Complex Electrode Microstructure Simulations using a Smoothed Boundary Method with Adaptive Mesh Refinement

Abstract

Lithium-ion batteries have gained significant attention in the research community due to their increasing utilization in various applications for energy storage. However, the dependence of macroscopic battery performance on microscopic electrode structures is not fully understood, thus hindering a systematic, comprehensive manner of optimizing electrode performance via the microstructures. Computer simulation can serve as a powerful tool to close the knowledge gaps in our understanding of microstructure phenomena. In this work, we present a smoothed boundary method (SBM) electrochemical simulation framework with adaptive mesh refinement (AMR). This method allows the use of mesh non-conforming to the domain of interest when solving the governing equations. Therefore, the arduous tasks of generating meshes conforming to the highly complex electrode microstructures required in the conventional sharp-interface methods can be circumvented. The accuracy of the SBM approach can be significantly enhanced with AMR. The material properties of Li x Ni1/3Mn1/3Co1/3O2 from literature data are parameterized to be the input of the simulations. One-dimensional and three-dimensional simulations are utilized to study the error behavior and demonstrate this framework’s capabilities. This simulation framework can be easily adapted and extended to study a wide variety of electrode microstructure phenomena in other electrochemical systems.

Multiphysics Electrochemical Impedance Simulations of Complex Multiphase Graphite Electrodes

“…The specific capacitance ( C sp ), originating from double-layer formation, was 140 μF/cm 2 . The details of simulation implementations can be found in refs and .…”

“…As in ref , the rest of the SBM electrochemical governing equations in the simulations are normal∇ · ( ψ p κ p ∇ ϕ p ) − | ∇ ψ p | z + F r x n = 0 ∂ C normale ∂ t = 1 ψ normale normal∇ · ( ψ e D e ∇ C e ) + false| normal∇ ψ normale false| ψ normale r x n t − ν + − bold-italici normale · normal∇ t + z + ν + F …”

“…We solved the electrochemical governing equations, eqs –, to obtain the reaction current responding to the oscillating voltage loadings. With AMR, SBM can produce simulation results almost identical to those obtained from conventional simulations with body-conformal meshes . Thus, the numerical accuracy is not discussed in this article.…”

“…The surface (de)intercalation reaction (charge -transfer process) is governed by the Butler–Volmer equation r x n = k normalf C normale nobreak0em0.25em⁡ exp ( − α z + F R T [ ϕ ] e p ) − k normalb C normalp nobreak0em0.25em⁡ exp ( false( 1 − α false) z + F R T [ ϕ ] e p ) where k f and k b are the forward and backward reaction rate constants, α is the symmetry factor, R is the ideal gas constant, T is the absolute temperature, C p is the Li concentration ( C p = ρX p ), and [ϕ] e p is the electrostatic potential drop across the particle–electrolyte interface. As in refs and , the rate constants can be calculated from the exchange current density and open-circuit voltage according to k f = i 0 z + F C e ⁡ exp ⁡ ( − α z + F R T ϕ <...…”

“…To increase the simulation accuracy, octree adaptive mesh refinement (AMR) , was performed to generate the mesh systems in which fine mesh was used near the diffuse interfaces while coarse mesh was used in the particle and electrolyte bulk regions. With one level of refinement, the diffuse interface thickness was controlled to be approximately two root-level grid spacings.…”