Kena Zhang‡
a,
Yanzhou Ji‡
a,
Qisheng Wu
b,
Seyed Amin Nabavizadeha,
Yue Qi
*b and
Long-Qing Chen
*a
aDepartment of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA. E-mail: lqc3@psu.edu
bSchool of Engineering, Brown University, Providence, RI 02912, USA. E-mail: yueqi@brown.edu
First published on 20th June 2025
The solid electrolyte interphase (SEI) governs the reversibility of advanced electrochemical devices such as batteries, but the role of cations in its formation remains poorly understood. Here, the thickness and compositional evolution of the SEI are tracked over time scales from nanoseconds to seconds with a newly developed atomically informed phase-field multiscale model. We deconvolve the complex interplay among electron tunneling, species diffusion, and chemical/electrochemical reactions by probing different controlling factors separately and jointly to determine the rate-limiting steps. We show that the SEI growth begins with the formation of organic products, followed by the conversion of these organic products into inorganic ones, and in the end the inorganic products fully cover the lithium metal surface to form a passivation layer. While electron tunneling determines the thickness of these layers, the growth rates of the organic and inorganic SEI layers are controlled by the rates of Li-ion diffusion and electrochemical reactions, respectively. This predictive model is universally applicable to multiphase and multicomponent electrochemical systems and represents a significant advancement in simulating complex reaction processes.
Broader contextThe solid-electrolyte interphase (SEI) plays a critical role in battery performance and longevity, yet its formation process remains one of the most ambiguous issues in battery science due to the complex, spatially and temporally dynamic nature of this interfacial layer. To capture the rapid SEI formation process across various scales, an atomically informed phase-field model (AI-PFM), capable of handling complex reaction networks with multiple species, is developed. This model enables the investigation of SEI formation and initial growth from nanoseconds to seconds in time and angstroms to 100 nm in length. By tracking the evolution of SEI products and electrolyte species up to surface passivation, the interplay among reaction kinetics, species transport, and electron tunneling during SEI formation is successfully deconvoluted with the identification of the governing factors. For the first time, this study reveals that the competition between Li-ion diffusion and reaction kinetics is a key determinant of the growth rates of different SEI products. Such deconvolution is difficult to achieve with current modelling and experimental techniques, which underscores the major advancement and benefits of this AI-PFM framework. It offers a unique approach to evaluate the competing complex mechanistic pathways and understand the formation mechanism of the SEI. |
At microscopic and mesoscopic timescales, atomic-scale theoretical approaches, such as density functional theory (DFT) calculations and ab initio molecular dynamics (AIMD) simulations, offer insights into the reaction energy profiles,10–12 species transport properties13,14 and electrolyte reduction pathway within a system11 that are otherwise unavailable from experiments. However, their simulation time is typically limited to scales of 10–100 picoseconds (10−11–10−10 s) for a system of hundreds of atoms,15,16 thus offering only limited information on SEI formation, which typically occurs over timescales approaching 1 s. A Monte Carlo-molecular dynamics (MC-MD) method can predict the time evolution of SEI species over 10 ns (10−8 s).15 Using classical reactive force fields, MD simulations can extend the process further up to 100 nanoseconds (10−7 s).17
At a macroscopic scale, continuum models have been developed to study the long-term SEI growth over hours and even months.18–23 Despite the widespread acceptance and observation of a two-layer structured SEI in many experimental works, the reaction networks and SEI compositions are simplified so that only a single SEI product is included in most continuum-level models.20,24,25 For example, Christensen and Newman20 proposed a mathematical model to estimate the growth rate of inorganic Li2CO3 and determined that the SEI grows around 20 nm in 15 h on graphite, which is limited by the electron transport via a Li interstitial diffusion mechanism. The continuum model in the study by Horstmann et al.23 predicted that the capacity fade shifts from a square-root-of-time dependence to a linear time dependence as the charging current density increased, suggesting a shift from diffusion-controlled to electron-migration-controlled SEI growth. Their simulations concluded that it would take several months for an SEI layer a few nanometers in thickness to form. While these models have been effective in predicting the battery lifetime25,26 at a macroscale, they overlooked several critical kinetic processes involved in SEI growth, which prevents them from accurately predicting the precise composition and morphology of the SEI. For instance, the detailed electrolyte reduction reaction networks and the competitive interactions between the various reaction products are neglected. Furthermore, these continuum models fail to account for the electron transport mechanisms, which is crucial for understanding the SEI formation and growth processes.
Since single-scale atomistic simulations are insufficient to capture the complex interfacial reactions and phase transformations involved in SEI formation, multiscale computational frameworks have therefore become indispensable for describing the growth, composition, and dynamic evolution of the SEI and its impact on battery performance. Among these, DFT and MD integrated kinetic Monte Carlo (kMC) methods have been used to track the stochastic reaction nature of electrolyte decomposition. For instance, Gerasimov et al.27 tracked EC decomposition and SEI formation on the Li metal for 100 ns, revealing an inorganic-rich inner layer (LiF/Li2CO3) and a porous organic-rich outer layer (Li2EDC) together forming a structure ∼11 nm thick. U. Krewer et al.28 constructed a DFT-kMC-continuum electroneutrality model that predicted a 7-nm-thick inorganic SEI layer within 1 μs (10−6 s), while the resulting bilayer architecture (porous Li2CO3 beneath dense LiF) deviates from experimental observations.29,30 Recently, chemical reaction networks (CRNs) have been developed to automatically identify the reaction pathways for over 80 million reactions among over 5000 species, in which DFT calculations are combined with kMC simulations to simulate the competition between SEI products within 10 μs (10−5 s), revealing the formation of distinct inorganic and organic layers in the SEI.31 While these kMC-based models have demonstrated success in capturing reaction mechanisms and compositional diversity at the molecular level, they remain limited in temporal and spatial scalability. Their inherently discrete spatial nature restricts the ability to simulate mesoscale structural evolution, such as growth, coarsening, polycrystallinity, and crack formation. Additionally, coupling external physical fields (e.g., mechanical stress relaxation, thermal transport, etc.) with kMC frameworks is generally indirect through modifications of reaction rates.
The phase-field (PF) method offers a continuum framework well-suited for modeling multicomponent, multiphase systems with intrinsic flexibility to incorporate physical fields. By introducing multiple concentrations or order parameter fields governed by free energy functionals, PF models can capture the spatiotemporal evolution of competing SEI phases, while naturally incorporating additional physical phenomena such as ion/electron transport, electrochemical reactions, elastic deformation, thermal transport, and other physical effects. Previously, phase-field modeling has been successfully applied to the investigation of Li electrodeposition32–38 and the interaction between Li dendrites and artificial SEIs.39,40 However, only a limited number of phase field investigations have been applied to the study of SEI formation and growth,29,41–43 with several important thermodynamic/kinetic parameters associated with SEI formation still absent. Compared with kMC-based models, previous PF models have simplified the SEI as a single homogeneous phase and thus failed to account for the chemical diversity observed experimentally.40,41 This is because PF simulations face numerical challenges in simulating multiple moving interfaces with distinct kinetics when tracking the evolution of reaction intermediates, which requires careful parameter calibration and efficient algorithms to ensure numerical stability and convergence.
In this work, we demonstrate that an atomically informed phase-field model (AI-PFM), which incorporates multiple electrochemical reactions, species transport and electron tunneling process, can track the temporal and spatial evolution of SEI formation from nanoseconds to seconds until it passivates the Li metal surface. The AI-PFM here incorporates these parameters obtained from DFT and MD calculations through simplification and parameterization. We apply this model to a 1-D prototypical battery system with a Li metal anode and a liquid electrolyte consisting of 1 M LiPF6 in ethylene carbonate (EC) and simulate the evolution of two common SEI products, i.e., organic component dilithium butylene dicarbonate (Li2BDC) and inorganic component lithium carbonate (Li2CO3). By tracking the temporal evolution of the spatial distribution of these products and electrolyte species, we analyze the effect of electron tunneling on SEI thickness, examine the competition between the reactive and diffusive processes during the growth of different SEI products, and identify the governing mechanism behind the formation of different SEI products. Our findings pinpoint the Li+ diffusion as the key limiting factor of the formation of organic Li2BDC during the initial 10−5 s scale, whereas Li2CO3 directly formed by two-electron reduction of EC is limited by its slow reaction kinetics within around 10−2 s. This multiscale approach, for the first time, provides profound insights into the SEI formation across time scales spanning 8 orders of magnitudes (from nanoseconds to seconds) and length scales spanning 3 orders of magnitudes (from angstroms to 100 nm). Furthermore, the ability of AI-PFM to simulate complex reaction networks that encompass multiphases and multicomponent systems has been demonstrated.
To obtain the atomic-scale input parameters, we perform an extensive DFT study to establish the predefined reaction network that contains both electrochemical reactions (magenta arrows) and purely chemical reactions (green arrows) (Fig. 2). For each reaction, we calculate its standard Gibbs free energy change ΔG0 (for purely chemical reactions) or reduction potential ψ0 (for electrochemical reactions), as well as the electron transfer kinetic barrier ΔG* according to Marcus theory.44,45 Fig. 2A shows all the reactions considered in our atomistic simulations, involving multiple reactants (Li+, c-EC, and e−), intermediate species (o-EC−, Li+/c-EC, Li+/o-EC−, Li+/CO32−, and 2Li+/o-EC−), and SEI products (Li2BDC, Li2CO3, and C2H4). Here, c-EC represents the neutral cyclic EC molecule, and o-EC− represents the reduced ring-opened EC.
While it is possible to develop a comprehensive phase-field model that incorporates all these reactions, such simulations would not efficiently bridge the length and time scales. Thus, we simplify the reaction paths and focus on the primary SEI products: the organic Li2BDC and inorganic Li2CO3 (Fig. 2B and C), based on DFT computed thermodynamics driving forces, consistent with extensive theoretical and experimental studies.15,28,46 We note that Li2BDC is thermodynamically more favorable than Li2EDC, in agreement with other computational studies,3,47 and both products have been experimentally observed to coexist within the SEI.46 Therefore, we consider Li2BDC as the representative organic product in our model. The impact of Li ions on EC reduction is considered, but the anions are not, as recent molecular dynamics simulations showed that the typical PF6− anions do not enter the electric double layer (EDL) in strong carbonate-based solvents.48 The simplification treatment involves two procedures: (1) for two or more parallel reactions, we select the smallest reaction barrier as the simplified reaction barrier and record the Gibbs free energy change (parallel reactions have the same Gibbs free energy change); (2) for series reactions, we select the largest reaction barrier as the simplified reaction barrier and record the sum of Gibbs free energies for these series reactions.
In the phase-field simulations, we focus on the formation kinetics of organic Li2BDC and inorganic Li2CO3 via simplified reactions (R1, R2, and R3 in Fig. 2C) at a constant voltage of −3.04 V with respect to the standard hydrogen electrode potential, SHE (or 0 V versus Li+/Li0). As illustrated in Fig. 1, we employ a 1-D system representing a half-cell, and the simulation domain spans from the Li metal electrode surface at x = 0 nm into the bulk liquid electrolyte comprising EC and 1 M LiPF6 at x = 100 nm. A set of non-conserved order parameters (ϕE, ϕS1, and ϕS2) represent the electrolyte (E), inorganic Li2CO3 (S1), and organic Li2BDC (S2) phases, respectively. The phase evolution is governed by the Allen–Cahn equations (eqn (3)–(5) in the Experimental section). The total Gibbs free energy change ΔGrm and the linearized reaction rate Rm for each reaction (m is the reaction index for R1, R2, and R3) are related to its standard Gibbs free energy change ΔG0, reduction potential ψ0, and the activation energy ΔG* from DFT, as well as the local activities of species including electrons, Li+ and EC molecules, as shown in eqn (6) and (7) in the Experimental section. Electron tunneling is a key short-term electron transport mechanism for SEI formation, which is governed by the tunneling barrier of SEIs. Therefore, we numerically solve the steady-state Schrödinger electron tunneling equation by formulating a phase-dependent tunneling barrier to calculate the probability of electrons in the SEI, so that the SEI/electrolyte interface positions do not need to be explicitly tracked, taking advantage of phase-field modeling. The local electron activity can then be defined as the probability of electrons in the SEI, i.e., ae− = |Ψ*Ψ|, where Ψ is the electron wave function (see “Electron tunneling” in the Experimental section for details). At the Li metal surface, ae− is presumed to be 1 and decays exponentially through the SEI and the electrolyte. The time-dependent evolution of the concentration distribution of Li+ and EC is dominated by the reaction-diffusion equation (eqn (9) in the Experimental section), and the diffusivities of species are obtained from MD calculations (see the “Species transport” section in the Experimental section for details). We assume that the concentration of both Li+ and EC at the Li/SEI interface is 0 M. At the right electrolyte boundary, their concentrations are fixed at 1 M for Li+ and 15 M for EC, corresponding to their initial bulk concentration. The activities of species are given by ai = xi/x0i, where xi is the concentration of species Li+ and EC, and the standard concentrations of Li+ and EC (x0EC) are 1 M and 15 M, respectively. Therefore, the initial activity of both aLi+ and aEC is 1.
ΔGrR1 = ΔG0R1 + F(ψe − ψsol − ψ0R1) − RT![]() ![]() | (1) |
ΔGrR3 = ΔG0R3 + F(ψe − ψsol − ψ0R3) − 2RT![]() ![]() | (2) |
To highlight the electron tunneling effect, we compare two cases: one assuming the electron activity ae− = 1 throughout the system (i.e., assuming that the SEI behaves like a metal) and the other with electron activity ae− obtained from the steady-state Schrödinger electron tunneling equation. As shown in Fig. 3C and D, starting with an initial thickness of 6 nm, the SEI will continuously grow when ae− = 1 until the electrolyte is fully consumed. However, when considering the electron tunneling effect, both organic and inorganic SEIs exhibit self-limiting growth behavior. They stop the initial quick growth after reaching a specific thickness. This occurs because the Gibbs free energy changes of reactions R1 and R3 (from eqn (1) and (2)) remain consistently negative, allowing the reactions to proceed indefinitely; but with electron tunneling, the electron activity decays exponentially as the SEI grows (Fig. S1, ESI†). Once the electron activity reduces to a certain level (i.e., when ΔGrR1 = 0 and ΔGrR3 = 0 in eqn (1) and (2)), reactions R1 and R3 reach equilibrium, where the SEI reaches a tunneling-limited thickness and stops further growth. In our model, the tunneling barrier for Li2CO3 (ΔELi2CO3 = 1.78 eV) is derived from the DFT calculation.49 The tunneling barrier for Li2BDC is estimated to be a lower bound of ΔELi2BDC = 0.24 eV due to porosity50 and the fact that the organic Li2DEC, structurally close to Li2BDC, has been experimentally measured to exhibit a tunneling barrier of ∼1 eV lower than that of inorganic SEI components.51 It aligns with the general trend that the inorganic component in the SEI blocks electron tunneling more effectively than the organic species. Using these values, our model predicts tunneling-limited SEI thicknesses of ∼29.4 nm and ∼11 nm for Li2BDC and Li2CO3, respectively, which are close to the experimentally reported values29,30 during SEI formation. These can be referred to as the “tunneling-limited thickness”, which leads to a good estimation of the first cycle capacity loss, corresponding to the Li consumed to form the SEI up to the tunneling-limited thickness, agreeing well with experiments.49,52
Fig. 3 also shows the time scales to grow the Li2BDC and Li2CO3 layers to reach a stable thickness. They are 66 ps and 20 ms for Li2BDC and Li2CO3 layers, respectively, under the assumption of no concentration variation of Li+ and EC during SEI growth. The electron tunneling generally occurs within a few attoseconds.53 Consequently, this discrepancy in timescales is primarily attributed to the kinetic barrier of the single-electron reduction reaction (R1), substantially lower than that of the two-electron reduction reaction (R3), despite the overall Gibbs free energy of R3 being much greater than that of R1.
In case (1) shown in Fig. 4A, the organic SEI layer growth via R1 will reach their tunneling-limited thickness within around 66 ps (solid blue line), and its rate is purely governed by the reaction kinetics. Furthermore, we find that the EC diffusion has no significant effect on the Li2BDC growth (the solid and dotted blue lines overlap) by comparing cases (1) and (2), as the EC concentration in the electrolyte closely matches that in Li2BDC, suggesting that EC molecules could be reduced on-site without requiring additional EC supplied by the electrolyte. Considering the Li+ consumption and diffusion by comparing cases (3) and (4), it is found that the predicted Li2BDC growth time in Fig. 4A increased from 36 ns to ∼57 μs (solid and dotted purple lines). This is consistent with the time scale (∼29 μs) for Li+ to diffuse from the right boundary of the electrolyte region to the Li2BDC surface. It is estimated by using , where L = 100 nm is the diffusion length and
is the diffusivity of Li+ in the electrolyte obtained from MD simulations. The simulated Li2BDC growth time (∼57 μs) is close to the
estimation, indicating the Li+ diffusion-controlled growth nature. This is because, in contrast to EC, the Li site density inside Li2BDC (∼13.5 M) is significantly higher than the initial concentration of Li+ in the electrolyte (1 M) and the reaction rate of R1 is much faster than that of the Li+ diffusion, which means that a large amount of Li+ needs to be consumed to grow the SEI, necessitating Li+ diffusion from the electrolyte to the SEI/electrolyte interface to sustain Li2BDC growth, as shown in Fig. S2A (ESI†).
![]() | ||
Fig. 4 1-D phase-field simulation of the growth of the organic and inorganic SEI products, considering reactions R1 and R3 in Fig. 2C. Parameter study for the governing kinetic factors for organic Li2BDC growth (A) and inorganic Li2CO3 growth (B). Four cases: (1) not evolving both Li+ and EC (aLi+ = 1 and aEC = 1): the concentrations of Li+ and EC remain constant at their initial values during SEI growth; (2) only evolving EC (aLi+ = 1, and aEC ≠ 1 calculated using eqn (9)): only the consumption of EC is considered while the Li+ concentration remains at its initial value; (3) only evolving Li+ (aLi+ ≠ 1 calculated using eqn (9), and aEC = 1): only the consumption of Li+ is considered, while the EC concentration remains at its initial value; (4) evolving both Li+ and EC (aLi+ ≠ 1 and aEC ≠ 1 calculated using eqn (9)): both Li+ and EC are consumed according to their stoichiometric ratio during SEI growth. |
Regarding the inorganic Li2CO3 growth via R3, the Li2CO3 layer grows to its tunneling-limited thickness of about 11 nm under ∼20 ms, which is much slower than the diffusion time of both Li+ (∼29 μs) and EC, and thus their diffusion does not influence the inorganic Li2CO3 SEI layer growth behavior (Fig. 4B and Fig. S2B, ESI†). In contrast to the organic Li2BDC, the growth rate of Li2CO3 is much (∼103 times) slower due to the significantly larger kinetic barrier of R3 than
for R1. We further show that by increasing the Li+ concentration from 1 M to 4 M, the time required for Li2BDC to reach its stable thickness decreases from 57 μs to 1 μs, while the growth rate of dense Li2CO3 remains unchanged (Fig. S3, ESI†). Consequently, the growth rate of Li2BDC is determined by Li+ diffusion, whereas the growth of Li2CO3 is controlled by the reaction rate.
To understand the underlying processes governing SEI formation, we conduct a detailed analysis of the temporal evolution in the distribution of chemical reaction species and SEI products, as shown in Fig. 5B and C. The corresponding SEI morphologies at 6 selected time frames are displayed in Fig. 5D. The diffusion rate of Li+ is slower than that of EC decomposition via R1 as the porous Li2BDC products gradually grow. As a result, Li+ ions are immediately consumed when they arrive at the SEI/electrolyte interface, leading to a concentration gradient in the electrolyte zone from 1 μs to 21.7 μs (stages I to II). This indicates that Li2BDC production is a Li+ diffusion-limited process. Despite the charge-transfer rate for the R2 pathway being slightly slower than that of R1, the formation of Li2CO3 via R2 does not occur in this stage due to limited Li+ availability as Li+ is preferentially consumed by the faster-growing R1 process. After 21.7 μs, when Li2BDC reaches its tunneling-limited thickness, additional Li+ begins to diffuse into this porous layer (stages II to III), enabling Li2BDC to react with Li+ and electrons to form Li2CO3 via R2, and the overall process still remains diffusion-limited. After ∼0.02 s, Li2CO3 can be generated inside the pores. Since direct two-electron reduction of EC to Li2CO3 via R3 has a much slower charge-transfer rate, the Li+ diffusion from the electrolyte rapidly compensates for the consumption of Li+ during the two-electron reduction of EC, which is a reaction-controlled process (stages IV to VI), as shown in Fig. 5C. In contrast to the Li+ concentration profiles, no EC-concentration gradient develops during the entire process, as shown in Fig. S5 (ESI†). From this, we conclude that the first two steps of one-electron reduction process including the electrolyte degradation to organic Li2BDC and transformation to Li2CO3 are Li+ diffusion-limited processes (stages I to III); then, the two-electron reduction reaction that directly formed dense Li2CO3 is a reaction-controlled process (stages IV to VI).
Furthermore, after 0.02 s, the Li metal surface is fully covered with SEI products and the EC can no longer be reduced due to the blocking of electron tunneling. This indicates that the initial SEI formation is completed within this short time frame, which agrees with the experimental results.7,54 Direct in situ measurements of the initial SEI formation are rather challenging, as these reactions occur very fast,55 as pointed out by Odziemkowski and Irish,7 who tracked the corrosion potential time transients of the Li-metal electrode in various electrolyte systems and indicated that the passivating reactions, which lead to SEI formation, are often completed in less than 1 second. The two-layered SEI model, with the inorganic species (LiF, Li2CO3, and Li2O) close to the electrode surface and the porous organic layer (e.g. LEDC) closer to the electrolyte, obtained from postmortem analysis, does not reveal the formation sequence and timelines of these species.56 Notably, the absence of operando tools with nanosecond-to-second temporal resolution and nanoscale chemical specificity is a well-recognized gap.3 Recently, the formation sequence obtained from gas evolution combined with other spectroscopy analysis revealed LEDC as the major product with little Li2CO3 during initial SEI formation, and LEDC eventually evolved into Li2CO3.57–60 Using isotope exchange along with in situ time-of-flight secondary ion mass spectroscopy (TOF-SIM) measurements, a bottom-up SEI growth mechanism was proposed, suggesting that the SEI components formed in the early stage (organic species) are on the outer side (electrolyte side), while those formed in the latter stage (inorganic species) are on the inner side (electrode side).61 These experimental results on the temporal and spatial evolution of SEI formation collectively support the prediction from our atomically informed phase-field model (AI-PFM). This sequence, LEDC forms first and converts into Li2CO3 near the electrode surface, is different from the CRN-kMC, which predicted that LEDC continues to grow even after Li2CO3 stops growing.31
The relative tunneling barriers play an important role in determining the SEI morphology. Higher electron-tunneling barriers led to a thinner Li2BDC layer via R1 and a Li2CO3 layer via R3 and a shorter time to reach the tunneling-limited thickness (Fig. S6A–C, ESI†). Since the tunneling barrier of the organic phase (Li2BDC) is more susceptible to factors such as porosity and electrolyte composition,50 while only varying ΔELi2BDC from 0.24 to 1.8 eV, the overall SEI formation sequence remained the same: rapid porous Li2BDC deposition via R1, partial conversion to Li2CO3 via R2, and final pore filling by Li2CO3 via two-electron EC reduction in R3. However, the bilayer morphology was only formed when ΔELi2BDC < ΔELi2CO3. Conversely, when ΔELi2BDC ≥ ΔELi2CO3, a thinner initial Li2BDC layer is ultimately fully consumed and converted to a thicker dense Li2CO3 layer, yielding a predominantly single inorganic SEI layer (Fig. S8, ESI†). These results underscore the critical role of relative tunneling barriers in determining the SEI morphology.
The effect of Li+ diffusivity on SEI growth has also been systematically examined. Increasing Li+ diffusivity in the liquid electrolyte from 10−11 m2 s−1 to 10−8 m2 s−1 significantly accelerates Li2BDC growth via R1, reducing the growth timescale from ∼10−4 s to ∼10−7 s (Fig. S9A, ESI†), with no impact on the Li2CO3 growth via R3, as it is governed by the reaction kinetics rather than diffusion (Fig. S9C, ESI†). Notably, variations in Li+ diffusivity within both solid phases have a negligible influence on both Li2BDC and Li2CO3 growth (Fig. S9B and D, ESI†), further underscoring that liquid-phase Li+ transport is the rate-limiting step for initial organic SEI formation. Additionally, Li+ diffusivity has a minimal influence on the SEI growth sequence and the resulting bilayer architecture (Fig. S10, ESI†).
We further evaluated the impact of the charge-transfer kinetic barrier (ΔG*) on SEI growth by sweeping ΔG* from 0.15 to 0.75 eV for both Li2BDC (R1) and Li2CO3 (R3). This range corresponds to a decrease in the intrinsic electron-transfer rate constant k0m from 2.08 × 1010 s−1 to 1.736 s−1. As shown in Fig. S11 (ESI†), two kinetic regimes emerge: (i) Li+-diffusion-limited region: for lower ΔG*, both SEI products reach their tunneling-limited thickness around the same time and remain largely insensitive to ΔG* and (ii) charge-transfer kinetic-limited: for higher ΔG*, the growth rates of both Li2BDC and Li2CO3 decrease exponentially with increasing ΔG*. The transition occurs at ΔG* ≈ 0.49 eV, where the calculated charge-transfer reaction rate equals the Li+ diffusion rate, delineating the shift between Li+-diffusion and electron-transfer-controlled regimes (Fig. S11C, ESI†). These results highlight variations in kinetic barriers for each reaction, and their relative relationship to Li+ diffusion rates can lead to multiple rate hierarchies among R1–R3, ultimately altering the overall SEI growth sequence and one-layer or two-layer SEI structures.
It should be clarified that our simulations focus on the initial formation of the SEI, occurring on the timescale of seconds. Although our phase-field model can simulate and demonstrate the SEI evolution from nanoseconds to seconds, this self-limiting behavior is featured only during the initial short-term growth of SEIs. Ideally, the SEI would stabilize after initial formation, preventing further Li+ consumption and electrolyte degradation, since it is electronic insulating. However, the SEI layer thickness can change during cycling and calendar aging.3 Electron leakage mechanisms through hole polaron migration,62 the formation and transport of Li-atom interstitials,63 radical species shuttling,50 as well as grain boundaries,64,65 may dominate the SEI evolution over longer timescales. Shi et al.66 reported that Li atoms can diffuse through the SEI via interstitial mechanisms, forming positive-charged Li interstitials and electrons. A continuum model20 predicted that the SEI can continue to grow to 1400 nm in 1000 days, where the neutral Li atoms carrying electrons facilitate this long-term SEI growth. Moreover, defects such as grain boundaries and heterogeneous interfaces,64 cracks, and pores67 can serve as short-circuit transport paths for electrons and other reacting species. These mechanisms lead to continuous “growth” of the SEI as the battery degrades. We intend to thoroughly investigate these possibilities in our forthcoming study with a 2-D model.
The major strength demonstrated by this model framework is its ability to resolve the spatial and temporal evolution of the SEI composition and thickness that span from nanoseconds to seconds and deconvolute the interplay among multiple physical phenomena (reactions, species transport, and electron tunneling), as well as reveal the governing factors for each electrolyte degradation process. Although this deconvolution provides insights into the governing mechanisms of electrolyte decomposition that are currently inaccessible to experimental microscopy or spectroscopy techniques, the predictions from our simulations, such as the initial SEI formation and thickness of the SEI within milliseconds and the preferential formation of inorganic vs. organic products near the Li surface, serve as testable hypotheses for future experimental studies and can guide experimentalists by identifying key mechanistic signatures to be probed indirectly through ex situ quenching or rapid-interruption experiments followed by surface analysis.
The modeling framework developed in this study is broadly extensible to other electrochemical systems beyond lithium-based batteries, owing to two central features. First, it is explicitly informed by DFT calculations, which capture the chemical changes at the electrode/electrolyte interface. Second, the model is formulated as a general multiphase, multicomponent phase-field framework capable of capturing complex couplings among interfacial reactions, species transport, and microstructural evolution. To adapt this framework to other electrochemical systems, such as sodium-ion, lithium–sulfur, or solid-state batteries, the key steps involve determining the reaction networks and corresponding parameters via DFT calculations, redefining the phase-field variables to reflect the relevant phases, and modifying the free energy functional to include new phases and reaction intermediates. Transport parameters (e.g., diffusivities and electron tunneling barriers) can be similarly updated to reflect system-specific physical properties. For instance, the same model structure can simulate Na SEI formation by introducing Na-containing decomposition reactions and products (e.g., Na2CO3 and Na2O68) and recalibrating the thermodynamic driving force and reduction kinetics accordingly. In solid-state systems, the framework can be further extended to include coupled electrochemical-mechanical effects by incorporating additional mechanical energy terms or coupling coefficients in the free energy functional, thereby enabling the simulation of multiplephase evolution at the solid–solid interface. By extending to higher dimensional simulations, it can potentially capture the detailed SEI morphology and its competition with Li stripping/plating. Combining this model with high-throughput calculations and virtual screening for materials discovery would provide data-based design guidance.
• The SEI products are considered stoichiometric compounds whose free energy only exists at their stoichiometric composition points rather than being a continuous function of composition, as shown in Fig. S12 (ESI†). Meanwhile, the electrolyte is assumed to be an ideal solution, whose realistic interaction behavior will be investigated in our future work using MD simulations or Debye–Hückel approximations. The Li metal anode is assumed to be at the left boundary of the simulation region and not explicitly simulated.
• The electric potential is assumed to be uniform within the electrolyte and the SEI. Therefore, the applied voltage is imposed, and the Poisson equation is not solved, which significantly improves numerical efficiency and stability. The electron transport within the system is assumed to be dominated by tunneling.
• To improve numerical convergence, we use linear kinetics for most of the simulations involving SEI products in this work.
• The organic Li2BDC is inherently micro-porous due to molecular disorder and low packing density. In our 1D model, porosity is represented by a fixed value rather than explicitly evolving pore structures, which is a common simplification in 1-D SEI simulations.18,22 Thus, the porous SEI layer is considered as a mixture of electrolyte and solid products. While the current framework does not incorporate dynamic porosity, it retains the ability to resolve the competitive formation, spatial distribution, and temporal evolution of major inorganic and organic SEI species.
• The evolution of the gas phase (e.g., C2H4) is neglected because it escapes from the SEI or system and does not contribute to further reactions and the SEI film.31 Their formation energies and reaction barriers are still accounted for when selecting the dominant solid-phase pathways, influencing the free energy landscape and kinetics of the phase-field model. Thus, neglecting explicit gas-phase evolution has a minimal impact on the predicted solid-state SEI growth kinetics.
• The decomposition of both lithium hexafluorophosphate (LiPF6) and the formed SEI products (i.e., Li2O) is not considered in this model. We assume that the diffusion and dissolution of primary electrolyte reduction products (Li2CO3 and Li2BDC) formed during SEI formation are ignored due to relatively low solubility.70,71
Three phases are distinguished by a set of non-conserved order parameters, in which (ϕE,ϕS1,ϕS2) = (1,0,0), (0,1,0), and (0,0,1) represent the liquid electrolyte (E), Li2CO3 (S1) and Li2BDC (S2) phases, respectively. The kinetic evolution of the primary order parameters ξ is governed by the following Allen–Cahn equations:69
![]() | (3) |
![]() | (4) |
![]() | (5) |
The total Gibbs free energy change ΔGrm and the linearized reaction rate Rm of reactions R1 to R3 can be written as follows:
![]() | (6) |
![]() | (7) |
![]() | (8) |
![]() | (9) |
![]() | (10) |
![]() | (11) |
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ee01030f |
‡ Kena Zhang and Yanzhou Ji contributed equally. |
This journal is © The Royal Society of Chemistry 2025 |