A Discussion of the Cell Voltage during Discharge of an Intercalation Electrode for Various C-Rates Based on Non-Equilibrium Thermodynamics and Numerical Simulations

In this work we discuss the modeling procedure and validation of a non-porous intercalation half-cell during galvanostatic discharge. The modeling is based on continuum thermodynamics with non-equilibrium processes in the active intercalation particle, the electrolyte, and the common interface where the intercalation reaction occurs. The model is in detail investigated and discussed in terms of scalings of the non-equilibrium parameters, i.e. the diffusion coefficients and of the active phase and the electrolyte, conductivity and of both phases, and the exchange current density , with numerical solutions of the underlying PDE system. The current density i as well as all non-equilibrium parameters are scaled with respect to the 1-C current density of the intercalation electrode. We compute then numerically the cell voltage E as function of the capacity Q and the C-rate Ch. Within a hierarchy of approximations we provide computations of E(Q) for various scalings of the diffusion coefficients, the conductivities and the exchange current density. For the later we provide finally a discussion for possible concentration dependencies