AI 中文总结
本文基于泊松-能斯特-普朗克方程推导了含任意数量离子的理想电解质双电层电容器的阻抗，发现扩散系数不等时电荷弛豫与中性模式耦合，为混合电解质的特殊阻抗谱提供了连续介质解释。
AI 中文摘要
我推导了阻塞平面电极间含任意数量可移动离子种类的理想电解质的阻抗响应，该体系由泊松-能斯特-普朗克方程描述。通过将线性化方程变换为电荷-盐基，响应可表示为多组分扩散-迁移矩阵及其特征值/特征向量的形式。当所有扩散系数相等时，电荷模式与中性浓度子空间解耦，得到经典二元电解质的结果；相反，扩散系数不等时，电荷弛豫会与一个或多个中性组成模式耦合。对于含两种阳离子和一种阴离子的三元电解质，这种耦合会产生额外的扩散特征，并拓宽电阻区与电容区之间的过渡。本文所得结果为混合电解质呈现无法用具有平均扩散系数的简单二元电解质解释的阻抗谱，提供了最小连续介质层面的解释。
英文摘要
I derive the impedance response of an ideal electrolyte containing an arbitrary number of mobile ionic species between blocking planar electrodes, described by the Poisson--Nernst--Planck equations. By transforming the linearized equations to a charge--salt basis, the response is written in terms of a multi-component diffusion--migration matrix and its eigenvalues/eigenvectors. When all diffusivities are equal, the charge mode decouples from the neutral concentration subspace and the classical binary-electrolyte result is recovered. In contrast, unequal diffusivities couple charge relaxation to one or more neutral composition modes. For a ternary electrolyte with two cations and one anion, this coupling produces additional diffusive features and broadens the crossover between resistive and capacitive regimes. The results found in this paper provide a minimal continuum explanation for why mixed electrolytes can display impedance spectra that cannot be interpreted as a simple binary electrolyte with an averaged diffusion coefficient.
Comments9 pages, 1 figure
