above have shown the excellent capability to predict SEI growth, they ignore nonzero charge density at the interfacial region between the SEI and the electrolyte. Recently, Deng et al. proposed a phase field model for SEI growth that takes into account the nonzero charge density at the interface and captures the double-layer structure during SEI growth [49]. In this model, the interface is diffuse such that material properties vary smoothly across it, and the equations are solved simultaneously in the whole domain, including bulk phases and interfacial regions. The implementation of a diffuse interface results in significant differences in the way in which species are transported across the interface. When modeling equations are solved at each bulk phase separately, heterogeneous reactions occurring at the interface determine fluxes of species moving across the interface. On the other hand, the diffuse interface in the phase field model allows species to go across the interface naturally, according to the nonequilibrium thermodynamics. As a result, fluxes of species across the interface are not only determined by SEI formation reactions but also by diffusion and electromigration. Deng's model found that SEI growth is mainly controlled by the diffusion of electrons, and it is approximately proportional to the square root of time. This behavior is similar to that observed with Colclasure's [51,52], Pinson and Bazant [54], and Ploehn's models [50]. The phase field model also found that the SEI growth rate is proportional to the temperature and that SEI thickness follows an Arrhenius relation.

Thermodynamic models have also been proposed to describe the formation of SEI layers on graphite anodes. Yan et al. employed classical nucleation theory to qualitatively explain the origin of the bilayer structure of the SEI and developed a theoretical foundation for the first electrochemical intercalation of Li into graphite as a special precipitation process [5557]. The precipitation of reduction products at a graphite surface takes place through two different steps: nucleation of solid species constituting the SEI layer, and growth of the solid nuclei at the graphite/electrolyte interface. Yan et al. introduced three different types of nucleation: (i) nucleation in the bulk electrolyte solution, (ii) nucleation directly on the graphite surface, and (iii) nucleation surrounding a particle already present on the graphite surface [57]. They showed that the smallest the shape factor of a given nucleation mode, the easier it is for the solid nuclei to form. The relative order of the shape factor associated with nucleation mode was determined to be: (i) > (ii) > (iii). Both nucleation modes (ii) and (iii) are employed by solid species located close to the graphite surface. Therefore, the number density of macroscopic solid particles growing close to graphite should be much larger than that away from the electrode. This growth explains the most compact nature of the inorganic film close to the anode. Additionally, since the concentration of organic species is higher than that of inorganic, a thicker porous layer composed of organic species is expected to form nearer to the electrolyte. Yang et al. also described the first Li intercalation into graphite, as the potential of the graphite electrode decreases from the open circuit potential (OCP) (fully delithiated state, 1.4 V versus Li/Li+) to 0 V. At potentials between 1.4 and 0.55 V, one-electron decomposition of electrolyte components may be observed, resulting in solid nuclei forming through nucleation modes (i) and (ii). Since the shape factor of nucleation type (ii) is smaller, resultant species have a higher tendency to precipitate on the graphite surface. When the anode is further polarized to potentials between 0.55 and 0.2 V, one- and two-electron decomposition of electrolyte components are observed. Nucleation modes (i), (ii), and (iii) are possible, but mode (iii) with the smallest shape factor will allow species such as LiF, Li2O, and Li2CO3 to surround eventually and replace the isolated solid deposits previously formed on graphite, constituting the compact inorganic film closer to the electrolyte. Solid organic species are in larger proportion in the electrolyte. Thus, a thicker porous layer will be formed closer to the electrolyte. When the potential of the anode is held between 0.2 and 0 V, the stable SEI layer has been established. Yan et al. also presented a thermodynamic argument demonstrating that most precipitation processes in the electrolyte followed the nucleation and growth mechanism [56], and treated in detail the growth of solid nuclei constituted by reduction products [55]. SEI thickness was found to increase with the square root of time, which demonstrated a diffusion-controlled growth, in agreement with results obtained using continuum mechanics models.

###### Growth of Li2EDC Film.

In this section, we report a new coarse-grained (CG)-KMC model to study the SEI film formation and growth. As discussed in the previous sections, KMC methods are powerful tools to study film growth [58,59] and electrochemical deposition at the atomistic scale [6062]. Recently, several models based on the KMC algorithm were employed to study electrochemical energy systems [63]. In the 2D Methekar's model [45], the formation of SEI was simplified to a one-step reaction, and the growth of the SEI thickness was not investigated due to limitations of the 2D model. Here, we introduced a CG-KMC three-dimensional (3D) model where multistep chemical/electrochemical reactions during the formation of SEI are explicitly incorporated. The main idea is to detect the evolution of the organic Li2EDC film, which involves multiple-step chemical and electrochemical reactions [8,32,64]. In this preliminary model, it was assumed that Li2EDC formation is dominated by the one-electron mechanism via a series of steps given by the following reactions [24]:

1. (1)EC + * →EC* with adsorption rate k1,
2. (2)EC* + e- →c-EC- with reduction rate k2,
3. (3)c-EC-→o-EC- with conformational transition rate k3,
4. (4)2 o-EC- + 2 Li+→ Li2EDC + C2H4($↑$) with formation rate k4.

The first step represents the adsorption of the EC molecule on the substrate. The second step represents the electrochemical reduction, in which an electron is transferred to the adsorbed EC and EC is reduced to a c-EC- with a closed-ring conformation. The c-EC can be converted to o-EC which has an open-ring conformation as shown in the third step. Finally, 2 o-EC anions can accept Li+ ions and form Li2EDC as an SEI film component.

The simulation domain includes $50×50×500$ simple cubic sites. The length scale of each site approximates to 0.5 nm. Sites in the bottom plane are predefined as the anode substrate. Other sites can be occupied by EC, c-EC, o-EC or Li2EDC. It is worth noting that EC adsorption can only take place at the empty sites, which are located on the anode substrate or predeposited Li2EDC sites. This analysis focuses on how the reduction rate k2 and the SEI formation rate k4 affect the growth rate of the SEI film. Hence, the adsorption rate k1 is set to 108 s−1 site−1, and the conformational transition rate k3 is set to 103 s−1 site−1. Both of these values and the ranges of variation of k2 and k4 are adopted from Leung's analysis based on DFT calculations [32].

The contour map in Fig. 5(a) demonstrates the effect of k2 and k4 on the SEI growth rate. Both k2 and k4 vary from 10−8 site−1 s−1 to 108 site−1 s−1. It was found that the SEI growth rate is limited by the electrochemical reduction rate k2. When k2 is smaller than 10-4 site−1 s−1, the SEI growth rate is extremely slow, and the variation of Li2EDC formation rate k4 does not affect the growth rate. When k2 is larger than 10−2 site−1 s−1, the SEI growth rate increases linearly first as k4 increases as shown in Fig. 5(b). Then the growth rate arrives at a maximum value as k4 further increases. The maximum growth rate is also dependent on the electrochemical reduction rate.

As the SEI thickness grows, electrons are harder to be tunneled to the SEI layer. Hence, the reduction rate k2 should decrease with the increase in SEI thickness. To mimic this effect, we use the following equation to describe the thickness-dependent reduction rate

$k2(δ)=k2(0)×l0α×δ+l0$

Here, l0 is the length scale of a lattice site, and $α$ is a dimensionless coefficient. In this model, the relation between thickness and reduction rate is assumed. A more accurate equation will be applied in the KMC model in future work where the α parameter will be obtained directly from the decay obtained for a given thickness from a first-principles approach demonstrated in our previous work [65]. Figure 6 shows the SEI thickness variation versus time. It clearly shows that the growth rate decreases as the thickness increases, which agrees well with the results of the continuum model developed by Christensen and Newman [53] and with the results obtained by a first-principles approach [65]. A larger value of $α$ indicates that it is more difficult for electrons being tunelled to the SEI/electrolyte interface.

According to Fig. 6(a), the larger $α$ can decrease the SEI growth rate. Christensen and Newman [53] used the electron transference number to characterize the difficulty of electrons tunelling through the SEI. It was found that the SEI film grew slower with a smaller electron transference number. The conclusion from the present coarse-grained molecular level model agrees well with that from the reported continuum model [53] and with a first-principles approach [65]. Figure 6(b) shows the fraction of species at the SEI/electrolyte interface. It can be seen that Li2EDC and EC* are the dominant species on the SEI surface. Snapshots in Figs. 6(c)6(f) show the distribution of species at the SEI top surface. c-EC and o-EC can be observed only when the SEI is thinner than around 1 nm. Once the SEI becomes thicker, only EC* and Li2EDC can be observed. The reason is that as SEI grows, the reduction rate k2 decreases fast while the other transition rates remain as constants. The EC adsorption event (formation of EC*) is the predominant event. Once an EC* is reduced to c-EC, it will be quickly converted to Li2EDC according to the respective governing reactions with high kinetic rates. These preliminary results illustrate how the coupling between different models could be done to achieve results even at the macroscopic level.

## Conclusions

In this article, we have reviewed recent progress on modeling components of LIBs technology, emphasizing the growth of SEI layers and anode/electrolyte interface chemistry. Multiscale modeling studies that mainly focused on the electrolyte decomposition and SEI formation on the surface were closely summarized and discussed. Issues and methodology pertaining to simulations were also summarized. A CG-KMC model is developed to study the growth of Li2EDC film. The model involves multiple-step reactions. It is found that the reduction of EC limits the film growth rate. A simple model is used to incorporate the effect of SEI thickness, which shows the reduction of the growth rate as the film thickness increases. The evolution of the surface pattern is detected as a function of SEI thickness. Although the CG-KMC model is very simple based only in one SEI component, it shows the main ideas that will be further elaborated in future work. An important question still to be answered is a direct comparison between the first-principles calculated rate of SEI growth and experimental rates. An important step in that direction has been given in our recent work [29], where we discussed the role of the nature of the electrolyte in determining the rate of SEI growth. We demonstrated that additives such as VC yield SEI products that lead to a much slower SEI growth, whereas in the absence of such additive, the electrochemical instability of the SEI products leads to a much faster growth. In the future, we plan to incorporate these ideas into the KMC model.

As the global demand for alternative renewable energy increases, electrochemical energy storage devices such as batteries are attracting greater attention than before. To develop a rechargeable LiB technology for a wide array of applications, the safety, cycle life, and energy density must be vastly improved. In order to move beyond these limitations, a rational electrolyte design investigation must take place. Although much progress has been done on studying the decomposition mechanism of electrolytes and SEI formation and growth as briefly reviewed in this work, much more effort is still required. The studies should be further extended to develop solutions to mitigate problems such as dendrite formation, formation of a “bad” SEI layer, and pulverization of the electrode. Regarding the SEI formation and growth, despite numerous debates and suggestions, the microscopic details of the evolution of organic components of the SEI layer based on specific electrolyte mixtures have not been fully elucidated at the anode/electrolyte interface and deserve intensive study.

## Acknowledgements

This work was supported by the Qatar National Research Fund (QNRF) through the National Priorities Research Program (NPRP 7-162-2-077). PPM and ZL acknowledge financial support from NSF Grant No. 1438431. Computational resources from Texas A&M Supercomputing Center, Brazos Supercomputing Cluster at Texas A&M University, and from Texas Advanced Computing Center at UT Austin are gratefully acknowledged.

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Turner, C. H. , Zhang, Z. T. , Gelb, L. D. , and Dunlap, B. I. , 2015, “ Kinetic Monte Carlo Simulation of Electrochemical Systems,” Rev. Comput. Chem., 28, pp. 175–204.
Aurbach, D. , Gofer, Y. , Ben-Zion, M. , and Aped, P. , 1992, “ The Behaviour of Lithium Electrodes in Propylene and Ethylene Carbonate: Te Major Factors that Influence Li Cycling Efficiency,” J. Electroanal. Chem., 339(1), pp. 451–471.
Benitez, L. , Cristancho, D. , Seminario, J. M. , Martinez de la Hoz, J. M. , and Balbuena, P. B. , 2014, “ Electron Transfer Through Solid-Electrolyte Interphase Layers Formed on Si Anodes of Li-ion Batteries,” Electrochim. Acta, 140(SI), pp. 250–257.
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Benitez, L. , Cristancho, D. , Seminario, J. M. , Martinez de la Hoz, J. M. , and Balbuena, P. B. , 2014, “ Electron Transfer Through Solid-Electrolyte Interphase Layers Formed on Si Anodes of Li-ion Batteries,” Electrochim. Acta, 140(SI), pp. 250–257.

## Figures

Fig. 1

Schematic figure of an electrochemical cell illustrating the chemical potentials at the anode (μa) and cathode (μc), the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and associated energy gap (Eg). The condition for electrochemical stability of the electrolyte is that Eg > eVoc, where eVoc is the energy associated with the open circuit voltage (Voc) and e is the electron charge.

Fig. 2

Schematic mosaic picture of the SEI layer as proposed by earlier work [1517]

Fig. 3

Schematic representation of solvent reduction proposed mechanisms during first stages of SEI formation. EC molecule is used as an example; any other cyclic carbonate molecule could follow the same mechanism. Red, gray, white and purple spheres represent oxygen, carbon, hydrogen, and lithium respectively. (See on line article for full color representation.)

Fig. 4

Schematic representation of the processes described in the KMC simulations by Methekar and co-workers (Adapted from Ref. [45])

Fig. 5

(a) Effect of the electrochemical reduction rate k2 and the EDC formation rate k4 on the growth rate of the EDC film. Both k2 and k4 vary from 10−8 site−1 s−1 to 108 site−1 s−1 and (b) SEI growth rate versus SEI formation rate k4 with different electrochemical reduction rates. The units of the growth rate (d δ /dt) are Å s−1.

Fig. 6

(a) SEI thickness variation versus time with different thickness-dependent reduction rate and (b) species fraction at the SEI/electrolyte interface with α=107. Here the reduction rate at clean anode surface is set to k2(0) = 108 site−1 s−1. Snapshots demonstrate the top view of SEI film in the coarse-grained model with α=107 and various thicknesses. Black: EC*, red: c-EC, blue: o-EC site, cyan: Li2EDC. (See on line article for full color representation.)

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