Abstract
The theory is developed for the chronoamperometry of first order homogeneous catalytic chemical reaction coupled with electron transfer ($\rm{EC^{\prime}}$) on a rough electrode. We obtained a solution for the diffusion problem on an arbitrary and random topography of the electrode to generalize Danckwerts' equation. Derived equation of random electrode roughness is used for developing theory of (statistically isotropic) self-affine fractal on limited length scales. The characteristics fractal morphological parameters, viz. $D_{H}$, $\ell$ and $\ell_{\tau}$, are varied for detailed analysis of current transient. The current transient shows anomalously enhanced response for a rough electrode. Our theoretical results explain both transient and steady-state behavior of the current response under the influence of roughness. Steady-state current response depends on the rate constant, the diffusion coefficient of electroactive species and width of roughness. Finally, the theory is compared and validated with experimental data of ferrocyanide and ascorbic acid coupled system on rough Pt electrodes.
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