Multiscale Simulation of Ion Migration for Battery Systems
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Multiscale Simulation of Ion Migration for Battery Systems Christian Neuen1,2, Michael Griebel1,2 and Jan Hamaekers1 1
Fraunhofer Institute for Algorithms and Scientific Computing SCAI, Schloss Birlinghoven, 53754 Sankt Augustin, Germany 2 Institute for Numerical Simulation, Bonn University, Wegelerstr. 6, 53115 Bonn, Germany
ABSTRACT 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. INTRODUCTION Batteries are important for a variety of mobile electronic devices. Moreover, future electric cars need efficient and lightweight batteries. Therefore, there is a great demand for new and improved types of batteries, which in turn requires improved and novel materials. Batteries work due to ion migration between electrodes. Important topics include the increase of charge capacity, the maximally allowed current and a high (cycle) life time. Additional challenges are present for materials which undergo substantial volume changes depending on temperature or intercalation. Simulations are an important tool to better understand the processes in existing batteries and to derive new batteries which may be based on novel materials. To address these issues, it is necessary that basic material properties can be predicted and their respective influence on the battery performance can be evaluated. We use molecular dynamics to investigate the influence of defects and artificial nanostructures on electrode and separator materials. The microscopic particle behavior is then scaled up to macroscopic values such as chemical potential, volume changes, diffusion coefficients, etc. In this paper we present an improved method for the derivation of diffusion values. These values are then fed to the time dependent Poisson-Nernst-Planck equations in three dimensions, which in turn are numerically solved by an adaptive finite element method. In this context, special challenges appear with the strong non-linear coupling of the ions’ electric field with the ions’ charge concentration. We treat this non-linearity by a Quasi-Newton iteration with adaptive direction- and step-size-control.
Figure 1: Scheme of the scales in material design. From left to right: electron density of Ethylene Carbonate (EC), and BF4 ions in EC, ion concentration in a battery cell demonstrator.
THEORY For the molecular dynamic problem on the
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