Smoothed Boundary Method Framework for Electrochemical Simulation of Li-ion Battery Cathode with Complex Microstructure: Model, Formulation and Parameterization

Abstract

Rechargeable battery electrodes have highly complex microstructures, consisting of nonuniform electrode particles, tortuous electrolyte channels, and irregular particle-electrolyte interfaces. Moreover, the electrochemical processes involve several coupled physical mechanisms, including mass transport in the electrode particles and electrolyte, current continuity in the solid and liquid, and electrochemical surface reactions. These geometric and mechanistic complexities create a challenging barrier of electrochemical simulations at the microstructural level using conventional methods. In this paper, we introduce a smoothed-boundary method (SBM) electrochemical simulation framework for modeling the electrochemical dynamics of complex battery electrode microstructures. The conventional governing equations are reformulated into SBM versions, and are solved using uniform Cartesian grids. The simulations utilize an image-based, experimentally reconstructed 3D microstructure as the input geometry, and the physical parameters acquired from experimental measurements. Two models of lithiation mechanisms, solid-solution and two-phase, are examined under potentiostatic discharging of a Li$_x$CoO$_2$ composite cathode. Detailed dynamics of the complex cathode microstructure are revealed through the simulations. The comparison between the two models indicates that modeling two-phase lithiation with Fick's diffusion will overestimate the electrode's performance. The presented simulation framework provides an innovative avenue in exploring the electrochemical dynamics at the microstructural level.

Figures (8)

• Figure 1: \ref{['FIB-SEM-1']} Image of the sample in the FIB-SEM experiment. The inset shows the cross section on the FIB milling plane. \ref{['Stacking-1']} Schematic illustration of stacking cross-sectional images of the cathode sample. \ref{['LCO-CSample-1']} Reconstructed composite cathode microstructure, where the yellow and blue phases are Li$_x$CoO$_2$ and carbon additive particles, respectively.
• Figure 2: \ref{['LCO-OCV-1']} Open-circuit voltage of a Li/Li$_x$CoO$_2$ cell based on the data reported in Ref. Bouwman:2002Thesis. \ref{['LCO-Chm-1']} Bulk chemical potential ($\mu_\text{b} = \mu^0 - \text{e} \Phi_\text{OCV}$) of Li in Li$_x$CoO$_2$ with respect to a reference value of $\mu^0=3.9$ V. \ref{['LCO-Chm-2']} Magnified view of Li chemical potential in the two-phase regime, $0.75 < X_\text{p} < 0.95$.
• Figure 3: \ref{['LCO-Dfsvt-1']} Li diffusivity in the solid-solution regime in Li$_x$CoO$_2$ crystal based on the data reported in Ref. Xia:2006A. \ref{['LCO-Mblt-1']} Li transport mobility: black represents the solid-solution regimes, and red represents the two-phase regime. \ref{['LCO-GrdCff-1']} Gradient energy coefficient used in the phase field simulations. \ref{['LCO-Cndctvt-1']} Electronic conductivity of Li$_x$CoO$_2$.
• Figure 4: Exchange current density for Li$_x$CoO$_2$ thin film as a function of the \ref{['i0-OCV-1']} equilibrium potential and \ref{['i0-Xp-1']} Li occupancy fraction based on the data reported in Ref. Bouwman:2002ThesisBouwman:2002A. Reaction rate constants for \ref{['KfKb-Cn-1']} the conventional Butler-Volmer equation calculated according to Eq. \ref{['ReacCnst-1']} and for \ref{['KfKb-Act-1']} the modified Butler-Volmer equation according to Eq. \ref{['ReacCnst-2']}.
• Figure 5: \ref{['LCO-Cell-Asem-1']} The virtual cell used in the simulations, where the semitransparent gray slab is the Li anode and the dark brown slab is the current collector. The empty space between the anode and cathode serves as the separator in the cell. \ref{['LIQ-Cell-Asem-1']} The electrolyte phase in the cell. The unit of length is $\mu$m.