Silicon, as a potential anode material, has a theoretical specific capacity of approximately 4200 mAh/g, more than ten times higher than the 372 mAh/g of graphite-based anodes. Its industrialization will significantly improve battery capacity. However, the main problems with silicon materials are: 1. Volume expansion of 300%-400% during charging and discharging; 2. High irreversible capacity and low coulombic efficiency leading to actual capacity loss and poor cycle life. When alloyed with lithium, the volume of silicon crystals changes significantly. This volume effect easily causes silicon anode materials to pulverize and peel off from the current collector. Furthermore, the peeling caused by the silicon volume effect leads to repeated damage and reconstruction of the SEI (Sediment Injection Layer), increasing lithium-ion consumption and ultimately affecting battery capacity. Currently, these problems are being addressed through silicon powder nano-sizing, silicon-carbon coating and doping, and binder optimization.
From an engineering perspective, improving battery energy density requires controlling the total mass of the electrode or battery. The electrode mass includes the active material, the liquid electrolyte filling the electrode pores, binders and conductive additives, and the current collector. Therefore, the energy density of an electrode depends on the mass ratio of active to inactive materials. Common techniques for improving the energy density of porous electrodes include increasing electrode thickness (active material/current collector ratio) and reducing porosity (electrolyte/active material ratio). However, due to limitations in lithium-ion transport within the electrode, both increasing electrode thickness and decreasing porosity reduce battery power density. Furthermore, the mixing ratio with the graphite anode affects the capacity and average volume expansion of the composite electrode. Therefore, optimizing these design parameters is crucial for developing high-energy, high-power lithium-ion batteries.
Heubner et al. considered the mixing ratio of silicon and graphite and the volume expansion of the materials to determine the optimization design criteria for silicon-based porous electrodes. They defined a "deformation threshold": due to the volume expansion of the silicon anode, the original pores in the electrode are filled, reducing the porosity. To avoid severe deformation and stress caused by electrode particle contact during charging, and to prevent a sharp drop in porosity, a minimum initial porosity exists for the electrode. The porosity must be greater than this value during electrode design. Furthermore, a "rate current threshold" was defined to ensure that the diffusion-limited current is not lower than the required rate current, thereby avoiding a significant reduction in capacity during fast charging. The impact of these design criteria on the performance parameters of the silicon-based anode was analyzed, and the derived criterion relationships were used to optimize the electrode design parameters to ensure electrode energy density and power density.
1. Porosity
The porosity ε0 of a lithium-ion battery electrode can be expressed by equation (1):
(1) Vi is the volume of each solid phase component in the electrode, including silicon (Si), graphite (C), binder (B), and conductive agent (A). V is the overall volume of the electrode coating. Assuming that the volume change of each solid phase component is linear between SOC=0 and SOC=1, and the expansion volume of each phase is ni times the initial value (the volume expansion of silicon, graphite, conductive agent, and binder are nSi=3, nC=0.1, nA=0, and nB=0, respectively), considering this volume expansion, the electrode porosity ε(soc) under different SOC states is given by equation (2):
(2) Assuming that the overall expansion of the battery is limited to ns times (e.g., 10%) under the constraint of the battery outer packaging shell, substituting the true density ρi of each solid phase (the densities of silicon, graphite, conductive agent, binder and electrolyte are ρSi=2336, ρC=2200, ρA=2200, ρB=1800, ρCC=8920, ρel=1500 respectively) and mass percentage ωi, we obtain equation (3):
(3) According to formula (3), for electrodes with different initial porosities, the relationship between electrode porosity and SOC during lithiation is shown in Figure 1a, and Figure 1b is a schematic diagram of the corresponding microstructure changes (assuming the overall electrode expansion is limited to ns=10%). With increasing SOC, the porosity decreases significantly. When the initial porosity is in the range of 20-40% (typical porosity of commercial graphite electrodes), the porosity of the silicon-based electrode will rapidly drop to zero during charging. This process causes enormous mechanical stress inside the electrode, leading to silicon pulverization, electrical contact failure, etc., resulting in capacity decay. With moderate initial porosity (50-70%), the reduction in porosity is not as significant. However, to maintain electrode porosity above 80% when SOC=1, it is necessary to prevent it from dropping to 0.
Figure 2a shows the relationship between porosity and initial porosity of electrodes in the SOC=1 lithiation state under different silicon contents. Increasing silicon content leads to a denser electrode after lithiation. For pure graphite electrodes, the graphite volume expands by 10%. If the electrode volume change is limited to 10%, the porosity remains unchanged after lithiation. Figure 2b shows the relationship between porosity and initial porosity of three electrodes with different silicon contents in the SOC=1 lithiation state under different overall electrode volume change limits (0%, 10%, and 20%). The smaller the overall electrode volume change limit, the smaller the decrease in electrode porosity after lithiation.
2. Li distribution in the electrolyte
In the lithiation reaction, lithium ions are inserted from the electrolyte into the active material, and the lithium concentration in the electrolyte decreases in the pores of the electrode. A concentration gradient is formed across the entire electrode, causing lithium to diffuse towards the negative electrode. If the lithium concentration in the electrolyte drops to zero, the lithium insertion reaction stops. Therefore, the maximum achievable current, the so-called limiting diffusion current jlim, can be expressed as Equation (4), while the effective diffusion coefficient is related to the porosity.
(4) Figure 3 is a schematic diagram of the lithium concentration distribution in the electrolyte during constant current charging under different porosities. (a) Under high porosity, the transport of lithium in the electrode is sufficient to make the lithium concentration in the electrolyte close to the initial value. (b) As the porosity is reduced, the lithium ion concentration in the electrolyte gradually decreases, forming a concentration gradient. (c) If the porosity is further reduced, the lithium concentration inside the electrode approaches 0. (d) At very low porosity, the lithium concentration in the entire electrode rapidly decreases to zero.
Figure 4 shows the evolution of the diffusion-limiting current rate during lithiation under different initial porosities. The rate performance decreases with increasing SOC. For example, at an initial porosity ε0 = 80%, the maximum diffusion-limited current of the electrode is 9.6C when SOC = 0, while it is approximately 0.85C when SOC = 1.
Figure 5 shows the relationship between diffusion-limited rate and initial porosity for different electrode thicknesses and silicon contents. Rate performance improves with increasing initial porosity. At a given initial porosity, the diffusion-limited current decreases with increasing electrode thickness. Electrodes that are particularly thick or have very small pores are typically diffusion-limited, with the maximum charge/discharge rate decreasing sharply at SOC=1. Furthermore, increasing the graphite content in the composite material can significantly improve the rate performance of the electrode.
Conclusion: Considering the significant volume expansion effect of silicon anodes, the porosity of the electrode decreases and the stress between particles increases during the expansion process, leading to pulverization. Therefore, for silicon-carbon anodes, the battery electrode design should have a higher porosity than that of graphite anodes.
