Memory Effect and Fractional Differential Dynamics in Planar Microsupercapacitors Based on Multiwalled Carbon Nanotube Arrays

Evgeny P. Kitsyuk, Renat T. Sibatov and Vyacheslav V. Svetukhin
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Evgeny P. Kitsyuk: Scientific-Manufacturing Complex “Technological Centre”, Moscow 124498, Russia
Renat T. Sibatov: Laboratory of Diffusion Processes, Ulyanovsk State University, Ulyanovsk 432017, Russia
Vyacheslav V. Svetukhin: Scientific-Manufacturing Complex “Technological Centre”, Moscow 124498, Russia

Energies, 2020, vol. 13, issue 1, 1-14

Abstract: The development of portable electronic devices has greatly stimulated the need for miniaturized power sources. Planar supercapacitors are micro-scale electrochemical energy storage devices that can be integrated with other microelectronic devices on a chip. In this paper, we study the behavior of microsupercapacitors with in-plane interdigital electrodes of carbon nanotube array under sinusoidal excitation, step voltage input and sawlike voltage input. Considering the anomalous diffusion of ions in the array and interelectrode space, we propose a fractional-order equivalent circuit model that successfully describes the measured impedance spectra. We demonstrate that the response of the investigated micro-supercapacitors is linear and the system is time-invariant. The numerical inversion of the Laplace transforms for electric current response in an equivalent circuit with a given impedance leads to results consistent with potentiostatic measurements and cyclic voltammograms. The use of electrodes based on an ordered array of nanotubes reduces the role of nonlinear effects in the behavior of a supercapacitor. The effect of the disordering of nanotubes with increasing array height on supercapacitor impedance is considered in the framework of a distributed-order subdiffusion model.

Keywords: supercapacitor; anomalous diffusion; fractional derivative; equivalent circuit; distributed-order subdiffusion (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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