Weierstraß-Institut für Angewandte Analysis und Stochastik Stochastic model for LFP-electrodes

Wolfgang Dreyer, Peter Friz, Paul Gajewski, Clemens Guhlke, Mario Maurelli
2010 Mathematics Subject Classification. 35Q84, 80A22, 74N30. 2010 Physics and Astronomy Classification Scheme. 05.10.Gg, 05.70.Fh, 05.70.Ce, 82.47.Aa   unpublished
In the framework of non-equilibrium thermodynamics we derive a new model for porous electrodes. The model is applied to LiFePO 4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by surface fluctuations leading to a system of stochastic differential equations. The model is capable to derive an explicit relation between battery voltage and current that is controlled by
more » ... trolled by thermodynamic state variables. This voltage-current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltage-charge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.