Mathematical Modeling of Rechargeable Batteries

该奖项支持一个关于可充电电池设计建模和分析的合作研究项目的规划。正在开发的研究项目将研究发生在新型电池材料中的动态过程。这项研究的目的是(I)扩展电池模型以包括弹性应力、界面张力和扩散以及慢电子传输；(Ii)对非线性波进行渐近和稳定性分析以及数值模拟；(Iii)研究波-缺陷相互作用作为一种新的功率损失机制；以及(Iv)模拟、分析和优化现实正极微结构中的传输。尽管在过去的几十年里，人们在应用研究上投入了大量的精力，但充电电池的性能只是逐步提高。原子模拟预测了具有更高能量密度的新材料，但几乎达到了物理极限。然而，对于电动汽车等新应用，功率密度(单位质量的充放电速率)和循环寿命必须大幅提高。这些性质由发生在更大长度和时间尺度上的动态过程控制，更适合于尚未开发的连续统或统计模型。迈向下一代可充电电池的突破性进展将需要对这种过程有新的基本理解，该领域已经成熟，可以利用应用数学做出贡献。为了满足这一需求，我们计划开展一个由电池原子模拟(CEDER)、微观结构模拟(Thornton)和电化学系统数学建模(Golovin和Bazant)专家组成的协作。该团队将建立在最近制定的电池材料相变动力学的一般连续模型和一种新的非线性波嵌入模式的基础上。

This award supports planning of a collaborative research project on modeling and analysis of designs for rechargeable batteries. The research project under development will address dynamical processes occurring in novel battery materials. The research aims to (i) extend battery models to include elastic stress, interfacial tension and diffusion, and slow electron transport; (ii) perform asymptotic and stability analyses and numerical simulations of the nonlinear waves; (iii) study wave-defect interactions, as a new mechanism for power loss; and (iv) simulate, analyze, and optimize transport in realistic cathode microstructures. While significant effort has been invested in applied research over the past few decades, the performance of rechargeable batteries has improved only incrementally. Atomistic simulations have predicted new materials with higher energy density, but the physical limit has nearly been reached. However, power density (charge/discharge rate per unit mass) and cycle life must improve drastically for new applications such as electric vehicles. These properties are governed by dynamical processes occurring on larger length and time scales, better suited for continuum or statistical models, which have not been developed. Breakthrough advances towards the next generation of rechargeable batteries will require new fundamental understanding of such processes, and the field is ripe for contributions from applied mathematics. To meet this need, we plan a collaboration consisting of experts on atomistic simulations of batteries (Ceder), microstructural simulations (Thornton), and mathematical modeling of electrochemical systems (Golovin and Bazant). The team will build on a recently-formulated general continuum model for phase-transformation dynamics in battery materials and a new mode of intercalation by nonlinear waves.