The increasing demand for sustainable mobility challenges the industry to implement high-energy lithium-ion batteries (LIBs) that meet the long-range requirements of electric vehicles. To meet these needs, materials with higher specific energy than conventional anode materials are being increasingly adopted in LIBs. Silicon (Si), with a maximum theoretical capacity of 3579 mAh/g, offers about ten times the capacity of graphite (372 mAh/g) [1,2]. However, using pure Si as an anode material presents significant challenges. In addition to the large volume change during lithiation and delithiation, Si half-cells exhibit voltage hysteresis, prolonged relaxation times, and a changing open circuit potential (OCP) below a certain threshold value of the lower-cutoff-potential. This threshold value is considered in the literature as the crystallization voltage [3]. Electrochemical models are a powerful tool for electric vehicle manufacturers, enabling operational strategy development and early requirements management. However, conventional electrochemical models, such as the Doyle-Fuller-Newman model claim to capture the electrochemical processes of LIBs but fail to adequately explain the aforementioned phenomena for Si. For state-of-the-art Si-containing LIBs, electrochemical models primarily rely on empirical methods, such as the Plett approach, to describe cell behavior, often overlooking the possible presence of a crystalline phase [4,5].

This work aims to provide a physical multi-phase multi reaction (MSMR) model that considers the allotropic nature of Si and can capture the phenomena of hysteresis and changing delithiation OCP with changing lower-cutoff-potentials [3]. The model depicts the physical phenomena by mapping each phase of the Si including the nucleation and crystalline phase. Thereby the individual equilibrium potentials of the phases are considered. Modified Nernst equations are used to describe the individual potential of the phases, which can distinguish between electrochemical single-phase and multiphase reactions.

The results of these studies show that the MSMR approach can successfully model the hysteresis and the lower-cutoff-voltage dependent OCP change. The validation of the model was conducted with experimental studies on Si half-cells which were cycled with different lower-cutoff potentials. In the future, it is planned to further validate this approach by material science studies e.g., in-situ XRD as well as in-situ Raman, and apply the developed MSMR model for Si for Si/Gr composite anodes.