Potential Step for Double-Layer Capacitances Obeying the Power Law.

Potential-step chronoamperometry was made at a platinum wire electrode in KCl aqueous solution at the aim of finding the behavior of the power law of the time or the constant phase element for the double-layer (DL) capacitances. The logarithmic current decays linearly with the time shorter than 0.1 ms, and then it obeys the power law in which it has a linear relation with the logarithmic time in the millisecond time domain. The transition from the exponential decay to the power law was expressed theoretically for the model of a series combination of the resistance and the DL capacitance. The expression predicts that the double logarithmic plots of the current-time provide a capacitance value at 1 s from the intercept, independent of the resistance. This prediction was demonstrated experimentally in KCl solutions of which concentrations ranged from 1 mM to 0.5 M. The capacitance can be evaluated simply by chronoamperometry on a 1 s time scale without considering any resistance effect. The capacitance values did not vary with the applied potential.