# Impedance of Corroding Metal – Volmer-Heyrovsky mechanism

Latest updated: August 21, 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)

$\text H^+ + \text{H, s} + \text e^- \overset{k_{\text r2}}{\rightarrow} \text{H}_2 + \text s$ (H2 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}\$.

corrosion polarization resistance EIS corrosion current Volmer-Heyrovsky anaerobic corrosion

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