Microscale Half-Cell Modeling of NMC and Graphite Electrodes
Authors: Usseglio-Viretta François Laurent Emilien , Graf Peter , Colclasure Andrew , Smith Kandler 
Published: February 2020

Performance of lithium-ion batteries (LIBs) is strongly influenced by the porous microstructure of their electrodes. Macro-homogeneous models are often used to predict LIB performance, albeit under restrictive limiting assumptions. Based upon porous electrode theory, macro models abstract the microstructure heterogeneity through effective parameters, which are a simplification of the actual complex electrode geometry. The typical 1D macro-homogenous model provides an approximation of heterogeneity in the electrode through-plane direction. The macro model cannot describe heterogeneity in the electrode in-plane direction. This lack of description prevents the macro model from accurately predicting degradation phenomena, such as lithium plating, especially at high C-rate and/or for thick electrodes for which significant in-plane variations of the volume (concentration and potential) and surface (Faraday current, overpotential and potential jump) fields are expected.
In this work, a finite element electrochemical microscale model is developed with the solver FEniCS (1) to calculate the concentration and potential fields of half-cell domains. The micromodel is first applied to a sphere-based numerically generated microstructure and its results compared with those of a macro-homogenous model in order to assess its validity. Positive NMC532 and negative graphite calendered electrodes, whose geometries have been obtained through X-ray tomography, are then used with the micromodel (cf. fig. 1). Prior to the simulation, the size of each electrodes’ representative volume element (RVE) is determined through the characterization of microstructure parameters usually employed in macromodels (porosity, particle size, specific surface area and tortuosity). This preliminary analysis allows determining the size of the electrode domain to analyze with the micromodel, as a RVE for the microstructure parameters is likely to be also a RVE for the electrochemical response of the electrode. A volumetric half-cell mesh is generated using the open-source Iso2mesh (2) Matlab toolbox, which allows to enforce a smooth active interface and to control the mesh density. This last feature is required to reduce the number of degree of freedom while preserving a fine resolution at the interface necessary to handle the local high gradients. Lastly, the separator domain of the half-cell model is considered as a homogenous medium with effective parameters taken from the literature.
Significant in-plane heterogeneities during charge are found especially for the tortuous graphite which exhibits poor electrolyte diffusion. Furthermore, local geometric features of the microstructure (such as tightening) appear to be over-utilized during charge (i.e. the local Faraday current has been found above its mean value), indicating an irregular surface is detrimental in regards with electrode degradation. In addition to the tomographic-imaged electrodes, several virtual geometries are numerically generated to analyze the effect of specific microstructure geometric features on the electrochemical response. It is found that, while the applied current enforces the overall slope of through-plane electrochemical concentrations and potentials, local microstructure features also cause significant local heterogeneity in electrochemical fields. The analysis provides valuable insight for future microstructure geometry optimization.
(1) M. S. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, and G. N. Wells, Archive of Numerical Software, 3 (100), 9–23 (2015).
(2) A. P. Tran and Q. Fang, Fast and high-quality tetrahedral mesh generation from neuroanatomical scans,2017 http://iso2mesh.sourceforge.net/cgi-bin/index.cgi?Home

Figure 1