A discussion of the reaction rate and the cell voltage of an intercalation electrode during discharge

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. This yields balance equations for the transport of charge and intercalated lithium in the intercalation compound, a surface reaction rate at the interface, and transport equations in the electrolyte for the concentration of lithium ions and the electrostatic potential. An expression for the measured cell voltage is then rigorously derived for a half cell with metallic lithium as counter electrode. The model is then in detail investigated and discussed in terms of scalings of the non-equilibrium parameters, i.e. the diffusion coefficients of the active phase and the electrolyte, conductivity of both phases, and the exchange current density, with numerical solutions of the underlying PDE system. The current density as well as all non-equilibrium parameters are scaled with respect to the 1-C current density of the intercalation electrode and the C-rate of discharge. Further we derive an expression for the capacity of the intercalation cell, which allows us to compute numerically the cell voltage as function of the capacity and the C-rate. Within a hierarchy of approximations of the non-equilibrium processes we provide computations of the cell voltage for various values of the diffusion coefficients, the conductivities and the exchange current density. For the later we provide finally a discussion for possible concentration dependencies and (surface) thermodynamic consistency