  Porous electrodes composed of multiphase active materials are widely used in
Li-ion batteries, but their dynamics are poorly understood. Two-phase models
are largely empirical, and no models exist for three or more phases. Using a
modified porous electrode theory based on non-equilibrium thermodynamics, we
show that experimental phase behavior can be accurately predicted from free
energy models, without artificially placing phase boundaries or fitting the
open circuit voltage. First, we simulate lithium intercalation in porous iron
phosphate, a popular two-phase cathode, and show that the zero-current voltage
gap, sloping voltage plateau and under-estimated exchange currents all result
from size-dependent nucleation and mosaic instability. Next, we simulate porous
graphite, the standard anode with three stable phases, and reproduce
experimentally observed fronts of color-changing phase transformations. These
results provide a framework for physics-based design and control for
electrochemical systems with complex thermodynamics.
