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Micro-structural Roughness of Electrodes Manifesting as Temporal Fractional Order Differential Equation in Super-Capacitor Transfer Characteristics

Shantanu Das, Nimai Chand Pramanik


The observation of micro-structural roughness of electrode material of super-capacitor; returns time fractional derivative in the transfer function; this is discussed in this paper. Here we try and relate index of heterogeneity that is the exponent of power law distribution of the rough porous electrode to the order of fractional differ-integration. This treatment is not being carried out before in detail earlier. Many researches pertaining to impedance spectroscopy, report this type of phenomena; perhaps treatment of this paper will be beneficial to the mathematical physics aspect of those researches to relate microscopic disorder with fractional calculus; with this new mathematical process developed and described in this paper.


Power law distribution, fractional derivative, Poisson equation, relaxation, electrochemical double layer capacity (EDLC)

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