Bates J B, Chu Y T
Solid State Division, Oak Ridge National Laboratory, TN 37830.
Ann Biomed Eng. 1992;20(3):349-62. doi: 10.1007/BF02368536.
The impedance of the junction between a solid or aqueous electrolyte and a metal electrode at which no charge transfer processes occur (blocking contacts) follows closely the constant phase angle form, Z = A(j omega)-n, over a wide frequency range, where A is a constant, and the frequency exponent n is typically in the range of 0.7 to 0.95. Several models have been proposed in which the magnitude of the frequency exponent n is related by a simple expression to the fractal dimension d of the rough electrode surface. But experiments with aqueous H2SO4 and roughened platinum and silicon electrodes show that there is no simple relationship, if any at all, between n and d when d is determined from the analysis of one dimensional surface profiles. Moreover, n is not a simple function of the average roughness of the electrode. In order to gain some insight into the effect of electrode topography and the interface impedance, a model for the response of the interface to a constant voltage pulse was constructed. This model is based on the idea that, following a pulse, locally concentrated regions of ions accumulate rapidly at the tips of large protrusions on the electrode surface which screens deeper regions of the electrode from the field driven flux of mobile ions. After this rapid charging, ions are able to reach the deeper, screened regions of the electrode by diffusion, and it is this diffusive process that gives rise to the observed t1-n dependence of the charge collected. Computer simulations, similar to the diffusion limited aggregation model, using measured profiles as fixed (non-growing) clusters, gave exponents n in good agreement with experiment.
在不发生电荷转移过程的固体或水性电解质与金属电极之间的结的阻抗（阻塞接触）在很宽的频率范围内紧密遵循常相角形式，即Z = A(jω)-n，其中A是一个常数，频率指数n通常在0.7至0.95的范围内。已经提出了几种模型，其中频率指数n的大小通过一个简单的表达式与粗糙电极表面的分形维数d相关。但是，对水性硫酸以及粗糙化的铂和硅电极进行的实验表明，当从一维表面轮廓分析确定d时，n与d之间根本不存在简单的关系（如果有的话）。此外，n不是电极平均粗糙度的简单函数。为了深入了解电极形貌和界面阻抗的影响，构建了一个界面对于恒定电压脉冲响应的模型。该模型基于这样的想法，即在脉冲之后，离子的局部集中区域会在电极表面大凸起的尖端迅速积累，从而使电极的较深区域免受移动离子的场驱动通量的影响。在这种快速充电之后，离子能够通过扩散到达电极的较深的、被屏蔽的区域，正是这种扩散过程导致了观察到的收集电荷对t1-n的依赖性。使用测量轮廓作为固定（不生长）簇的类似于扩散限制聚集模型的计算机模拟给出了与实验结果高度一致的指数n。
