Modeling Phase Separating Materials in Porous Electrodes Using Non-Equilibrium Thermodynamics

Phase separating materials are prevalent in lithium-ion batteries.  Commercial lithium-ion battery anodes typically consist of graphite, a material known to go through multiple ?stages? as the filling fraction (i.e. percentage) of lithium in the material changes.  Other phase separating materials, such as lithium iron phosphate (LFP), have gained a lot of interest due to rate and capacity improvements. 

Despite their widespread use, the behavior of phase separating materials inside batteries isn't very well known. The disappearance of voltage plateaus with increased discharge rates and the existence of a non-vanishing voltage gap in the limit of zero current are two phenomena which are not very well understood.

We present a thermodynamically consistent form of porous electrode theory.  This set of equations, derived from concentrated solution theory using non-equilibrium thermodynamics and a general reaction rate equation, is used to model phase separating materials in lithium-ion batteries.   These models demonstrate phenomena often observed in phase separating battery materials, such as a non-vanishing voltage gap, the mosaic effect, current dependent suppression of phase transformation, and porous electrode effects in phase separating materials (i.e. discrete filling). 

This model can be expanded to address a wide range of materials, including LFP and graphite, using thermodynamic models for the materials.  The kinetics, equilibrium potential, and particle dynamics are all coupled to the thermodynamics of the material.  These dynamics are then coupled to transport in the electrolyte during simulation of the cell, producing a wide variety of behavior typically observed in phase separating materials.