(556d) 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.