(Invited) Relationship between the Resistivity Profiles Obtained from the Power Law Model and the Physico-Chemical Properties of Passive Films
Authors: Zhang Zhiheng , Ter-Ovanessian Benoît , Marcelin Sabrina , Normand Bernard 
Published: December 2020

Passive film (PF) could be considered a particular nanomaterial with its growth, chemical composition, microstructure, performance and evolution of its performance. The understanding of the film construction, its maintenance and its resistance is the result of a total complementarity between characterization from enhanced physico-chemical analysis techniques, especially those developed by P. Marcus and his group[1], and electrochemical measurements, mainly the electrochemical impedance spectroscopy (EIS).
EIS gives access to the capacitive and resistive properties of the passive film. The first, complemented by the Mott-Schottky theory, allows a quantitative approach of electronic properties (semi-conductivity) and the maintenance process of passive films. The second involves the corrosion resistance of the film. Nevertheless, it is important to make a rigorous adjustment of the parameters resulting from the impedance diagrams. An adjustment that takes into account the physical meaning of parameters, especially for the analysis of the constant phase elements (CPE) used in the treatment of the diagrams that present one depressed semicircle [2]. The knowledge of the oxi-hydroxide character of the PF, evidenced from physicochemical characterizations, allows considerations of the spatial distribution of the heterogeneities (3D) within the thickness of the PF from the variation of its resistivity obtained from the Power Law Model (PLM)[3,4]. In fine, the resistivity profiles give information about interface reactivity and distribution of species along the thickness of the passive layer.
The use of the PLM requires the assessment of several parameters, especially a and Q defining the CPE or the thickness of the PF, which is generally assessed by physicochemical measurements. Most of them can be determined by advanced graphical analysis of impedance diagrams[5,6]. It can then be used to guide the adjustment of the diagrams by inputting known parameters into the model.
To exemplify the interdependency between physicochemical analysis and electrochemical impedance measurements, two studies illustrate the contribution of in-depth analyses of the resistivity profiles for two passive materials. That will be the opportunity to highlight which information can be drawn and finally, to propose reaction mechanism.
First of all, the passivity of the Ni-20Cr alloy has been studied in different solutions[7]. In this work, the electrochemical impedance diagrams have been successively performed under applied potential in passive region. From PLM analysis, it was observed that the evolution of the resistivity at the Ni-20Cr/PF interface explains the evolution of the current density during polarization. The resistivity profiles obtained for increasing applied potentials on the passive plateau showed a decrease of the resistivity plateau at the substrate/PF interface and an increase of the resistivity at the PF/electrolyte interface, highlighting the modification of the passive film according to the anodic polarization.
The second example concerns 316L stainless steel immersed in a 0.02M sodium sulphate solution and under proton irradiation[8]. It was shown that the impedance diagrams obtained before and after irradiation were almost superimposed, suggesting that the system was reversible. However, the resistivity profiles showed that under irradiation, the resistivity at the PF/electrolyte interface decreased and reached its initial value after irradiation. On the other hand, the length of the plateau at 316L/PF interface disappeared during irradiation and was reduced after irradiation by comparison with before irradiation.
The case studies presented show that the advances proposed in the analysis of impedance diagrams, combined with physicochemical analyses, provide a global knowledge of passivation mechanisms.

Maurice, P. Marcus, Current opinion in solid state & material science, 22 (2018) 156-167.

Tribollet, V. Vivier, M.E. Orazem, in Encyclopedia of Interfacial Chemistry (2018), Ed. Elsevier, 93-107.

B Hirschorn, M. E. Orazem, B. Tribollet, V. Vivier, I. Frateur, M. Musiani, Journal of the Electrochemical Society 157 (2010) C452-C457.

B Hirschorn, M. E. Orazem, B. Tribollet, V. Vivier, I. Frateur, M. Musiani, Journal of the Electrochemical Society 157 (2010) C458-C463.

E. Orazem, N. Pébère, B. Tribollet, Journal of the Electrochemical Society 153 (2006) B129-B136.

Benoit, C. Bataillon, B. Gwinner, F. Miserque, M. E. Orazem, C. M. Sánchez-Sánchez, B. Tribollet, V. Vivier, Electrochimica Acta 201 (2016) 340-347.

Zhang, B. Ter-Ovanessian, S. Marcelin, B. Normand, submitted to Electrochimica Acta.

Normand, N. Bererd, P. Martinet, S. Marcelin, M. Moine, J. Ferreira, D. Baux, T. Sauvage, N. Moncoffre, submitted to Corrosion Science.