Theory-based Investigation of the Solid Electrolyte Interphase in Lithium-ion Systems

The primary research focus of this thesis is the Solid Electrolyte Interphase (SEI). This is a thin lm covering the surface of negative electrodes in many electrochemical cells such as modern lithium-ion batteries. The SEI has an essential protective function in the battery as it stabilises the electrode interface with the liquid electrolyte. At low potentials, pristine electrodes reduce the electrolyte and SEI is formed from solid products of these reduction reactions. Once established, SEI passivates the electrode and electrolyte reduction is mostly suppressed. However, the slow rate at which these reactions continue to proceed cause sustained SEI growth during battery life. This process leads to irreversible loss of cyclable lithium and reduces the capacity of modern lithium-ion batteries. The main part of this work is about models that describe this long-term growth. These models share the same overall objective, which is to identify the underlying mechanism responsible for this e ect. The nal part of the thesis is about an electrochemical impedance model. It predicts the impedance signal of a symmetric cell with two metal Li-electrodes that are coated with SEI layers. As a physics-based model, it is designed to improve the reliability and consistency of impedance spectra interpretation in comparison to commonly used equivalent circuits. Previous theoretic studies about long-term SEI growth are almost entirely based on the assumption of transport-limited growth. This concept considers a homogeneous surface lm and models SEI thickness evolution by assuming that the rate of the formation reaction is limited by the availability of a single precursor. aid precursor can reach the reaction interface because an unknown mechanism allows it to cross the SEI. Below, this mechanism is referred to as the long-term growth mechanism (LTGM). Prominent examples studied in previous literature include electron migration, electron tunnelling, and solvent di usion. However, each of these LTGMs results in a qualitatively similar prediction for the long-term evolution of SEI thickness. Therefore, previous studies have not been able to identify the LTGM conclusively. Only Tang et al. addressed this issue by studying multiple mechanisms and the corresponding potential dependence of SEI formation [2]. SEI growth models developed and studied in this thesis follow a similar approach. Some extend the rate-limiting idea and aim to predict additional SEI features that can be validated with experiments while others consider additional dependencies to identify the LTGM. The fi rst such model is published in Paper I. It assumes lectron conduction as the LTGM and utilises a novel continuum description of the growing SEI. This enables the model to predict SEI morphology in addition to the growth behaviour. In the basic version, the model predicts that the SEI has a non-zero porosity which is constant throughout the lm. The model shows how these pores are established by the competition between two counter-moving transport mechanisms. Paper I also reports how a dual-layer SEI can be formed when two distinct SEI formation reactions are considered. Speci cally, the model predicts that the SEI features a dense inner layer and a porous outer layer if co-solvent reduction is considered. Paper II is based on the same model and includes the theory and results of the fi rst publication. In comparison, these parts are more detailed and comprehensive. Additionally, two new model modi cations are presented. Firstly, the model is extended with solid convection to describe mechanical deformation of the SEI. This truly allows lm growth to occur at the electrode/SEI interface or within the SEI itself. In this way, the model can be used to describe SEI growth with solvent di usion acting as the LTGM as well. However, it predicts an unstable SEI growth rate if this mechanism facilitates SEI growth. The rate of solvent di using through the SEI is orders of magnitudes more sensitive to porosity uctuations of the SEI than any other mechanisms. Local porosity fuctuations occur during charge and discharge of a battery and would lead to an inhomogeneous distribution of SEI thickness. This is not observed in experiments and suggests that solvent di usion cannot be the LTGM. Secondly, Paper II is the fi rst publication that uses the di usion of neutral lithium-interstitials through the SEI as the LTGM in an SEI growth model. As suggested in previous theoretical studies, neutral lithium-interstitials exist at interstitial sites in Li2CO3 [3]. Their concentration in the solid SEI matrix depends on the potential and is multiple orders of magnitude smaller than the concentration of lithium-ions. Using lithium-interstitial di usion as the LTGM (instead of electron migration) does not result in a di erent growth behaviour of the surface layer. The mechanism also produces qualitatively similar SEI morphologies. Therefore, other SEI properties or dependencies need to be considered for conclusive identi cation of the LTGM. This approach is used in the subsequent publication, Paper III. It was inspired and enabled by a publication of Keil et al. who published a comprehensive study on capacity fade in commercial lithium-ion batteries with a long-term storage experiment [4] . They showed that capacity fade depends strongly on the state of charge (SOC) at which the battery is stored. In Paper III, the storage experiment is modelled with the assumption that long-term SEI growth is the primary degradation mechanism. The potential dependence of capacity fade produced by four di erent LTGMs is compared to experimental data. Solvent di usion shows no such dependence at all. Both electron tunnelling and electron conduction do produce a potential dependence; however, it is not consistent with the experiment. Only assuming lithium-interstitial di usion as the LTGM results in a quantitative agreement with experiment. In conclusion, the comparison suggests once again that solvent di usion cannot be the mechanism that causes long-term SEI growth. In turn, the di usion of neutral lithium-interstitials emerges as a new prominent LTGM candidate. These results motivated Paper IV, a review paper on previous and current theoretic studies on SEI. It comprehensively summarises results from multiple computational methods that have been used to study di erent aspects of the SEI. This includes results from Paper I-Paper III which are discussed in the context of other publications on this subject. In the nal part of this thesis, the focus shifts from models that describe SEI growth to models that can be used for SEI characterisation. To this aim, an impedance model for a symmetric lithium cell with planar electrodes has been developed. Both lithium electrodes are covered by surface lms that are considered by the model. The model is published in Paper V and features two improvements over other similar models. Firstly, it is based on a comprehensive theory of lithium-ion transport in the SEI and the electrolyte phase. The theory uses a well-de ned set of transport parameters and considers convection with the centre-of-mass reference frame. Secondly, the model is fully analytical and reveals the complete parameter dependence of the complex impedance signal. Measurements by Wohde et al. [5] are used for model validation. With this experiment, parameter identi cation is not completely unambiguous because individual impedance features overlap. This is a common problem for electrochemical impedance measurements of complex systems. Nonetheless, the model suggests that lithium-ion transport through the SEI has a transference number of nearly one. Therefore, lithium-ion transport in the SEI has solid electrolyte character and is most likely facilitated by the solid phase of the SEI. The full potential of the model could be utilised with a well-tailored experiment, e.g., by designing the system such that the overlap of di erent resonances is minimised. Apart from these results, the impedance model also reveals the complex parameter dependence of the nite-length Warburg impedance, which is produced at very low frequencies in the symmetric cell. This complexity emerges at high salt concentration and necessitates the consideration of convection in the electrolyte. Convective motion must be described with a well-de ned reference frame and all transport parameters must be adapted accordingly. In this context, the model is suited for consistent determination of electrolyte transport parameters in a complete theoretical framework