Cyclic voltammetry of supercapacitors with the simplest equivalent circuit
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Russian Chemical Bulletin, International Edition, Vol. 69, No. 9, pp. 1672—1678, September, 2020
Full Articles Cyclic voltammetry of supercapacitors with the simplest equivalent circuit* T. L. Kulova and A. M. Skundin A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Building 4, 31 Leninsky prosp., 119071 Moscow, Russian Federation. Fax: +7 (495) 952 0846. E-mail: [email protected] Analytical equations for the voltammetric curve at the linear voltage sweep and for cyclic voltammograms for the system of connected in series resistance and capacitance were derived. The presence of the resistance results in an substantial distortion and curvature of the voltammogram, which distinguishes this system from the system with the parallel connection of the capacitance and resistance. The character of the voltammograms is determined by the ratio of the following parameters: resistance (R), capacitance (C), voltage sweep rate (v), and voltage (U). The system is capacitive in character at RC > U/v. Key words: supercapacitor, equivalent circuit, linear voltage sweep, cyclic voltammetry.
Serious attention is recently given to the development and studies of electrochemical supercapacitors, and interest of researchers is significantly concentrated on pseudocapacitors, asymmetrical supercapacitors, and other devices in which Faraday processes occur. Meanwhile, important fundamental problems remain unsolved even in the studies of the simplest double layer supercapacitors. Cyclic voltammetry is a popular method of investigation of supercapacitors, but an analytical description of voltammetric curves is absent even for the single potentiodynamic pulse. In the ideal case when the only unit of equivalent circuit is the constant capacitance С, current i at the lin* Based on the materials of the XXI Mendeleev Congress on General and Applied Chemistry (September 9—13, 2019, St. Petersburg, Russia).
ear voltage sweep is equal to the product of the voltage sweep rate v and the capacitance i = Cv.
(1)
When voltage U changes in time t according to the law shown in Fig. 1, а, the cyclic voltammogram looks like a rectangle symmetrical relative to the abscissa (Fig. 1, b). For the equivalent circuit consisting of the parallel combination of the capacitance and resistance, the cyclic voltammogram looks like a parallelogram (Fig. 1, c). In practice, even if no redox processes with the fixed redox potential appear during supercapacitor functioning, the cyclic voltammogram represents a distorted lenticular curve or a sloped curve with the pod-like shape. The real cyclic voltammograms differ from rectangles symmetrical relative to the voltage axis, and this distinction is primarily
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1672—1678, September, 2020. 1066-5285/20/6909-1672 © 2020 Springer Science+Business Media LLC
Cyclic voltammetry of supercapacitors
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Russ. Chem. Bull., Int. Ed., Vol. 69, No. 9, September, 2020
U
i/A
a 0.10
U+ 1 0.05
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2 0
U–
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