(Corrosion Division H. H. Uhlig Award) The Journey from Numerical Simulations to Impedance Analysis
Authors: Orazem Mark E. 
Published: November 2022

Our work in corrosion has encompassed numerical simulations and electrochemical impedance spectroscopy. This presentation provides an overview of insights gained from these endeavors.
Numerical simulations train insight
In collaboration with Kevin Kennelley and Lee Bone, then from Arco, our group developed boundary-element models to simulate cathodic protection (CP) of pipelines with coating defects that exposed bare steel. Designed initially for the trans-Alaska pipeline,1 the model was extended to account for multiple pipes, multiple CP systems,2 buried tanks, and tank bottoms.3 The program could be used to simulate rectifier wars in which impressed current on one CP system can induce corrosion on adjacent or crossing systems. This program was used to demonstrate the behavior of heterogeneous anodes. For example, addition of impressed current anodes to an inadequate set of sacrificial anodes runs the risk of protecting the sacrificial anodes at the expense of protecting steel exposed by coating defects.
In collaboration with Richard Woollam, then with BP, and, later, with Scott Briggs, NWMO, our group developed finite-element COMSOL models that accounted for corrosion under droplets containing dissolved oxygen.4 The models include coupled, nonlinear, conservation equations for ionic species, which account for migration, diffusion, local electroneutrality, homogeneous reactions, and formation of precipitates. The presence of anodic and cathodic regions was not assumed a priori, but was rather the result of numerical simulations, which revealed galvanic coupling caused by differential aeration cells. This work showed that, while differential aeration created nonuniform corrosion for steel covered by a deposit or droplet, corrosion of copper was largely uniform.
Impedance spectroscopy can provide useful parameters
While the use of the Stern-Geary relationship to extract corrosion current is well known, this approach applies only for systems under kinetic control. More information may be extracted from the ubiquitous constant-phase-element (CPE) behavior. In collaboration with scientists/engineers from France and Italy, our group developed the power-law model, which provides an equation that relates CPE parameters to film thickness, dielectric constant, and film resistivity at the film-electrolyte interface.5,6 This model can be augmented with the measurement model, from which capacitance may be extracted.7 Thus, if the dielectric constant is known, the measurement model can yield the corresponding film thickness and the power-law model can yield the resistivity distribution in the film.8 An early version of this approach is now in commercial use.9

Acknowledgements

I am grateful for all the students and collaborators who walked part of this journey with me. These include students J. Matthew Esteban and Doug Riemer (CP models), Ya-Chiao Chang and Chen You, (droplet models), and Bryan Hirschorn (power-law model). I thank collaborators Bernard Tribollet, Vincent Vivier, Marco Musiani, and Nadine Pébère, with whom I have explored the arcane arts of impedance spectroscopy. Finally, I thank the Corrosion Division awards committee for bestowing upon me the 2022 H. H. Uhlig Award.

References

E. Orazem, J. M. Esteban, K. J. Kennelley, and R. M. Degerstedt, “Mathematical Models for Cathodic Protection of an Underground Pipeline with Coating Holidays: 1. Theoretical Development,” Corrosion, 53 (1997), 264-272.

Liu, A. Shankar, M. E. Orazem, and D. P. Riemer, “Numerical Simulations for Cathodic Protection of Pipelines,” in Underground Pipeline Corrosion: Detection, Analysis, and Prevention, M. E. Orazem, editor, Woodhead Publishing Limited, Cambridge, UK, 2014, 85-126.

P. Riemer and M. E. Orazem, “A Mathematical Model for the Cathodic Protection of Tank Bottoms,” Corrosion Science, 47 (2005), 849-868.

-C. Chang, R. Woollam, and M. E. Orazem, “Mathematical Models for Under-Deposit Corrosion: 1. Aerated Media,” Journal of The Electrochemical Society, 161 (2014), C321-C329.

Hirschorn, M. E. Orazem, B. Tribollet, V. Vivier, I. Frateur, and M. Musiani, “Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films: 1. Theory,” Journal of The Electrochemical Society, 157 (2010) C452-C457.

E. Orazem, B. Tribollet, V. Vivier, S. Marcelin, N. Pébère, A. L. Bunge, E. A. White, D. P. Riemer, I. Frateur, and M. Musiani, “Dielectric Properties of Materials showing Constant-Phase Element (CPE) Impedance Response,” Journal of The Electrochemical Society, 160 (2013), C215-C225.

Liao, W. Watson, A. Dizon, B. Tribollet, V. Vivier, and M. E. Orazem, “Physical Properties Obtained from Measurement Model Analysis of Impedance Measurements,” Electrochimica Acta, 354 (2020), 136747.

You, A. Titov, B. H. Kim, and M. E. Orazem, “Impedance Measurements on QLED Devices: Analysis of High-Frequency Loop in Terms of Material Properties,” Journal of Solid-State Electrochemistry, 24 (2020), 3083-3090.

P. Riemer and M. E. Orazem, “Impedance-Based Characterization of Raw Materials as Used in Electrochemical Manufacturing,” The Electrochemical Society Interface, Fall 2014, 23:3 (2014), 63-67.