A Semi-Empirical Aging Model for Lithium Iron Phosphate Electrode
Authors: Rajabloo Barzin , Wakem Walter , Jokar Ali , Desilets Martin , Brisard Gessie M 
Published: February 2020

First, galvanostatic performance of a pristine lithium iron phosphate (LFP) electrode is studied by introducing a variable resistance single particle model (SPM) that is verified by experimental data from a Li/LFP coin cell. The empirical variable resistance is coupled with SPM to account for the poor ionic and electrical conductivity features of LFP. This variable resistance represents two features of LFP active material: 1. The low ionic conductivity of LFP active material results in increasing the diffusion overpotential especially at the end of discharge where the larger particles participate in the intercalation/deintercalation of ions. 2. The resistive-reactant feature of this material increases the ohmic resistance where poorly coated particles (intraparticle resistance) and poorly connected particles to the matrix (interparticle resistance) play important roles at the end of discharge process.
Based on an inverse method, a Parameter Estimation (PE) process is conducted to provide the most influential electrochemical parameters of the LFP positive electrode. These parameters are the solid diffusion coefficient (Ds,p), the intercalation/deintercalation reaction-rate constant (Kp), the total electroactive area of particles (Sp), and the unknown coefficients in the cell resistance equation. In this regard, a least square function and the Genetic Algorithm (GA) are employed as the objective function and the optimizer of the inverse method, respectively.
After finding all unknown parameters for a pristine Li/LFP half-cell, the most important parameters, which change by aging, are detected from the analysis of experimental data. These data are extracted from a high-power Li/LFP coin cell built at the Laboratoire d'électrochimie interfaciale et appliquée (LÉIA) of Université de Sherbrooke. The experimental data consist of galvanostatic 1C charge/discharge curves and electrode impedance spectroscopy (EIS) of the cathode versus Li foil as the counter and reference electrode. Based on EIS, we conclude that the charge transfer and the electrolyte resistances both increase with cycling. In fact, damage made in the conductive coating around active material particles results in both decreasing reaction sites and losing active materials. Consequently, charge transfer resistance increases. A variable total electroactive area, representing the reduction in the reaction sites and the increase of the charge transfer resistance, is considered as the main parameter changed by aging. The increase of the electrolyte resistances, on the other hand, is addressed by the variable resistance, which also introduced to consider diffusion overpotential and ohmic resistance at the end of discharge process.
Comparisons between the experimental results and the model predictions show that the variable resistance SPM is able to predict the performance of LFP positive electrode. Decreasing total electroactive surface area and increasing resistivity of LFP active material are found to be the most important parameters to simulate aging phenomena in this active electrode material.

References:

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Figure: Schematic of the coated LFP active material particles and corresponding SPM for a) a pristine electrode and b) an aged electrode with higher resistivity and molar wall flux

Figure 1