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Revealing SEI Morphology: In-Depth Analysis of a Modeling Approach

  1. Fabian Singlea,b,z,
  2. Birger Horstmanna,b,z and
  3. Arnulf Latza,b,c
  1. aGerman Aerospace Center (DLR), Institute of Engineering Thermodynamics, 70569 Stuttgart, Germany
  2. bHelmholtz Institute Ulm (HIU), 89081 Ulm, Germany
  3. cUlm University, Institute of Electrochemistry, 89069 Ulm, Germany

Abstract

In this article, we present a novel theory for the long term evolution of the solid electrolyte interphase (SEI) in lithium-ion batteries and propose novel validation measurements. Both SEI thickness and morphology are predicted by our model as we take into account two transport mechanisms, i.e., solvent diffusion in the SEI pores and charge transport in the solid SEI phase. We show that a porous SEI is created due to the interplay of these transport mechanisms. Different dual layer SEIs emerge from different electrolyte decomposition reactions. We reveal the behavior of such dual layer structures and discuss its dependence on system parameters. Model analysis enables us to interpret SEI thickness fluctuations and link them to the rate-limiting transport mechanism. Our results are general and independent of specific modeling choices, e.g., for charge transport and reduction reactions.

Keywords

In the near future, automotive and mobile applications demand power storage with large energy and power density. Currently, lithium-ion batteries (LIBs) are the technology of choice for devices with these demands. They operate at high cell potentials and offer high specific capacities while providing long lifetimes. The latter is a consequence of the stable chemistry of modern LIB systems. A significant part of this stability can be attributed to the passivation ability of the solid electrolyte interphase (SEI). This thin layer forms between the negative electrode and the electrolyte. Hence contact between these phases is prevented and the continuous reduction of electrolyte molecules is suppressed. These reduction processes occur because the operating potential of the negative electrode lies well below the stability window of the electrolyte.1 They are suppressed because reduction products quickly form the SEI during the first charge of a pristine electrode. The self passivating ability is one of the most important distinctions between a well and a badly performing lithium-ion battery chemistry. It is of such importance because the reduction reactions consume lithium-ions, directly reducing battery capacity. However, a real SEI is not perfectly passivating and electrolyte reduction is never completely suppressed. Consequently, the lifetime of a battery is directly related to the long-term passivating ability of the SEI.

Numerous studies on SEI have been conducted since Peled reported on this correlation in 1979.2 Most of these studies are experimental, investigating cycling stability as well as SEI impedance and composition. Theoretical studies are scarce in comparison, despite established methods such as DFT and DFT/MD derivatives. This can be partially explained with the chemical diversity of SEI, which has been investigated by Aurbach et al. for decades. Results are summarized in Refs. 3, 4 and include the study of SEI formation on graphite electrodes in organic solvent mixtures. The most significant finding of this time is that ethylene carbonate (EC) forms a stable SEI on graphite as opposed to propylene carbonate (PC). Another focus of early studies is the SEI composition, which has been probed by FTIR and XPS and other techniques. Lithium carbonate (Li2CO3) and lithium alkyl carbonates have been reported as products from the reduction of organic carbonates.

Studies of simplified systems, i.e., binder-free electrodes have improved our understanding of SEI composition only recently.5 This advance is also due to the use of novel experimental techniques such as solid state NMR and TEM.6,7 The focus of these studies are the standard LiPF6/organic carbonate mixtures on graphite and silicon anodes. They find that SEI in EC containing solvents is primarily composed of lithium ethylene dicarbonate ((CH2OCO2Li)2, Li2EDC). Polyethylene oxide is also found as a major product of EC reduction. Linear carbonates like dimethyl carbonate (DMC) are reduced to lithium alkyl carbonates, such as lithium methyl carbonate (CH3OCO2Li, LiMC). These compounds play a secondary role when EC is in the solvent mixture. This is linked to the solvation shell of lithium-ions which are preferably coordinated to EC.6,8 Furthermore, EC has a higher reduction potential.9 Li2CO3 is not present or only found in small quantities in recent studies.6,7,10 Its presence in several older studies is believed to correlate to water and CO2 contamination.

The electrolyte salt has a large impact on SEI composition and performance. It can shift the onset potential of SEI formation and influence the total irreversible capacity during the first cycle.10,11 In LiPF6 solutions, LiF is another major SEI compound while lithium oxyflurophosphates (LixPFyOz) are present in low quantities.12 The complex LiPF6 decomposition process is investigated by Campion and Lux.13,14

Additionally, SEI composition depends on the electrode material. Solvent decomposition reactions proceed differently on graphite and lithium storage alloys.15 Electrode materials exhibiting large volume change, i.e., silicon, fail to form a stable SEI. SEI needs to be flexible to accommodate volume changes of the underlying substrate without damage by cracking or rupture. It is believed that these properties can be, to some degree, provided by polymeric SEI compounds as found when FEC is used as solvent or additive.12 Harris and Lu16,17 show, that SEI consists of a porous outer layer and a dense inner (close the the electrode) layer by using isotope tracer and depth profiling techniques such as TOF-SIMS. Evidence for a dual-layer structure is found in the chemical composition of the film. Solid state NMR studies also suggest that SEI is at least partially porous.7

To summarize, there is a general understanding of SEI composition and morphology for few specific systems. Especially SEIs on graphite electrodes in organic solvents are studied and optimized for battery performance in several studies. This vast amount of information creates the elusive conclusion that SEI is well understood. However, several key questions about basic SEI mechanisms have yet to be answered. Most striking is the fact that the mechanism for lithium-ion transport through the SEI is still debated. Shi et al. propose a ”knock-of” diffusion mechanism for lithium-ion interstitials in Li2CO3.18 Diffusion of lithium-ions through Li2EDC is modeled by Borodin et al.19 At the same time Zhang et al. suggest that lithium-ions diffuse and migrate along boundaries between different SEI species.20 Another open question is the process of initial SEI formation where nucleation and precipitation could play an important role. Ushirogata et al. have recently suggested a “near-shore aggregation” mechanism of electrolyte decomposition products.21 This is supported by the fact that the occupation of the lithium-ion solvation shell seems to have a large impact on SEI properties,6,8 which suggests that reduction reactions occur in solution. Alternatively, solvent molecules could be reduced when adsorbed to the electrode. In this case, reduction products could attach to the electrode immediately. Finally, there is an open discussion about the mechanism driving long term SEI growth. The passivation of the SEI is not perfect and irreversible reduction reactions continue throughout the battery life.22,23 This could be enabled by several different mechanisms, for example electron leakage through the SEI. However, a porous SEI allowing slow solvent diffusion through the film is equally plausible. In this scenario, solvent molecules would reach the electrode if the SEI is porous or ruptured by the “breathing” of the underlying electrode.

The lack of information on these issues can be attributed to several reasons. The results of many common experimental techniques are to some degree ambiguous. Interpretations of FTIR and XPS spectra are difficult because many SEI compounds are similar to each other and to residual electrolyte within the sample.24 Rinsing the sample of excess electrolyte before the measurement is common, but known to selectively damage SEI. Therefore, SEI is difficult to access experimentally. Furthermore, too many variables influence SEI properties significantly, preventing a systematic investigation. Not only the solvent/salt combination but also the electrode material and its surface treatment influence SEI formation and properties.25 Formation can take place at different potentials, cycling rates and temperatures. Finally, SEI chemistry is known to be sensitive to air exposure which often occurs during sample transfer. All this makes analyzing and comparing different studies and their results difficult. Especially the identification of universal SEI properties and mechanisms becomes complicated.

Continuum theories describe SEI formation in a simplified way and elucidate such universal properties. In this way, they circumvent specifying the reaction kinetics of the SEI formation reaction. Instead, the formation rate is limited and determined by the throughput of the so called “rate-limiting” transport mechanism. These models assume one such mechanism as the cause for long-term SEI growth, i.e., electron conduction26,27 and tunneling28,29 or solvent/salt diffusion.30,31 However, independent of the assumed mechanism, all of these models predict similar long-term SEI thickness evolution. Therefore, even a successful measurement of this prediction cannot be used to confirm the underlying assumptions.

In conclusion, theoretical models based on transport through the SEI should predict additional measurable properties and dependencies. Tang et al.32 approach this task by comparing experiments with different models, each based on a single rate-limiting mechanism. Because of the dependence of SEI growth rate on electrode potential, they finally conclude that electron conduction rather than solvent diffusion is rate-limiting.

For this reason, we extend the standard approach, using two potentially rate-limiting transport mechanisms at the same time and modeling a dynamic SEI porosity. This is done in a one dimensional framework. We describe the evolution of SEI thickness and morphology along the axes perpendicular to the electrode surface. The overall objective of this work is to make new observable predictions which allow to test and validate our assumptions. Besides thickness evolution, our model can predict the formation of a porous SEI and explain several dual-layer scenarios. These results are obtained for two different rate-limiting transport mechanisms namely electron conduction and diffusion of neutral lithium interstitials. Additionally, solvent diffusion through the SEI pores can become the rate-limiting transport mechanism. In fact we can smoothly transition the rate-limiting role from the solid phase transport mechanism to solvent diffusion. This reveals an intermediate regime where both transport mechanisms influence the formation rate.

The model and its numerical implementation are discussed in the Model and Model implementation section. We then proceed to study different sets of model scenarios, in the Simulation results section. In this way, we show how measurable SEI properties depend on specific assumptions and allow their experimental verification. First, we study our reference scenario, a SEI formed by a single reduction reaction. Then, the impact of an additional SEI formation reaction is studied. This slightly more complex SEI chemistry results in the observed dual-layer structure of the SEI. At the end of the results section we evaluate the effect of material laws dictating a minimum value of the SEI porosity. We find that solvent diffusion can become the rate-limiting transport mechanism under this assumption. We conclude the Simulation results section by illustrating for which parameter set solvent diffusion in the electrolyte or charge transport in the SEI are rate-limiting. We elaborate how these mechanisms can be distinguished by experiments. Finally, we discuss and summarize our results in two dedicated sections.

Previous SectionNext Section

Model

As mentioned above, experimental studies suggest that the SEI is at least partially porous. We want to capture this property in our model. Therefore, we average the SEI density in planes parallel to the electrode surface. This results in the volume fraction profile of the SEI εSEI, as depicted in Fig. 1. Our model describes the temporal evolution of this profile within the simulation domain [0,xmax] which reaches from the electrode surface at x = 0 into the bulk electrolyte phase. We capture the local formation of each individual SEI compound i = Li2EDC, LiMC, ... which changes the corresponding volume fraction εi∂εi∂t=V¯SEIiṅi,[1]where ṅi is the production rate of SEI compound i and V¯SEIi is the corresponding partial molar volume. The total SEI volume fraction equals the sum of solid phase volume fractions εi. It is directly related to porosity ε εSEI=∑iεi,εSEI=1−ε.SEI is formed when solvent or salt species are reduced. Reduction processes are driven by local quantities such as the electronic potential and the concentration of active species. These quantities are traced within the simulation domain as they determine the reduction rates. Therefore, mass balance equations are solved for all relevant electrolyte species ∂εci∂t=−div(jM,i+jD,i+jC,i)+ṅi,[2]where div denotes the divergence, divj = ∇ · j. Migration of charged species (jM, i) and diffusion (jD, i) are the microscopic processes which transport particles inside the electrolyte. Together with convection (jC, i) they determine the evolution of ci, the concentration of electrolyte species i = EC, DMC. A source term ṅi couples the concentrations to consumption by reduction reactions, see Eq. 11. The local porosity ε appears on the left-hand side as we use porous electrode theory to describe the mass balance within the nano-porous SEI.33

Figure 1.

(a) Cross section through the graphite electrode (left, x < 0), and a SEI with dual layer structure (right, x > 0). Solvent, Li-ions and electrons are mobile species and move as indicated by the corresponding arrows. Reduction reactions (indicated red), consume these species and facilitate SEI growth. (b) SEI volume fraction gained by averaging the structure above in planes parallel to the electrode surface.

As mentioned in the introduction, SEI chemistry is complex and highly dependent on the lithium-ion battery chemistry. Our framework is capable of modeling this chemistry in detail for each system individually, however such a realization requires many parameters which are not readily available. Large amounts of parameters for transport and reaction kinetics would make the identification of qualitatively significant results difficult. We simplify SEI chemistry and consider only one or two representative reduction reactions.

Reduction reactions take place at the interface between solid SEI material and the liquid electrolyte. SEI products precipitate immediately. Furthermore, the influence of charged species within the electrolyte is simplified. We assume that the electrochemical potential of lithium-ions is in equilibrium and constant. Lithium consumption due to SEI growth does not perturb the concentration locally because Li+ mobility inside the SEI is very high compared to the rate of SEI formation. Furthermore the salt anion is neglected as an active species.

To summarize, solvent molecules are the only electrolyte species considered in our simulation. Assuming a binary mixture of solvent and co-solvent, two mass balance equations of type Eq. 2 are solved. Fickian diffusion and convection are the relevant transport processes for these species jD,i=−Di∇ci,jC,i=civ,jM,i=0,[3]where Di is the effective diffusion coefficient and v the convection velocity in the center of mass frame. One mass balance equation can be eliminated with the constitutive relation341=∑iV¯Elyteici,yielding0=∑iV¯Elytei∇ci.[4]Here, we assume that partial molar volumes V¯Elytei are constant and independent of concentration. By summing all mass balance equations (see Eq. 2) multiplied with V¯Elytei, we obtain divv=div∑iV¯ElyteiDi∇ci−∂ε∂t=V¯ElyteECdiv(DEC−DDMC)∇cEC−∂ε∂t.[5]In the second line, we applied Eq. 4 to a binary solvent mixture of EC and DMC specifically. This definition of the convection velocity ensures that all pores are filled with an incompressible electrolyte.35,36 Because v is the center of mass velocity, the diffusive mass fluxes in the electrolyte add up to zero ∑iMijD,i=0,[6]where Mi is the molar mass of solvent species i. Thus, in the binary mixture, both diffusion coefficients are related, MECDECV¯ElyteDMC=MDMCDDMCV¯ElyteEC.

In the solid SEI phase, we take a second transport mechanism into account. This mechanism needs to transport a reduced species or electrons from the electrode/SEI interface through the SEI. As discussed in the Simulation results section, our results do not depend on the specific transport mechanism chosen. This is important because several different mechanisms seem plausible. For simplicity, we use electron conduction inside the solid SEI phase in our reference case. According to Ohm’s law, the electronic current is driven by a potential gradient jE=−κ∇Φ,[7]where κ is the effective electronic conductivity, assumed equal for all SEI compounds. jE is an electron leakage current through the SEI which fuels SEI formation and is much smaller than the lithium-ion intercalation current. Charge conservation is modeled by coupling the current to the reaction rate of each individual reaction 0=−divjE+F∑jnjrj.[8]Here, njrj is the rate of electron consumption of reduction reaction j.

We consider faradaic surface reactions. Each reaction j is of the general type ∑is̃ijSi+njLi++e−→∑kskjSk,[9]where s̃ij and and sji are the stoichiometric coefficients. The sums include all electrolyte species and SEI compounds. In our simplified SEI chemistry each solvent reacts to a single SEI compound. Therefore, we use the solvent precursor as the reaction index j = EC, DMC. Reaction rates rj, see Eq. 8, are determined with symmetric Butler-Volmer expressions, see recent works by Latz and Bazant,37,38 or standard literature, e.g.,33,39rj=kBThexp−EAkBT∏icici0s̃i2sinhnjFηjRT,[10]where EA is the energy difference between the initial and the transition state.

The overpotential ηj is the driving force of reaction j and will be discussed below. Oxidation of SEI compounds is only possible at high voltages (>3.25 V, see ref. 40) which are not met in normal battery operation. Generally, anodic reactions do not occur in our simulations because we always polarize the electrode below the onset potential of SEI formation. However, we need to actively prevent anodic reactions if a second SEI compound is considered. This is achieved by using η̃j=max(0,ηj) for these reactions.

Source terms ṅi in Eqs. 1 and 2, consist of the sum over all reduction reactions ṅi=∑jsij−s̃ijρjrj,[11]where ρj is the reaction site density which depends on the type of the reaction j. It equals εj/V¯SEIj for bulk reactions in the solid SEI phase. For solvent reduction reactions which occur at the interface between solid SEI material and the liquid electrolyte, ρj equals the product ΓA, where A is the specific surface area and Γ is the surface site density. A is a function of porosity, as discussed below, while Γ is assumed constant.

SEI formation reactions

As mentioned above, every reaction considered in our model introduces additional parameters. Therefore, we simplify SEI chemistry. We study all reactions listed below in different combinations, namely I, I + II and I + III. This means we consider up to two reactions at a time.

We assume a single reduction reaction for solvent and co-solvent 2EC+2·(Li++e−)→Li2EDC+R,[I]DMC+Li++e−→LiMC+R.[II]Gaseous by-products R are neglected in our simulation, as they quickly escape the simulation domain. Given the potential Φ and the concentration of each electrolyte species, we can express the overpotential for these reactions. ηEC=ΦEC0−Φ+12RTFlncECcEC0,[12a]ηDMC=ΦDMC0−Φ+14RTFlncDMCcDMC0,[12b]where Φ0i is the reduction onset potential of solvent species i and c0i is the corresponding reference concentration.

It is known that SEI species are to some degree unstable, especially at low potentials.41 Therefore, aside from solvent molecules, SEI compounds can be reduced as well, forming new compounds and by-products. Lithium oxide (Li2O) has been reported as SEI compound which is mostly found close to the electrode surface.17,42 Therefore, we assume the formation of Li2O by successive reduction of Li2EDC410.1Li2EDC+Li++e−→0.6Li2O+0.4C,[III]where C denotes carbon. We have normalized this reaction to one lithium-ion, i.e., electron respectively. We calculate the kinetics of this reaction with Eq. 10. The overpotential of conversion reactions has no concentration contribution ηLi2EDC=ΦLi2EDC0−Φ.[13]

Solid convection

Independent of the specific conversion reaction chosen, a volume mismatch between the educts and products is typical. This volume mismatch creates an “excess volume” when the reaction is ongoing. Excess volume can be accommodated by a porosity change or by a displacement of the whole SEI such that porosity remains constant at the location of the reaction. We consider a mixture of both mechanisms by adding solid convection to the model and defining a suitable solid convection velocity ṽ. Convective fluxes need to be considered in Eq. 1, which is therefore modified ∂εi∂t=V¯SEIiṅi−divεiṽ.[14]In two extreme cases, the solid convection velocity is given as εSEIdivṽ=0,[15a]εSEIdivṽ=∑j=convΔV¯SEIjρjrj,[15b]where the sum includes all conversion reactions. ΔV¯SEIj is the excess molar volume of the reaction. When the porosity is high, volume changes of individual SEI particles do not induce solid convection, as established by Eq. 15a. In Eq. 15b, the convection velocity is defined such that SEI porosity remains unchanged locally. Therefore, the SEI expands in response to SEI formation. Such a behavior can be expected when the porosity is almost zero and SEI cannot become any denser.

We model a smooth transition from local accumulation to SEI expansion as the SEI becomes denser. The solid convection velocity is calculated from εSEIdivṽ=α(εSEI)∑j=convΔV¯SEIjρjrj,[16]where α(εSEI) models a smooth transition between Eqs. 15a and 15b. This transition is performed in a linear way α(εSEI)=0εSEI≤εSEIcrit−Δα,1εSEI≥εSEIcrit,1+εSEI−εSEIcritΔαotherwise.[17]

Here Δα is the width of the transition, chosen to be 0.1. The influence of the empirical parameter εSEIcrit on SEI formation will be studied in the Simulation results section. It is one unless mentioned otherwise. It constitutes the greatest volume fraction that the SEI material can reach. Several versions of α(εSEI), differing in the choice of this parameter are shown in Fig. 2a.

Figure 2.

(a) α(εSEI) as a function of the SEI volume fraction for εSEIcrit=0.99,0.75 and 0.5, see Eq. 17. The location of the critical value is indicated for α3(εSEI). (b) Spatial dependence of α for a given SEI volume fraction εSEI.

Transport in porous media

The local porosity ε determines the phase distribution in our simulation domain. Pure electrolyte and SEI phase are represented by ε = 1 and ε = 0, respectively. If ε is between zero and one, both electrolyte and SEI phase are present, arranged in a porous structure. As each transport mechanism is restricted to a single phase only, the corresponding transport parameters have to depend on the porosity. They decrease with the volume fraction of the phase they belong to. We use the Bruggeman ansatz to describe this behavior, i.e., we use a power law to relate these parameters at a given porosity to their bulk values. Bruggeman coefficients encode the structural information of the porous structure which is lost when averaging to obtain a one dimensional system. High values of β correspond to large tortuosity. The effective diffusion coefficient depends on the porosity Di=εβDiBulk,[18]where the Bruggeman coefficient β is a parameter in our model whose influence will be part of our study. Analogously, electron conduction scales with the SEI volume fraction κ=εSEI1.5κBulk.[19]We have chosen 1.5 as the Bruggeman coefficient for transport in the solid SEI phase because it is the standard value. Percolation effects are not considered by this description. Therefore transport through a phase remains possible until the phase disappears completely, i.e., if ε = 0 or εSEI=0.

Specific surface area

Solvent reduction and SEI formation take place at the interface between solid SEI material and the liquid electrolyte. Consequently, the source term of solvent reduction reactions is directly proportional to the specific surface area A (see Eq. 11). The specific surface area depends on the local porosity. We derive an approximation for this dependence from the assumption that SEI particles and pores are arranged on a cubic lattice with edge length a0. This parameter corresponds to the average particle and pore size of the SEI. We consider a large volume Va30 in which all sub-cubes are randomly assigned to SEI/pores with uniform probability εSEI/ε. The total surface area in V can be approximated as Atotal≈Va03·6·a02·εεSEI,[20]where Va− 30 is the number of cubes. Every cube has six surfaces, each with an area of a20. The probability of a cube being empty while a neighboring cube is filled equals the product εεSEI. Here, surfaces on the edge of V have been neglected. Then the specific surface area of V reads A=Atotal/V=6a0εεSEI.[21]We need to adjust this expression because we study porosity profiles, this means porosity changes in one direction. To this aim, we study a slice V with the thickness of a single cube a0. Now, surfaces on the edge of V can no longer be neglected and have to be taken into account. Therefore, we use the SEI volume fraction of the neighboring slices A=εa04εSEI+εSEI(x−a0)+εSEI(x+a0).Using a second order Taylor expansion for εSEI(x±a0) we find A(ε)≈6a0εεSEI+a026∂2εSEI∂x2.[22]In comparison to Eq. 21, an effective, non-local SEI volume fraction replaces the local value. This modification enables growth into the pure electrolyte phase where εSEI, and thus A according to Eq. 21, is zero.

This approximation is good, when the porosity changes slowly in space relative to a0, i.e., |∂2xε| < 2a0− 2. If ε(x) has a larger curvature, the Taylor expansion is not valid and Eq. 22 can become negative. However, these situations are averted in our simulations and the small quantitative errors do not influence our main results.

Regularization

During our simulation SEI is formed and εSEI increases. When εSEI reaches unity at a certain location, a pure SEI phase would be formed. Pure phases are numerically difficult because transport equations for the absent phase become ambiguous. To avoid such problems, we implement two regularizations.

We prevent the formation of a dense SEI with vanishing porosity. This is achieved by modifying the specific surface area such that ε < 1 − Δε is guaranteed at all times


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