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首页> 外文期刊>The journal of physical chemistry, C. Nanomaterials and interfaces >Theory of Generalized Gerischer Admittance of Realistic Fractal Electrode
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Theory of Generalized Gerischer Admittance of Realistic Fractal Electrode

机译：分形电极的广义Gerischer导纳理论

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摘要

We developed a theory for the generalized Gerischer admittance for an irregular interface, operating under diffusion and homogeneous kinetics coupled with a fast heterogeneous charge transfer reaction. The generalized admittance expressions are obtained for a deterministic surface (viz, the exact mathematical function of roughness profile is known) as well as for a stochastic surface (viz, the statistical properties of roughness profiles are known). A roughness power spectrum or structure factor is sufficient to characterize the statistical properties of stochastic geometrical irregularities. An elegant expression for the generalized Gerischer admittance is obtained as a functional of the roughness power spectrum. This equation is applicable for fractal as well as nonfractal stochastic roughness. Realistic fractal electrodes have a fractal nature over limited length scales and possess an approximate self-affine property, which is characterized in terms of a band-limited power law function for the power spectrum. The generalized Gerischer impedance shows three frequency regimes, viz, (i) low frequency region, which has a kinetic-controlled frequency (ω) independent impedance and phase angle that follows constraint, 0 ≤ φ(ω) < 45°, (ii) anomalous power law behavior for intermediate frequency and their phase angle φ(ω) > 45° and shows an approximately constant phase angle region, and (iii) high frequency limiting Warburg impedance behavior.
机译：我们为不规则界面的广义Gerischer导纳开发了一种理论，该理论在扩散和均相动力学以及快速异质电荷转移反应下运行。对于确定性表面（即，已知粗糙度轮廓的确切数学函数）以及随机表面（即，已知粗糙度轮廓的统计特性），可以获得广义的导纳表达式。粗糙度功率谱或结构因子足以表征随机几何不规则性的统计特性。获得了广义Gerischer导纳的一个优雅表达式，作为粗糙度功率谱的函数。该方程式适用于分形和非分形随机粗糙度。现实的分形电极在有限的长度尺度上具有分形性质，并具有近似的自仿射特性，其根据功率谱的带限功率定律函数来表征。广义Gerischer阻抗显示了三个频率范围，即（i）低频区域，其具有动力学控制频率（ω）独立的阻抗和相位角遵循约束，0≤φ（ω）<45°，（ii）中频及其相角φ（ω）> 45°的异常幂定律行为，并显示出大致恒定的相角区域，以及（iii）高频极限Warburg阻抗行为。

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