  Mathematical models of capacity fade can reduce the time and cost of
lithium-ion battery development and deployment, and growth of the
solid-electrolyte interphase (SEI) is a major source of capacity fade.
Experiments in Part I reveal nonlinear voltage dependence and strong
charge-discharge asymmetry in SEI growth on carbon black negative electrodes,
which is not captured by previous models. Here, we present a theoretical model
for the electrochemical kinetics of SEI growth coupled to lithium
intercalation, which accurately predicts experimental results with few
adjustable parameters. The key hypothesis is that the initial SEI is a mixed
ion-electron conductor, and its electronic conductivity varies approximately
with the square of the local lithium concentration, consistent with hopping
conduction of electrons along percolating networks. By including a lithium-ion
concentration dependence for the electronic conductivity in the SEI, the bulk
SEI thus modulates the overpotential and exchange current of the electrolyte
reduction reaction. As a result, SEI growth is promoted during lithiation but
suppressed during delithiation. This new insight establishes the fundamental
electrochemistry of SEI growth kinetics. Our model improves upon existing
models by introducing the effects of electrochemical SEI growth and its
dependence on potential, current magnitude, and current direction in predicting
capacity fade.
