Treatments of Impedance Behavior of Various Circuits and Modeling of Double-Layer Capacitor Frequency Response

Abstract

In earlier chapters it has been emphasized that the high-area, porous carbon structures that provide large specific (per gram) capacitance values (in practice, 5 to 50 F g^-1) cannot be represented by a simple capacitance or even by a simple RC circuit. The diagrams in Fig. 17.1 represent a hierarchy of equivalent circuits, from those for a simple capacitor through those involving simple combinations of a capacitor element with either one or two ohmic or equivalent ohmic resistors, to more complex equivalent circuits involving distributed capacitance with ohmic elements in series or parallel coupling with the capacitative elements and, for some conditions, with Faradaic leakage resistances in parallel with the capacitative elements. The latter may also include contributions from pseudocapacitances associated with surface redox functionalities (Chapter 9) on the interfaces or edges of carbon particles or the main pseudocapacitance associated with redox oxide capacitor materials (Chapter 11). In some cases, considered later, the equivalent circuit may also include an inductive element, L.

This Chapter owes much to the derivations and analyses given by Dr. Miller at the various Deerfield Beach (Florida) seminars on electrochemical capacitors held in recent years.