MATHEON-ICM WORKSHOP on Free Boundaries and Materials Modeling - Abstract
Dreyer, Wolfgang
Rechargeable lithium-ion batteries have become the most promising devices to convert chemical energy into electrical energy because they currently already offer 900 kJoule per kilogram with a maximum power of 3000 Watts per kilogram. During discharging of a lithium ion battery, the interstitial lattice sites of a small crystal are filled up with lithium atoms and these are removed from the crystal during charging. Unfortunately the voltage - charge plot exhibits a hysteretic behaviour. The characteristics of voltage against the total charge of the battery during charging is different from discharging. We show within the context of a sharp interface model that two mechanical phenomena go along with a phase transition that appears in the crystal during supply and removal of lithium atoms. For the simulation of the dynamics of the phase transitions and of the observed hysteresis we establish a new initial and boundary value problem for a nonlinear PDE system that can be reduced in a limiting case to an ODE system.