Scaling analysis of mosaic phase separation in Li-ion batteries

Lithium-ion batteries charge and discharge via ion intercalation reactions that store and release energy in evolving electrochemically active regions. In common electrode materials which consist of phase-separating nanoparticles, such as lithium iron phosphate (LFP) and graphite, this process often results in heterogeneous "mosaic" patterns with evolving populations of nearly homogeneous particles. These electrode-scale heterogeneities create hotspots in current and temperature, which can drive degradation by side reactions or mechanical deformation. While mosaic phase separation has been observed experimentally using x-ray or optical microscopy, and computationally in simulations using multiphase porous electrode theory (MPET), there is still no mathematical theory to predict the relevant time scales and active population dynamics. Here, starting from a single-particle conservation equation, we develop a population scale model and use eigendecompositions to predict the transition between a stochastic regime in the spinodal gap to a deterministic regime in the solid solution regime. In the stochastic regime, a strong asymmetry in timescales is observed driven by the single-particle instability at the barrier maxima, which is validated by MPET simulations and experimental data. This transition occurs based on the predicted nonequilibrium free energy barrier, which arises from competition between process and reaction timescales of population dynamics. The theory predicts charge/discharge asymmetries in the active particle fraction due to autocatalysis at the population scale, consistent with experiments and simulations [Y. Li et al., Nat. Mater. 13, 1149 (2014)1476-112210.1038/nmat4084, K. Xiang et al., Chem. Mater. 30, 4216 (2018)0897-475610.1021/acs.chemmater.7b05407].