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# Impedance of Corroding Metal – Volmer-Heyrovsky mechanism

Latest updated: October 8, 2024## Introduction – Corrosion series

*Corroding systems can show different impedance graphs depending on the nature of the corrosion mechanism. In the first article in this series, we considered a Tafelian system (Part 1) and in this article we will examine a system following the Volmer-Heyrovsky mechanism (article 2). You will learn how to express the faradaic impedance and what is the equivalent circuit.*

## Part II

Let’s study the impedance in the case of anaerobic corrosion of a metal. Following the Volmer Heyrovský corrosion mechanism, valid in deaerated acidic medium, the rate of corrosion depends on the rate of H+ adsorption and H2 release.

### How to express the faradaic impedance?

Let’s consider the Volmer-Heyrovsky mechanism:

$\text H^+ + \text s + \text e^- \overset{k_{\text r1}}{\rightarrow} \text{H, s}$ (H+ adsorption)

$\text H^+ + \text{H, s} + \text e^- \overset{k_{\text r2}}{\rightarrow} \text{H}_2 + \text s$ (H_{2} release)

Where $\text s$ is an adsorption site and $\text{H, s}$ is a proton adsorbed on the electrode surface.

In our case, we also consider $\text{M, s} a surface metal atom and the third reaction in the mechanism is:

$\text{M, s} \overset{k_{\text o3}}{\rightarrow} \text{M}^{n+} + n\text e + \text s$ (metal corrosion)

The faradaic impedance is expressed by:

$$Z_f = R_\text{ct} + Z_\text{H} +Z_\text{s}$$

$Z_f = R_\text{ct} + Z_\theta$ where $Z_\theta= \frac{R_\theta}{1+R_\theta C_\theta j 2\pi f}$ is the impedance related to the adsorbed species.

$R_\theta, C_\theta = R_\theta C_\theta (K_{\text r 1},K_{\text r 2})$ for a simple VH mechanism and in our case

$R_\theta, C_\theta = R_\theta C_\theta (K_{\text r 1},K_{\text r 2}, K_{\text o 3})$ One should note that $R_\theta, C_\theta \lt \text{or} \gt 0$. We will see how this impacts the Nyquist plot.

### What is the equivalent circuit?

The equivalent circuit for the faradaic impedance is $R_\text{ct} = R_\theta / C_\theta$ and can be illustrated by the following circuit. Compared to Wagner-Traud (article I), $R_\theta$ and $C_\theta$ are additional components. The ohmic drop is expressed by the resistance $R_\Omega$.

The polarization resistance is $R_\text{p} = R_\text{ct} + R_\theta$.

The Nyquist plot can correspond to a capacitive behavior (top) or an inductive behavior (bottom).

In the case of $R_\theta, C_\theta \gt 0$, a capacitive behavior can be observed on the Nyquist plot. In the case of $R_\theta, C_\theta \lt 0$, an inductive behavior can be observed. For a potential around $E_\text{corr}$, the Nyquist diagram shows an inductive behavior.

###### Figure 2: Nyquist plot evolution with the electrode potential for VH mechanism (top), VH corrosion mechanism (bottom)

### How to calculate the corrosion current?

In the previous article, we have seen that the Stern – Geary relationship is used to determine the corrosion current and is valid at the corrosion potential:

$$I_\text{corr} = \frac{B}{R_{\text p, E_\text{corr}}}$$

Where $B=b_1b_2/(2.3(b_1 +b_2))$ with $b_{1,2}$ the Tafel slopes,

And $R_{\text p, E_\text{corr}}$ the polarization resistance at the corrosion potential.

In our case, the impedance equivalent circuit has an inductive loop at low frequencies, and it does not follow the Wagner-Traud relationship, $R_\text p \neq R_\text{ct}$. So, the Stern-Geary relationship is not valid anymore.

It can be used but an error will be induced if $R_\text p$ is used instead of $R_\text{ct}$.

## Conclusion

For a the VH corrosion mechanism, the impedance equivalent circuit is $R_\theta + R_\text{ct} + R_\theta / C_\theta$ and it has an inductive loop at low frequencies. As $R_\text p \neq R_\text{ct}$, the Stern-Geary relationship is not valid anymore. The corrosion current can still be calculated but an error will be induced if $R_\text p$ is used instead of $R_\text{ct}$.

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