Mathematical models for time-dependent impedance of passive electrodes

Three mathematical models are reported for the analysis of time-dependent electrode impedance data of passive electrodes. These models describe the complex relationships between the impedance, the components of the electrical equivalent circuit, the characteristics of the passive layer, the ac frequency, and the measurement time. Hence, they can be used to analyze time-dependent electrode impedance data obtained from the anodic oxidation of metals, alloys, conducting or semiconducting metal compounds in aqueous solutions. Both single and double passive layer models predict that the real impedance and negative imaginary impedance are approximately proportional to the square root of the resistivity of the passive layer and the measurement time. A solid-state transport model predicts that the impedance increases with measurement time, and with a decrease in either the concentration and/or transport coefficient of the electroactive ions.