Diffusion impedance and equivalent circuit of a multilayer film

The paper analyses the equivalent circuit corresponding to two consecutive planar diffusion layers of finite thickness (porous Warburg or O elements) present in an electrochemical system. This case often occurs in important systems, such as protective coatings or membranes, which are routinely studied using electrochemical impedance spectroscopy (EIS). Relations are obtained that connect the diffusion impedance of a multilayer to the impedances of individual layers and also take into account partitioning effects. It is shown that the equivalent circuit that correctly represents the total diffusion impedance (e.g., for use in EIS spectra fitting algorithms) consists of several O and T (bounded Warburg) elements connected in a complex way. Analysis of limiting cases shows that the low-frequency limiting behavior of a multilayer film may significantly differ from those of individual layers showing asymmetry and synergism. In particular, it is shown that a thin layer of solution between an electrode and a resistant film to be characterized may seriously interfere with the measurements.