Barbero G
Dipartimento di Scienza Applicata del Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
Phys Chem Chem Phys. 2016 Oct 26;18(42):29537-29542. doi: 10.1039/c6cp05049b.
The derivation of Warburg's impedance presented in several books and scientific papers is reconsidered. In the past it was obtained by assuming that the total electric current across the sample is just due to the diffusion, and that the external potential applied to the electrode is responsible for an increase of the bulk density of charge described by Nernst's model. We show that these assumptions are not correct, and hence the proposed derivations are questionable. When the electrochemical impedance of a cell of an insulating material where external charges are injected of a given sign is correctly determined, in the high frequency region the real and imaginary parts do not follow the trends predicted by Warburg's impedance. The analysis presented in this paper is relevant to a symmetric cell, in the Nernstian approximation. It can be easily generalized to the case of an asymmetric cell, assuming boundary conditions where the conduction current across the electrodes is proportional to the surface electric field.
几本著作和科学论文中给出的瓦尔堡阻抗的推导过程被重新审视。过去，它是通过假设穿过样品的总电流仅由扩散引起，并且施加在电极上的外部电势导致了能斯特模型所描述的体电荷密度增加而得到的。我们表明这些假设是不正确的，因此所提出的推导是有问题的。当正确确定注入给定符号外部电荷的绝缘材料电池的电化学阻抗时，在高频区域，实部和虚部并不遵循瓦尔堡阻抗所预测的趋势。本文给出的分析适用于能斯特近似下的对称电池。假设电极间传导电流与表面电场成正比的边界条件，它可以很容易地推广到非对称电池的情况。
