A Classical Newman-Type Model for Pure-Silicon Anodes
Authors: Durdel Axel , Friedrich Sven , Hüsken Lukas , Jossen Andreas 
Published: July 2022

Due to its high gravimetric and volumetric capacity, silicon is a promising candidate as a new anode material for lithium-ion batteries. In studies over the last two decades, silicon has been investigated in various designs such as silicon nanowires, silicon thin films, silicon wafers, or silicon nanoparticles. Silicon is also found in commercially available cells, both as a pure-silicon anode as well as a silicon-graphite composite anode.
In addition to experiments, lithium-ion batteries containing conventional anode materials like graphite as well as novel anode materials like silicon are also studied simulatively. Various modeling approaches for lithium-ion batteries can be found in the literature. Focusing only on physicochemical approaches, the Newman model and its variations are the most widely used for conventional material combinations. However, the literature does not provide any physicochemical modeling approach tailored specifically to alloying reactions that provides the same insight into the battery as the Newman model does. Thus, the question arises whether classical models such as the Newman model can also be applied to lithium-ion batteries with pure-silicon anodes.
To examine whether the Newman model can provide accurate results even for pure-silicon anodes, we parameterized a classical Newman model for a lithium-ion battery with a pure-silicon anode and a nickel cobalt aluminum oxide (NCA) cathode. The silicon anode consists of 70 wt% silicon, 20 wt% graphite, and 10 wt% binders and additives. However, the graphite is considered electrochemically inactive. The parameterization is based on values from a) the electrode manufacturing process (e.g., initial porosity, coating thickness), b) measured values (e.g., open-circuit potentials), and c) literature data (e.g., exchange current density, solid-phase diffusivity). For parameterization, we used laboratory cells in CR2023 coin cell format with a capacity of about 5 mAh. The model was validated using 3 mAh Swagelok T-cells with an three-electrode setup using a lithium-metal reference as well as custom-built large-format 5 Ah multilayer pouch cells.
The simulation results of CC-CV charge and discharge processes at different current rates show good agreement with measurements with a root-mean-squared error of about 22 mV at a current rate of C/10 (see Figure a), and less than 5% deviation in discharge capacity at a current rate of 2C (see Figure b). Overall, the Newman model appears to be a viable choice for pure-silicon anodes as well. However, care must be taken in parameterization. A literature review revealed that material parameters such as the exchange current density can vary by up to 13 orders of magnitude. In addition, reconstruction of the full-cell potential via half-cell potentials is of paramount importance when using partially lithiated materials, since the degree of lithiation does not necessarily approach the 0 and 1 limits. For the deliberately partially lithiated silicon used in our study, we found the utilization to be between 0.04 and 0.31, thus, a comparison between measurements and simulations during the crystallization process in the fully lithiated state is not possible. Discharge tests with multilayer pouch cells showed that the temperature rise cannot be neglected and might become rate-limiting at even higher current rates, while the discharge capacity shows that the electrode kinetics is most likely not rate-limiting.
Since simulation studies are a cost-effective method for designing new cells, our results are of practical importance. Demonstrating that the Newman model is applicable not only to conventional intercalation materials such as graphite but also to cells containing a pure-silicon alloy material with micrometer-sized particles may encourage more researchers to simulatively explore novel electrode materials. However, in general, any model and parameterization should be validated by experiments.

Figure 1