Multiscale simulation of ion migration for battery systems

In this paper we describe a multi-scale approach to ion migration processes, which involves a bridging from the atomic scale to the macroscopic scale. To this end, the diffusion coefficient of a material i.e. a macroscopic physical quantity, will be appropriately determined from molecular dynamics simulations on the microscale. This way, performance predictions become possible prior to material synthesis. However, standard methods produce in general wrong results for ensemble setups which correspond to battery or capacitor applications. We introduce a novel method to derive correct values also for such problems. These values are then used in a macroscopic system of partial differential equation (Poisson-Nernst-Planck system) for the numerical simulation of ion migration in a battery.