  Cycle life is critically important in applications of rechargeable batteries,
but lifetime prediction is mostly based on empirical trends, rather than
mathematical models. In practical lithium-ion batteries, capacity fade occurs
over thousands of cycles, limited by slow electrochemical processes, such as
the formation of a solid-electrolyte interphase (SEI) in the negative
electrode, which compete with reversible lithium intercalation. Focusing on SEI
growth as the canonical degradation mechanism, we show that a simple
single-particle model can accurately explain experimentally observed capacity
fade in commercial cells with graphite anodes, and predict future fade based on
limited accelerated aging data for short times and elevated temperatures. The
theory is extended to porous electrodes, predicting that SEI growth is
essentially homogeneous throughout the electrode, even at high rates. The
lifetime distribution for a sample of batteries is found to be consistent with
Gaussian statistics, as predicted by the single-particle model. We also extend
the theory to rapidly degrading anodes, such as nanostructured silicon, which
exhibit large expansion on ion intercalation. In such cases, large area changes
during cycling promote SEI loss and faster SEI growth. Our simple models are
able to accurately fit a variety of published experimental data for graphite
and silicon anodes.
