Multi-Physics Modeling of Lithium-Ion Battery Electrodes

Abstract

Lithium-ion batteries (LIBs) dominated the market due to their relatively high energy/power density, and long cycle life. However, a multitude of factors need to be addressed which have hindered further development of LIBs such as limited current density and safety issues. One of the effective methodologies to enhance the LIBs energy/power density is to employ alloy-based anode materials with higher theoretical capacity compared with graphite which is the common anode active material in LIBs. For instance, silicon has approximately ten times more capacity than graphite; however, intrinsic issues of silicon, such as high volume change during cycling and an unstable solid-electrolyte interphase (SEI) layer, lead to poor cyclability and cell degradation. One of the common strategies to alleviate the aforementioned silicon challenges is to use a composite graphite/silicon electrode. On one hand, experimental design and optimization of composite electrodes can be time-consuming, and in some cases, such as measuring stress evolution at the particle level of composite electrodes, unfeasible. On the other hand, incorporating multi-physics simulation can shed light on the chemo-mechanical behavior of composite electrodes and provide invaluable insights regarding lithiation-induced stress evolution and ultimately pave the path toward design and optimization of composite electrodes. Moreover, one of the main drawbacks of LIBs is safety concerns because of flammable liquid electrolytes. All-solid-state lithium-ion batteries (ASSBs) are a safer alternative to the conventional liquid electrolyte LIBs. ASSBs are based on utilizing a solid electrolyte to eliminate safety concerns such as thermal runaway and leakage of flammable liquid electrolytes. Additionally, the solid electrolyte can facilitate using high-capacity anode active materials, such as silicon and lithium plate, by inhibiting lithium dendrite formation and suppressing silicon volume expansion during the battery operation. Despite the clear advantages of ASSBs, critical challenges hinder their widespread application, including poor solid electrolyte/solid active material interfacial contact, low ionic conductivity of solid electrolytes, and poor electrochemical stability. Solid electrolyte/active material (SE/AM) interface adversly affects the performance of the ASSBs. Since the two solid phases are not perfectly in contact with each other, void spaces block the ion pathways at the SE/AM interface. Moreover, due to the solid/solid nature of this interface, lithiation-induced stress during the battery operation can cause stress peak points at the interface which leads to crack propagation within the solid electrolyte, loss of contact, and subsequently capacity fade and mechanical degradation. Therefore, ASSB microstructural investigation can enlighten the multi-physics behavior of ASSBs. Using electrode imaging techniques, such as focused ion beam-scanning electron microscopy (FIB-SEM) and X-ray computed tomography (XCT), can accurately capture the microstructures of electrodes. In particular, the XCT method is non-destructive and can provide a quantitative analysis of the electrode morphology such as particle and pore size distribution, porosity, and surface area. Moreover, the XCT reconstructed morphology can be adopted as the multi-physics simulation domain. The modeling framework in this study is comprised of an electrochemical model including conservation of mass/charge and a solid mechanics model based on the thermal-mass analogy to obtain lithiation-induced stress within the electrode microstructure. The presented work aims to adopt the 3D reconstructed morphology of the electrode to study the physical, mechanical, and electrochemical properties of LIBs. In the first study, a multiscale framework was developed and validated for a composite graphite/silicon electrode. The model is an electrochemical-solid mechanics integration used to estimate the composite electrode performance, silicon deformation, and stress evolution. The effects of silicon percentage and current on cell performance, hydrostatic stress, lithium concentration, and deformation are investigated. Considering the effect of stress on the lithium chemical potential within silicon particles in microscale modeling can shed light on the formation of a lithium concentration gradient due to the stress, and thus can enhance the composite electrode model accuracy. Moreover, physical constraints can cause the co-existence of compressive and tensile stress, while lithiation-induced stress inside the silicon particles retard the lithiation process. In fact, lithiation retardation would form a core-shell structure that comprises a lithiated shell and an unlithiated core with an incompatible strain at the interface, causing higher von Mises stress. Physical constraints highly affect the hydrostatic stress formation in silicon particles and may impact the cell life cycle due to the anisotropic swelling of particles. The developed methodology is compatible with different composite electrodes, considers the effect of active material expansion/contraction, and can pave the path for developing physics-based battery state estimation models for composite Si-based electrodes. In the second study, a synchrotron transmission X-ray microscopy tomography system has been utilized to reconstruct the 3D morphology of ASSB electrodes. The electrode was fabricated with a mixture of Li(Ni1/3Mn1/3Co1/3)O2, Li1.3Ti1.7Al0.3(PO4)3, and super-P. For the first time, a 3D numerical multi-physics model was developed to simulate the galvanostatic discharge performance of an ASSB, elucidating the spatial distribution of physical and electrochemical properties inside the electrode microstructure. The 3D model shows a wide distribution of electrochemical properties in the solid electrolyte and the active material which might have a negative effect on ASSB performance. The results show that at high current rates, the void space hinders the ions’ movement and causes local inhomogeneity in the lithium-ion distribution. The simulation results for electrodes fabricated under two pressing pressures reveal that higher pressure decreases the void spaces, leading to a more uniform distribution of lithium-ions in the SE due to more facile lithium-ion transport. The approach in this study is a key step moving forward in the design of 3D ASSBs and sheds light on the physical and electrochemical property distribution in the solid electrolyte, active material, and their interface. In the last study, a chemo-mechanical model was developed for the ASSBs’ composite electrode using the reconstructed morphologies in the second study. This study aimed to shed light on the effects of the electrode microstructure and solid electrolyte/active material interface on the stress evolution during the battery operation. The simulation results show that active material particles encounter compressive hydrostatic stress up to 4 GPa at the solid electrolyte/active material interface during lithiation while solid electrolyte limits their expansion. While, void spaces can partially accommodate active material volume expansion, and areas near void spaces have tensile stress within the range of 0-1 Gpa. Therefore, the electrode with the higher external pressing pressure experiences a relatively higher hydrostatic stress due to a higher solid electrolyte/active material interface and less void space volume fraction. In other words, although increasing the external pressing pressure may alleviate contact resistances and improve the ion pathways, it can intensify lithiation induced stress within the electrode microstructure and causes fracture formation, contact loss, and mechanical degradation. For instance, at the end of lithiation, the von Mises stress in the active material particles is approximately zero while at the surface, AM confronts up to 4.9 GPa stress and the average von Mises stress within the microstructure with higher pressing pressure is 2.4 GPa compared to 1.5 GPa. Thus, microstructural investigation of ASSBs is critical to find an optimal design to maximize the ion pathways and limit the stress evolution within an acceptable range. Integrating the developed multi-physics models with data-driven methods can decrease the computational cost and leads to a holistic modeling framework for LIBs. Incorporating the self-learning feature of data-driven methods can mimic the experimental performance of batteries and predict the behavior of batteries with high fidelity.