FRG: Collaborative Research: Mathematical Modeling of Rechargeable Batteries

FRG：协作研究：可充电电池的数学建模

• 批准号: 0853488
• 负责人: Gerbrand Ceder
• 金额: $ 37.5万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-06-01 至 2012-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0853488&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Mathematical; Modeling

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The project will develop a new framework for mathematical modeling of rechargeable batteries, taking into account statistical thermodynamics, concentrated-solution reaction rates, elasticity, crystal anisotropy, stochastic effects, and composite microstructures. Existing engineering models simply fit the open circuit voltage empirically and postulate dynamics by linear diffusion of intercalated lithium, but recent experiments contradict this picture for phase-separating materials. In contrast, the team will develop robust mathematical models to predict the voltage and current response over the full range of operating conditions. The basis for modeling at the single-crystal level will be Cahn-Hilliard partial differential equations with nonlinear boundary conditions, expressing chemical-potential dependent reaction reactions. The goal will be to provide the first mathematical description of emerging high-rate materials, where phase transformations occur via nonlinear intercalation waves, coupling anisotropic diffusion and electrochemical reactions. This effort will also raise basic mathematical questions in linear and nonlinear stability, degenerate wave solutions, and numerical methods.In spite of extensive engineering over the past few decades, the performance of rechargeable batteries has improved only incrementally. Power density (charge/discharge rate per unit mass) and cycle life must still improve drastically for applications such as electric vehicles and renewable energy storage, and this will require a better fundamental understanding of how ions are inserted and extracted from porous electrodes. To meet this need, the project creates a Focused Research Group from mathematics, chemical engineering, and materials science to develop a new theoretical paradigm for Li-ion batteries. The group will guide the engineering of new ultrafast Li-ion batteries, capable of charging and discharging in seconds rather than hours, while opening fruitful directions for applied mathematics. The group will train graduate and undergraduate students and postdocs, organize annual workshops, and develop a course on mathematical modeling of electrochemical energy systems.

该奖项是根据2009年的《美国回收与再投资法》（公法111-5）资助的。该项目将考虑统计热力学，弹性反应率，弹性，晶体各向异性，定位效应和组合微型结构，为可充电电池的数学建模开发一个新的框架。现有的工程模型只是通过经验拟合开路电压，并通过线性扩散的锂锂来假定动力学，但最近的实验与相位分离的材料相矛盾。相比之下，团队将开发强大的数学模型，以预测整个操作条件范围内的电压和当前响应。在单晶水平上进行建模的基础将是具有非线性边界条件的Cahn-Hilliard部分微分方程，表达化学势依赖性反应反应。目的是提供新兴高速材料的第一个数学描述，其中相位转换是通过非线性插入波，耦合各向异性扩散和电化学反应的。这项工作还将在线性和非线性稳定性，退化波解决方案和数值方法中提出基本的数学问题。在过去的几十年中，广泛的工程中，可充电电池的性能仅逐步改善。对于电动汽车和可再生能源存储等应用，电源密度（每单位质量的充电/排放率）和循环寿命仍必须大大改善，这将需要更好地了解如何从多孔电极中插入和提取离子。为了满足这一需求，该项目创建了一个专注的研究小组，从数学，化学工程和材料科学创建了一个针对锂离子电池的新理论范式。该小组将指导新的Ultrafast锂离子电池的工程，能够在几秒钟而不是数小时内充电和排放，同时为应用数学打开富有成果的方向。该小组将培训毕业生和本科生和博士学位，组织年度研讨会，并开发有关电化学能源系统数学建模课程。