Constant-phase-element behavior caused by inhomogeneous water uptake in anti-corrosion coatings

The impedance of a substrate/coating/electrolyte system was calculated with the assumptions: (i) the coating uptakes electrolyte to an extent that progressively decreases from the coating/electrolyte interface to the substrate/coating interface where it becomes negligible; (ii) the volume fraction of the electrolyte varies along the coating thickness according to a power-law; (iii) the resistivity and permittivity profiles of the electrolyte-penetrated coating can be calculated through an effective medium theory (EMT) formula corresponding to a parallel combination of the two media (electrolyte and coating material); and (iv) some pores extend from the coating/electrolyte interface to the substrate/coating interface, providing a low resistance path. The impedance plots thus calculated exhibited a constant phase element (CPE) behavior in a large frequency range. Some experimental results obtained with 2024 aluminum alloy/hybrid sol-gel coating samples immersed in a NaCl solution were analyzed with reference to the above described model. The extension of the recently developed power-law CPE model to anti-corrosion coatings is shown to yield insight into the distribution of resistivity and associated water uptake. Evaluation of mixing rules for conductivities and permittivities of the two media (coating and electrolyte) showed that the linear combination provided results that were consistent with the observed impedance response; whereas, distributions resulting from a series combination of the two media, an EMT formula proposed in the literature, and the Maxwell approximation were incompatible with the observed CPE impedance response.