Potential Step for Double-Layer Capacitances Obeying the Power Law

Impedance Response of a Thin Film on an Electrode: Deciphering the Influence of the Double Layer Capacitance

The different contributions of the interfacial capacitance are identified in the case of passive materials or thin protective coatings deposited on the electrode surface. The method is based on a graphical analysis of the EIS results to determine both the passive-film capacitance in the high-frequency domain and the double-layer capacitance in the low-frequency domain. The proposed analysis is shown to be independent of the physicochemical origins of the frequency dispersion of the interfacial capacitances which results, from an analysis point of view of the experimental results, in the use of a constant-phase element However, for a correct evaluation of the thin-film properties such as its thickness, the high-frequency data must be corrected for the double-layer contribution. In particular, it is shown that if the double-layer capacitance gives a frequency-dispersed response, it is necessary to correct the high-frequency part for the double-layer constant-phase elements. This is first demonstrated on synthetic data and then used for the determination of the thickness of thin oxide film formed on Al in neutral pH solution.

Electric Field-Dependence of Double Layer Capacitances by Current-Controlled Charge-Discharge Steps

Voltage vs. time curves of double layer capacitances (DLCs) by current-controlled charge and discharge steps have been recognized to be composed of triangular waves. They are deviated slightly from triangles from the viewpoint of the time dependence or the constant phase element of the DLC. In order to evaluate the deviation, we measured DLCs of a platinum (Pt) electrode in KCl solution by current-control. Each time-voltage curve was convex rather a line, and was followed by the power law. Even if the time dependence was subtracted from each curve, the enhancement of the DLC was noticeable with an increase in the time well as the voltage. It can be attributed to the electric field effect, in which dipoles of solvents are oriented on an electrode so strongly that the DLC may be increased. The field dependence can be justified with the kinetic theory of interacting dipoles of solvents on an electrode through the observed linearity of the logarithmic DLC with the net voltage. This concept was applied to a commercially available super-capacitor to demonstrate a significant contribution of the field effect.