The behavior of a many-particle electrode in a lithium-ion battery

We study a rechargeable lithium-ion battery that uses a many-particle FePO₄ electrode to reversibly store lithium atoms. This process is accompanied by a phase transition and charging/discharging run along different paths, so that hysteretic behavior is observed.Although there are experimental studies suggesting that the overall behavior of the battery is a many-particle effect, most authors exclusively describe the phase transition within a single particle model of the electrode.In this work, we study in detail a many-particle model for the electrode. The model is capable to describe a kind of phase transition where each individual particle of the electrode is homogeneous. It will be shown that the particles are either in the first phase or in the second phase. This phenomenon is due to the non-monotone relation between the chemical potential and the lithium mole fraction of a single particle.The pressure-radius relation of a spherical elastic rubber balloon also exhibits non-monotone behavior. In fact, a system of many interconnected balloons behaves correspondingly to an electrode consisting of many storage particles. The analogy between the two systems is important, because the predictions of the many-particle model can easily be tested with rubber balloons of macroscopic size than with an ensemble of microscopically small (FePO₄) particles.