Population effects driving active material degradation in intercalation electrodes.

In battery modeling, the electrode is discretized at the macroscopic scale with a single representative particle in each volume. This lacks the accurate physics to describe interparticle interactions in electrodes. To remedy this, we formulate a model that describes the evolution of degradation of a population of battery active material particles using ideas in population genetics of fitness evolution, where the state of a system depends on the health of each particle that contributes to the system. With the fitness formulation, the model incorporates effects of particle size and heterogeneous degradation effects which accumulate in the particles as the battery is cycled, accounting for different active material degradation mechanisms. At the particle scale, degradation progresses nonuniformly across the population of active particles, observed from the autocatalytic relationship between fitness and degradation. Electrode-level degradation is formed from various contributions of the particle-level degradation, especially from smaller particles. It is shown that specific mechanisms of particle-level degradation can be associated with characteristic signatures in the capacity-loss and voltage profiles. Conversely, certain features in the electrode-level phenomena can also provide insight into the relative importance of different particle-level degradation mechanisms.