Cyclic voltammetry (CV) is widely used to study Li ion batteries. Most explanations of CV experiments, however, are based on traditional electrochemical kinetic models of all reactive species in electrolytes, possibly leading to non-physical lithium accumulation on electrode surfaces due to several orders of difference in magnitude between Li⁺ diffusion coefficients in electrode and electrolyte. Here, by considering size-effects of electrodes, we show that analytic expressions of the peak current density I_p of CV can be derived by combining Nernst diffusion layer model with conservation law of matter, leaving the coefficients of the analytic expressions undetermined. We then develop a complex model by considering the maximum stoichiometric intercalation sites (MSIS) of Li⁺ in electrode and name it as the MSIS model. Numerical simulations of the MSIS model on three shapes of electrodes confirm the validity of the analytic expressions, and the coefficients in the analytic expressions are determined from simulations. The plots of log(I_p) versus log(v) with v the scan rate show split lines, each of which can be further divided into low and high scan rate regions with two distinguished slopes, while the plots are always a single straight line in the MSIS-free model without the consideration of MSIS. The MSIS model and the present analytic and simulation results may provide a tool to characterize the MSIS effect and the Li⁺ diffusion coefficient in an electrode in experiments.

循环伏安法 (CV) 被广泛用于研究锂离子电池。然而，对 CV 实验的大多数解释都是基于电解质中所有活性物质的传统电化学动力学模型，由于电极和电解质中Li ⁺扩散系数之间存在几个数量级的差异，可能导致电极表面上的非物理锂积累. 在这里，通过考虑电极的尺寸效应，我们表明，通过将能斯特扩散层模型与物质守恒定律相结合，可以导出 CV峰值电流密度I _p的解析表达式，而解析表达式的系数未确定。然后，我们通过考虑 Li 的最大化学计量嵌入位点 (MSIS) 来开发一个复杂的模型⁺在电极中并将其命名为 MSIS 模型。MSIS模型在三种电极形状上的数值模拟证实了解析表达式的有效性，解析表达式中的系数由仿真确定。log( I _p ) 与 log( v ) 的图，v为扫描速率，显示了分割线，每条分割线都可以进一步分为具有两个不同斜率的低扫描率区域和高扫描率区域，而这些图始终是一条直线在不考虑 MSIS 的无 MSIS 模型中。MSIS 模型和目前的分析和模拟结果可以提供一种工具来表征实验中电极中的 MSIS 效应和 Li ⁺扩散系数。