The pseudo-two-dimensional (P2D) model of lithium-ion batteries couples a volume-averaged treatment of transport, reaction, and thermodynamics to solid-state lithium diffusion in electrode particles. Here we harness the linear and nonlinear physics of the P2D model to evaluate the fundamental (linear) and higher harmonic (nonlinear) response of a LiCoO₂|LiC₆ cell subject to moderate-amplitude sinusoidal current modulations. An analytic-numeric approach allows the evaluation of the linearized frequency dispersion function that represents electrochemical impedance spectroscopy (EIS) and the higher harmonic dispersion functions we call nonlinear electrochemical impedance spectroscopy (NLEIS). Base case simulations show, for the first time, the full spectrum second and third harmonic NLEIS response. The effect of kinetic, mass-transport, and thermodynamic parameters are explored. The nonlinear interactions that drive the harmonic response break some of the degeneracy found in linearized models. We show that the second harmonic is sensitive to the symmetry of the charge transfer reactions in the electrodes, whereas EIS is not. At low frequencies, NLEIS probes aspects of the cell thermodynamics that are not accessible with EIS. In short, NLEIS has the potential to increase the number of physicochemical parameters that can be assessed in experiments similar in complexity to standard EIS measurements.

中文翻译：

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扩展纽曼的伪二维锂离子电池阻抗仿真方法以包括非线性谐波响应

锂离子电池的伪二维（P2D）模型将体积平均的输运，反应和热力学处理与电极颗粒中固态锂的扩散结合在一起。在这里，我们利用P2D模型的线性和非线性物理性质来评估LiCoO ₂ | LiC ₆的基波（线性）和高次谐波（非线性）响应。电池受到中幅正弦电流调制的影响。一种解析数字方法可以评估代表电化学阻抗谱（EIS）的线性化频率色散函数，以及我们称为非线性电化学阻抗谱（NLEIS）的高次谐波色散函数。基本案例模拟首次显示了全频谱的二次谐波和三次谐波NLEIS响应。探索了动力学，传质和热力学参数的影响。驱动谐波响应的非线性相互作用打破了线性化模型中的某些简并性。我们表明，二次谐波对电极中电荷转移反应的对称性敏感，而EIS则不敏感。在低频下 NLEIS探测了EIS无法访问的电池热力学方面。简而言之，NLEIS具有增加物理化学参数数量的潜力，这些物理化学参数可以在复杂性上与标准EIS测量相似的实验中进行评估。