Supercapacitors are promising electrochemical energy storage devices due to their prominent performance in rapid charging/discharging rates, long cycle life, stability, etc. Experimental measurement and theoretical prediction on charging timescale for supercapacitors often have large difference. This work develops a matched asymptotic expansion method to derive the charging dynamics of supercapacitors with porous electrodes, in which the supercapacitors are described by the stack-electrode model. Coupling leading-order solutions between every two stacks by continuity of ionic concentration and fluxes leads to an ODE system, which is a generalized equivalent circuit model for zeta potentials, with the potential-dependent nonlinear capacitance and resistance determined by physical parameters of electrolytes, e.g., specific counterion valences for asymmetric electrolytes. Linearized stability analysis on the ODE system after projection is developed to theoretically characterize the charging timescale. The derived asymptotic solutions are numerically verified. Further numerical investigations on the biexponential charging timescales demonstrate that the proposed generalized equivalent circuit model, as well as companion linearized stability analysis, can faithfully capture the charging dynamics of symmetric/asymmetric electrolytes in supercapacitors with porous electrodes.

翻译：超级电容器因其在快速充放电速率、长循环寿命、稳定性等方面的卓越性能，成为极具发展前景的电化学储能装置。然而，超级电容器充电时间尺度的实验测量与理论预测往往存在较大差异。本文发展了一种匹配渐近展开方法，用于推导多孔电极超级电容器的充电动力学，其中超级电容器采用堆叠电极模型进行描述。通过离子浓度和通量的连续性耦合相邻两个堆叠层之间的主阶解，可得到一个常微分方程组，该方程组是描述ζ电位的广义等效电路模型，其中与电位相关的非线性电容和电阻由电解质的物理参数（如非对称电解质中特定反离子价态）确定。通过对投影后常微分方程组进行线性化稳定性分析，理论上表征了充电时间尺度。本文对所推导的渐近解进行了数值验证。进一步针对双指数充电时间尺度的数值研究表明，所提出的广义等效电路模型及其伴随的线性化稳定性分析，能够准确捕捉具有多孔电极的超级电容器中对称/非对称电解质的充电动力学行为。