On Impedance Spectroscopy of Supercapacitors

Abstract

Supercapacitors are often characterized by responses measured by methods of impedance spectroscopy. In the frequency domain these responses have the form of power-law functions or their linear combinations. The inverse Fourier transform leads to relaxation equations with integro-differential operators of fractional order under assumption that the frequency response is independent of the working voltage. To compare long-term relaxation kinetics predicted by these equations with the observed one, charging-discharging of supercapacitors (with nominal capacitances of 0.22, 0.47, and 1.0 F) have been studied by means of registration of the current response to a step voltage signal. It is established that the reaction of devices under study to variations of the charging regime disagrees with the model of a homogeneous linear response. It is demonstrated that relaxation is well described by a fractional stretched exponent.