Electrochemical noise analysis: detection of electrode asymmetry

doi:10.1016/S0010-938X(02)00179-8

Corrosion Science

Volume 45, Issue 5, May 2003, Pages 941-955

https://doi.org/10.1016/S0010-938X(02)00179-8 Get rights and content

Abstract

One major application of electrochemical noise (EN) analysis for corrosion studies is the estimation of corrosion rate via impedance measurement. The measurement involves coupling two electrodes, whereupon the associated EN is measured and the noise resistance and the spectral noise impedance are computed. However, the two electrodes are required to be “nominally identical” (i.e. symmetrical) for the noise resistance and spectral impedance techniques to be valid. This paper proposes that the correlation between the measured potential and the current noise can be used to detect an asymmetric electrode pair and thus provides a necessary but not sufficient test for electrode symmetry. The potential/current coefficient of correlation is derived based on an equivalent circuit to demonstrate the concept and experimental data is presented to support the theory.

Introduction

Electrochemical noise (EN) refers to the spontaneous fluctuations in potential (electrochemical potential noise, EPN) that can be observed on a corroding metal (electrode) and/or the spontaneous fluctuations in current (electrochemical current noise, ECN) when the electrode is externally polarized, either by a potentiostat or by another electrode.

Eden et al. [1] proposed an experimental setup for measuring EN that enables quantities known as the noise resistance and the spectral noise impedance to be computed. These quantities have been linked to the electrochemical equivalent impedance of the electrodes [2], [3], [4], [5], [6], which can provide much valuable information regarding the corrosion process and, in particular, the rate of corrosion [7], [8]. Bertocci et al. [9], and Mansfeld and co-workers [10], [11] have observed good experimental correlation between the spectral noise impedance and the magnitude of the electrode impedance determined by AC polarization techniques. The noise resistance and spectral noise impedance have been shown to be helpful in corrosion studies in many practical research cases [10], [11], [12], [13], [14], [15], [16], [17], [18].

Fig. 1 shows the measurement setup proposed by Eden et al. [1]. Two electrodes are electrically coupled via an ammeter so that the ECN flowing between them, i(t), can be logged. Simultaneous to the ECN measurement, the EPN at the point of coupling, v(t), is logged with respect to a reference electrode. This measurement setup will be referred to as a noise resistance measurement or an EPN/ECN measurement.

The noise resistance is defined by Eden et al. [1] as $R_{n} = σ_{v} σ_{i}$ where σ_v² is the variance of v(t) and σ_i² is the variance of i(t).

Xiao and Mansfeld [19] introduced the concept of spectral noise impedance, originally in terms of the Fourier transforms of v(t) and i(t). Bertocci et al. [2] define it in terms of the power spectral densities (PSDs): $R_{sn} (f)= S_{v} (f) S_{i} (f)$ where S_v(f) and S_i(f) are respectively the PSDs of v(t) and i(t).

Fig. 2 shows the equivalent circuit model of the noise resistance measurement, which is similar to the model used by Bertocci et al. [2]. In Fig. 2, i(t) and v(t) are respectively the ECN and EPN measurements, v₁(t) and v₂(t) are the EPN sources and Z₁(f) and Z₂(f) are the respective electrochemical impedances of each electrode about v(t). (That is, Z₁(f) and Z₂(f) are the frequency dependent gradients of the potential/current curves associated with each electrode at the mixed potential of the average value of v(t). These gradients may or may not be equal to the gradients about each individual electrode’s free corrosion potential, depending on the degree of polarization and non-linearity of the electrodes.) The solution resistance is taken to be incorporated into Z₁(f) and Z₂(f).

Using the equivalent circuit model, the work of Bertocci et al. [2] and Bautista and Huet [20] provides analysis of how R_n and R_sn(f) are related to the impedance and source EPN of each electrode. The theory shows the spectral noise impedance to be given by $R_{sn}^{2} (f)= |Z_{2} (f)|^{2} S_{v1} (f)+|Z_{1} (f)|^{2} S_{v2} (f) S_{v1} (f)+S_{v2} (f)$ where S_v1(f) and S_v2(f) are the PSDs of v₁(t) and v₂(t) respectively.

When the two electrodes have identical impedances of Z(f)=Z₁(f)=Z₂(f), the spectral noise impedance becomes $R_{sn} (f)=|Z(f)|$ Eqs. , show that the spectral noise impedance can be used for impedance estimation, but typically only if the electrode pair has identical impedances.

In order to ensure identical impedances, the impedance of each electrode can be directly measured using non-EN techniques such as AC polarization. However, this negates the need for a spectral noise impedance measurement as the electrodes’ impedances already will be known. Also, polarization techniques involve the application of external signals to the electrodes, which may be undesirable and they require the use of a potentiostat and other relatively expensive hardware. In this work, the correlation between the measured EPN and ECN (v(t) and i(t)) is proposed as a means for detecting electrode pairs with dissimilar impedances and EPN characteristics. This allows the symmetry of the electrode pair to be assessed entirely from the EN data. No additional measurements are required.

For this work, an electrode pair is considered symmetrical if they possess equal impedances and the EPN originating from each of the electrodes are statistically equal, i.e. if Z₁(f)=Z₂(f) and S_v1(f)=S_v2(f) then the electrodes are symmetrical.

Section 2 derives the coefficient of correlation and coherence function as a function of the equivalent circuit parameters (S_v1(f), S_v2(f), Z₁(f) and Z₂(f)) and discusses how they can be used to detect asymmetry. A graphical representation is also discussed. 3 Experimental procedure, 4 Experimental results describe the experimental procedure and the results obtained to support the theory. The cross correlation between an observed EPN/ECN measurement is compared with the cross correlation as predicted by the theory using data obtained by independent measurements (linear polarization (LP) and EPN measurements on each electrode separately).

Section snippets

Potential/current correlation

The coefficient of correlation between v(t) and i(t) obtained from an EPN/ECN measurement is defined as $r_{vi} = E[v(t)i(t)]−E[v(t)]E[i(t)] σ_{v} σ_{i}$ where ‘E’ denotes statistical expectation, and σ_v² and σ_i² are the variances of v(t) and i(t) respectively. For stationary v(t) and i(t), the coherence function is defined as $P_{vi} (f)= |S_{vi} (f)| S_{v} (f)S_{i} (f)$ where S_v(f) and S_i(f) are the PSDs of v(t) and i(t) respectively. S_vi(f) is the cross spectral density of v(t) and i(t), defined as the Fourier transform of the

Experimental procedure

A set of experimental data has been collected to test the relationship suggested by Eq. (16). A system with nominally symmetric electrodes has been obtained by placing an electrode pair of equal surface area in solution together. Asymmetric systems have been obtained in two ways: (i) by use of an electrode pair of differing exposed surface area; and (ii) by placement of electrodes with equal exposed surface in separate solution of differing concentration with a salt bridge to provide

Experimental results

Table 1 summarises the results of the LP and EN measurements. The signal variances listed under the EPN column are normalized such that σ_v1²+σ_v2²=1. The r_vi under the EPN/ECN column were computed over a bandwidth of [0.02,0.2] Hz for experiments A1–A3, and over [0.1,1] Hz for B1 and B2.

Table 2 lists the observed corrosion potentials of each electrode individually, and for when the two electrodes are coupled. The table shows that, in all cases, the two electrodes were never observed to have free

Conclusions

The cross correlation between the potential and current EN has been proposed as a means of assessing the symmetry of an electrode pair. It has been shown that when the EN originating from each electrode is statistically independent, non-zero correlation indicates an asymmetric electrode pair and that symmetric electrode pairs yield zero correlation. Consequently the potential/current correlation provides a necessary but not sufficient test for symmetric electrodes. Good agreement between theory

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Electrochemical noise analysis: detection of electrode asymmetry

Abstract

Introduction

Section snippets

Potential/current correlation

Experimental procedure

Experimental results

Conclusions

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