Multiscale modeling and numerical simulations of Lithium ion battery electrodes using real microstructures

该项目的长期目标是建立一种跨学科的方法，允许对多孔电极进行模型驱动的优化。作为一个特例，我们考虑锂离子电池(Lib)的电极，这对现有的可再生能源战略具有越来越大的技术兴趣。现有技术的锂离子电池由两个多孔电极(阳极和阴极)组成，它们执行将锂存储在晶体结构内并将其提供给液体电解液的任务，液体电解液填充孔洞并充当两个电极之间的离子连接。电子连接由电极和金属集电器提供，它们充当外部电路的端子。结合精确的三维重建和电极的详细建模，可以识别限速过程并获得改善的微观结构。要实现这一目标，一个必要的前提是对电极微观结构进行定量表征，并确定其对电化学机理的影响。需要对微结构参数进行精确的量化，以执行可用于电极优化的基于模型的模拟。特别是，关于下列过程和相关参数的表征是必不可少的：(A1)电化学反应(还原和氧化)和(A2)表面与体积比和体积分数；(B1)离子和电子物种在渗滤系统中的传输以及(B2)有效传输参数(曲折度)；(C1)将锂存储在活性物质的晶体结构中以及(C2)活性粒子的分布和尺寸。最新方法的主要限制影响所有这些方面，因为它们使用简化的模型，没有达到所有物质相的所需分辨率，并且没有使用允许所需多尺度精度的数值方法。特别是，需要一种更精确的定量方法：(A3)获得所需的活动表面的近似值，(B3)定义是否可以使用有效参数以及它们需要以何种精度确定，(C3)在微观水平上实现必要的近似值。在这个项目中，我们将进行LiB电极多尺度暂态模型的推导、实现和验证，该模型将基于部分模型简化方法，该方法需要电工研究所(IWE)和数学研究所(IAM)的贡献。IWE将专注于可靠和独创的电极重建方法，模型和微结构参数的建模和量化。IAM将专注于使用高性能计算技术和新的误差估计方法进行模型降阶和数值求解的数学方法。

The long-term objective of this project is to establish an interdisciplinary method that allows the model-driven optimization of porous electrodes. As a special case we consider electrodes for Lithium-ion batteries (LIB), which are of increasing technological interest for existing renewable energy strategies. A state of the art Lithium-ion cell consists of two porous electrodes (anode and cathode) performing the tasks of storing the Lithium within the crystal structure and of providing it to the liquid electrolyte which fills the porosity and serves as an ionic connection between the two electrodes. The electronic connection is provided by the electrodes and the metallic current collectors, which serve as the terminals to an external circuit. Combining precise 3D reconstructions and detailed modeling of the electrodes, the rate limiting processes can be identified and improved microstructure can be obtained.To reach this goal one essential prerequisite is the quantitative characterization of the electrode microstructure and the determination of its influence on the electrochemical mechanisms. The precise quantification of microstructural parameters is required to perform model based simulations that can be used for electrodes optimization. In particular, the characterization with respect to the following processes and related parameters is essential: (a1) electrochemical reaction (reduction and oxidation) and (a2) surface to volume ratio and volume fractions; (b1) transport in percolating systems for ionic and electronic species and (b2) effective transport parameters (tortuosity); (c1) storing the lithium in the crystal structure of the active material and (c2) distribution and dimension of the active particles.The main limits of the state-of-the-art methods affect all these aspects, since they use simplified models, do not reach the needed resolution of all material phases, and do not use numerical methods that allow the needed multi-scale accuracy. In particular, a more precise quantitative method is needed: (a3) to obtain the required approximation of the active surface, (b3) to define whether effective parameters can be used and with which precision they need to be determined, (c3) to achieve the necessary approximation at the microscopic level. In this project we will perform the derivation, implementation and verification of a multi-scale transient model for LIB electrodes, which will be based on a method of partial model reduction that needs the contribution of the Intitut für Werkstoffe der Elektrotechnik (IWE) and Institut für Angewandte Mathematik (IAM). IWE will focus on reliable and original methods for the electrode reconstruction, the modeling and quantification of model and microstructure parameters. IAM will focus on mathematical methods for the model reduction and numerical solution using high performance computing techniques and novel error estimation approaches.