Based on the work by Boukamp (Boukamp, 2017), the method of Fuoss and Kirkwood (Fuoss and Kirkwood, 1941) is applied to derive an analytical distribution function of relaxation times for physics based porous electrode impedance cases. These impedance models are typically described by transcendental transfer functions. The porous electrode impedance treated here reflects a balance of the effective ionic and electronic impedances inside a porous electrode consisting of particles. Therefore, first the DFRT of the single particle interface impedance is derived. This includes treatment of charge transfer, double layer charging, solid state diffusion inside the particles, open-circuit voltage variations due to solid-state concentration, and insulating layers surrounding the particles. The resulting single particle DFRT relations are then incorporated into a mathematical description of the porous electrode DFRT. The results show that the DFRT of the porous electrode can be clearly separated into distributions of time constants corresponding to charge transfer, solid state diffusion and in case of intercalating particles, like in lithium-ion batteries, a third distribution of time constants is identified. A novelty of this work is the explicit treatment of the low-frequency capacitance and the resulting distribution of time constants in porous electrode systems. Analytical relations for the individual time constants are derived and reported. Since the ideal distribution of time constants can be represented by a series of R||C circuit elements, validation is performed by reconstruction of the impedance spectra, based on the analytical results.

基于 Boukamp (Boukamp, 2017) 的工作，应用 Fuoss 和 Kirkwood (Fuoss 和 Kirkwood, 1941) 的方法来推导基于物理的多孔电极阻抗情况的弛豫时间的分析分布函数。这些阻抗模型通常由超越传递函数来描述。此处处理的多孔电极阻抗反映了由颗粒组成的多孔电极内的有效离子阻抗和电子阻抗的平衡。因此，首先导出单粒子界面阻抗的DFRT。这包括电荷转移、双层充电、颗粒内部的固态扩散、固态浓度引起的开路电压变化以及颗粒周围的绝缘层的处理。然后将得到的单粒子 DFRT 关系合并到多孔电极 DFRT 的数学描述中。结果表明，多孔电极的 DFRT 可以清楚地分为与电荷转移、固态扩散相对应的时间常数分布，并且在嵌入粒子的情况下，如在锂离子电池中，确定了第三种时间常数分布。这项工作的新颖之处在于对低频电容的显式处理以及由此产生的多孔电极系统中的时间常数分布。导出并报告了各个时间常数的解析关系。由于时间常数的理想分布可以用一系列 R||C 电路元件来表示，因此通过重建阻抗谱来进行验证，