Generalization of the Anson Equation for Fractal and Nonfractal Rough Electrodes
Generalization of the Anson Equation for Fractal and Nonfractal Rough Electrodes
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DOI：
10.1016/j.electacta.2011.02.047
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发表时间：
2011-04-30
影响因子：
6.6
通讯作者：
Kant, Rama
中科院分区：
文献类型：
--
作者：
Islam, Md. Merajul;Kant, Rama
我们在确定性和随机粗糙电极/电解质界面形态下推广了Anson方程。随机粗糙电极表面用粗糙度功率谱表征。得到了表面粗糙度功率谱与电荷瞬态之间的数学关系式。用近似幂律法和高斯功率谱分别对分形电极和非分形电极的时色响应进行了详细的分析。现实的有限分形粗糙度包括以下四个形态特征：分形维数（D-H）；分形强度(u)，表示单位粗糙度波数处功率谱的大小；以及下(l)和上(l)截止长度，它们与功率谱中的截止波数有关。非分形高斯粗糙度由粗糙度的均方宽度（h(2)）和横向相关长度(a)两个形态学特征组成。这种粗糙电极的测时反应在双对数图中显示出三种时间状态。粗糙度的增加增加了电荷瞬态的大小，这在传统的Anson图中引入了非线性行为。最后，这一推广揭示了分形和非分形形态无序对势能阶跃法下能思电荷转移的计时测量的影响。(c) 2011 Elsevier Ltd.版权所有。
We have generalized the Anson equation for chronocoulometry at deterministic and randomly rough electrode/electrolyte interface morphologies. The randomly rough electrode surface is characterized by the power spectrum of roughness. An elegant mathematical formula between the surface roughness power spectrum and the charge transient is obtained. Detailed analysis of this formula is performed for the chronocoulometric response of fractal and nonfractal electrodes using an approximate power-law and Gaussian power spectra, respectively. Realistic finite fractal roughness consists of the following four morphological characteristics: fractal dimension (D-H); the strength of fractality (u), which is the magnitude of the power spectrum at the unit roughness wavenumber; and the lower (l) and upper (L) cut-off lengths, which are related to cut-off wavenumbers in the power spectrum. Nonfractal Gaussian roughness consists of two morphological characteristics, the mean square width of roughness (h(2)) and the transversal correlation length (a). The chronocoulometric response for such rough electrodes shows three time regimes in double logarithmic plots. An increase in roughness increases the magnitude of charge transients, which introduce non-linear behavior in traditional Anson plots. Finally, this generalization provides insight into the effect of fractal and nonfractal morphological disorder on the chronocoulometric measurements of Nernstian charge transfer under the potential step method. (c) 2011 Elsevier Ltd. All rights reserved.