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Theory of impedance for initial corrosion of metals under a thin electrolyte layer: a coupled charge transfer-diffusion model

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Abstract

An impedance model for a metal surface corroding under a thin electrolyte layer is presented. The model describes the oxygen diffusion in the electrolyte, the cathodic current via the oxygen reduction reaction (ORR) reaction and the anodic current via metal dissolution reaction (MDR) at the metal/electrolyte interface under the pseudo-steady approximation. The results for the impedance are obtained in terms of the thickness of electrolyte, the diffusion coefficient of oxygen, the concentration of dissolved oxygen and the anodic/cathodic reaction rates. The impedance characteristic are analysed through Bode and Nyquist plots which unveils six distinctive frequency regimes viz., (i) purely oxygen diffusion controlled regime, (ii) electrolyte film thickness controlled regime, (iii) activation controlled regime, (iv) mixed diffusion-kinetic controlled regime, (v) capacitive electric double layer controlled regime and (vi) solution Ohmic controlled regime. The impedance response shows two asymmetrical depressed arc on the Nyquist plots indicating the Faradaic charge transfer controlled regime and purely electrolyte thickness diffusion controlled regime with an intervening straight Warburg line. The arc at low frequencies is strongly dependent on the concentration and diffusion coefficient of dissolved oxygen indicative of pseudo-steady state behaviour of interface whereas the high frequency arc represents Faradaic regimes due to MDR and ORR which is indicative of the dynamic nature of corrosion reaction rates at the interface. At thick electrolyte layer, the interface shows a mass transport controlled kinetic regime with a finite length Warburg type impedance whereas at thin electrolyte layer the interface is activation controlled with a finite diffusion Randles type impedance response. A comparison of the model with the experimental data of corroding metal shows reasonable agreement.

Graphical abstract

Atmospheric corrosion of metal in contact with a thin electrolyte film via diffusion of dissolved oxygen coupled with oxygen reduction reaction and metal dissolution reaction in pseudosteady state.

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Abbreviations

\(\omega \) :

Frequency

\(\omega _{\text {D}}\) :

Characteristic diffusion frequency

\(\omega _C\) :

Characteristic Faradaic frequency

\(\alpha _{{O_{2}/OH^{-}}}\) :

Transfer coefficient of ORR

\(\alpha _{{M/M^{n_{1}^{+}}}}\) :

Transfer coefficient of MDR

\({\Delta }C\) :

Deviation of oxygen concentration from steady state concentration \(C_{\text {st}}\)

F :

Faraday’s constant

\(Z_{\text {FLW}}(\omega )\) :

Finite length Warburg impedance

\(R_{{\Omega }}\) :

Resistance of electrolyte

\(R_{\text {ct}}\) :

Charge transfer resistance

\(C_{\text {dl}}\) :

Capacitance of EDL

D :

Diffusion constant of species

T :

Temperature in Kelvin

\(\Phi \) :

Phase of impedance

E :

Potential

\(E^{0}_{{M/M^{n_{1}^{+}}}}\) :

Reduction potential of MDR

\( E^{0}_{{O_{2}/OH^{-}}}\) :

Reduction potential of ORR

R :

Universal gas constant

\(Z'(\omega )\) :

Real component of impedance

\(Z''(\omega )\) :

Imaginary component of impedance

\(|Z(\omega )|\) :

Magnitude of impedance

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Acknowledgements

MBS acknowledges the DST, New Delhi, India for the award of DST Inspire Faculty. MBS also acknowledges CSIRO (Australia) where initial part of research was carried out as Visiting Scientist.

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Authors and Affiliations

  1. Department of Chemistry, National Institute of Technology (NIT) Manipur, Imphal, 795004, India

    Maibam Birla Singh

  2. Department of Chemical Engineering, University of Washington, Seattle, WA, 98195, USA

    B Infant Gabriel

  3. Institute for Frontier Materials, Deakin University, Melbourne, Australia

    B Infant Gabriel

  4. Data Analytics and Al, Energy, Water and Food, NEOM, Riyadh, Saudi Arabia

    Murali S Venkatraman

  5. Advanced Manufacturing and Fabrication Research & Innovation, RMIT University Melbourne, Victoria, 3000, Australia

    Ivan S Cole

  6. Alagappa University, Karaikudi, Tamilnadu, India

    C Ganesa Moorthy

  7. Institute of Mathematical Sciences, Chennai, 600113, India

    B Emmanuel

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  1. Maibam Birla Singh
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Singh, M.B., Gabriel, B.I., Venkatraman, M.S. et al. Theory of impedance for initial corrosion of metals under a thin electrolyte layer: a coupled charge transfer-diffusion model. J Chem Sci 134, 32 (2022). https://doi.org/10.1007/s12039-021-02025-x

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