Electrodes Coated by Passive Oxide Films with a Thickness Profile: Modeling and Measurement

The impedance of a rectangular electrode coated by a resistive film is calculated for the cases of linear and exponential thickness profiles along the electrode length. The local film capacity and local film resistance of each surface element are assumed to be inversely and directly proportional to local film thickness, respectively. Experimental model electrodes are prepared by anodizing niobium or tantalum rectangular sheets with a setup allowing the progressive extraction of the electrode from the electrolyte, at a constant rate, while the cell voltage is increased according to a suitable program. The impedance of the coated electrode, measured at a potential close to the lowest anodization potential, agrees well with theory. In particular, the plot of the ohmic resistance corrected phase angle vs frequency shows a minimum. The effect of experimental parameters such as thickness profile or solution concentration can be interpreted on the basis of the calculations.