The unique polarization behavior of LiFePO 4 electrodes was investigated using mathematical simulations with a many-particle model, which have a non-monotonic potential profile for each LiFePO 4 particle, and analyzed by the active population concept. The present simulations reveal two known polarization behaviors, namely the memory effect and path dependence. Notably, a hitherto unknown polarization behavior, the so-called relaxation-induced polarization (RIP), was also identified. The memory effect requires, at a minimum, a sequential four-step operation. By comparison, RIP is triggered only by a one-step operation, namely a long rest. In effect, the polarization associated with the memory effect and RIP was caused by a reduction of the active particles in the two-phase region via relaxation during a rest. The path-dependence mechanism was attributed to kinetically inhomogeneous reactions for each particle. We further found that narrowing the particle size distribution was an effective means to reduce polarization viz. the memory effect and path dependence of LiFePO 4 electrodes. However, RIP could not be suppressed by narrowing the particle size distribution. A comprehensive understanding of these polarization behaviors with our model provides a more accurate way to estimate the state of charge in Li-ion batteries with LiFePO 4 electrodes. As a promising cathode material, LiFePO 4 has been commercialized in Li-ion batteries for power tools and electric vehicles because of its low cost, high power, and thermal stability. Unlike other current commercial cathode materials, LiFePO 4 undergoes a two-phase reaction between a Li-rich phase and a Li-poor phase with a flat potential profile during charging and discharging.1 It also shows two sloping potential regions at each limit in the Li composition (Li x FePO 4 , 0 ≤ x ≤ 1) corresponding to the solid-solution reaction regions.
2,3LiFePO 4 has been reported to exhibit a number of unique polarization behaviors, including voltage hysteresis, 4 path dependence, 5 and memory effect. 6 Voltage hysteresis refers to the phenomenon wherein the charge and discharge potentials of a LiFePO 4 electrode do not collapse even at an extremely low rate (C/1000).4 Path dependence refers to a change of polarization in the charge/discharge profiles depending on whether the previous process is charging or discharging.5 Finally, memory effect refers to an unusual polarization bump during charge/discharge, at a state of charge (SOC) where a partial charge/discharge had been terminated previously. 6 This effect has been known to be an essential issue for Ni-metal hydride (Ni-MH) batteries 7,8 and believed to be absent in Li-ion batteries.Several mathematical models have been developed to account for these unique phenomena in the electrochemical behavior of LiFePO 4 , including the shrinking-core model, 5 the resistive-reactant model, 9 and the many-particle model. 4,10 Among all these models, the manyparticle model proposed by Dreyer et al. 4 shows behavior that is consistent with all the...