1. Application of electrochemical techniques for determining corrosion rates

In the section below, practical examples are described of how a number of electrochemical techniques could be used to forecast corrosion or tribocorrosion behavior in practical case studies. The focus is on laboratory tests for rapid corrosion or tribocorrosion tests. The examples do not provide bit-by-bit procedures for screening most or all potentialities. Also, the discussion is not about how to set up and conduct electrochemical corrosion or tribocorrosion experiments. Such

information can be readily found in instruction guidelines manual or standard references [1–17]. The accent is put on the interest and validity of combination techniques to provide a better understanding of the corrosion process and more reliable predictions.

#### 1.1 Linear polarization resistance (LPR)

The concept of "polarization resistance" has presumably been initiated by Bonhoeffer and Jena in 1951 [18]—a subsequent to Wagner and Traud's works [19, 20]. In their study of the electrochemical behavior of iron samples of different carbon contents, they found that the slope of the polarization curve, i.e., the rate of potential change E with external current i, at the corrosion potential (or opencircuit potential of a mixed electrode), was low for some iron samples and large for others. Defining this slope as "polarization resistance," RP, as a result of Lange's suggestion, it was found that there was an unambiguous correlation between the polarization resistance and the corrosion rate, whereas no correlation was found between the carbon content and the rate of corrosion.

Subsequently, Stern and Geary [21] were the first authors to theoretically establish a linear relationship between the polarization resistance and the corrosion rate based on the kinetics of electrochemical reactions (i.e., corrosion current at opencircuit conditions) and the concept of mixed potential theory, first formulated by Wagner and Traud in 1938 (i.e., parameters of the cathodic and anodic E/i relations) [19]. The advantages and limitations of their method have been discussed in a series of published articles [19, 21, 22], and the linearity of the slope of currentpotential plot around the corrosion potential has been verified by experimental evidence, thereby avoiding the problem of large current densities. Their theory has been experimentally supported by other authors [19, 21, 22] for different materials and under a variety of environmental conditions. From the 1960s, plenty of publications [23, 24] reported on the use of the polarization technique, which quickly became one of the main electrochemical techniques routinely adapted to rapid corrosion rate measurements, a condition necessary to its success in industrial monitoring corrosion operations.

For a system in which electrode processes involve a slow reaction step at the electrode surface, the rate of reaction is limited by activation overvoltage; the relationship between the reaction rate, or net current density i, and the driving force for the reaction, or potential E, is given by the Butler-Volmer equation. This equation relates i, for a single electrode process, such as Eq. (1) to E by the formula (2),

$$\mathbf{Fe} \leftrightarrow \mathbf{Fe}^{2+} + \mathbf{2e}^- \tag{1}$$

Stern and Geary's theory [21] is based on a simplified corrosion process assuming that only one anodic reaction and one cathodic reaction are involved during the corrosion process. It is therefore inevitable that erroneous results occur when the corrosion process involves more than one anodic or cathodic reaction. To address

Current density (i)-overpotential (η) curves for the system O + e \$ R at 25°C. α = 0.5, il,a = �il,c = il. Partial current densities: ia, ic (dashed line), il limit current density (horizontal line), and RP the polarization

It is well known that the electrochemistry of corroding metals involves two or more half-cell reactions. Suppose there is a simple corrosion system, such as an iron metal (a corroding working electrode) immersed in a sulfuric acid solution, in addition to Eq. (1), the following half-cell reaction (Eq. (3)) also occurs:

The dissolution of Fe takes place in the acid electrolyte. At equilibrium, the total anodic rate is equal to the total cathodic rate. In this case, the net rate of either Fe dissolution or hydrogen evolution can be measured at the electrode potential of the steady-state freely corroding condition. This potential refers to the corrosion potential Ecorr, which lies between the equilibrium potentials of the two individual half-cell reactions. At Ecorr, the net rate corresponds to the uniform corrosion rate, icorr, at free corrosion condition. In such system, the relationship between the overpotential (η, applied potential minus corrosion potential) and the current (flowing between the working electrode and the auxiliary counter electrode) is

� \$ H2 (3)

<sup>H</sup><sup>2</sup><sup>þ</sup> <sup>þ</sup> <sup>2</sup><sup>e</sup>

governed by the fundamental Butler-Volmer equation given as follows:

this problem, Mansfeld and Oldham [25] presented a modification of the Stern-Geary equation by including more than one oxidation and one reduction reaction in a complicated corrosion process. The current-overpotential relationship at electrodes is set by a number of complex physical and chemical phenomena based on experimental conditions. The reactions occurring at the electrode/electrolyte interface are heterogeneous chemical processes that may involve elementary electron-transfer steps (one or more steps) over the electrochemical double layer,

Electrochemical Techniques for Corrosion and Tribocorrosion Monitoring: Methods…

DOI: http://dx.doi.org/10.5772/intechopen.86743

ion-transfer, potential independent or chemical steps, etc.

Figure 1.

169

resistance (circle).

$$\begin{split} i &= i\_0 \left[ \exp\left(\frac{\alpha nF\eta}{RT}\right) - \exp\left(\frac{(1-\alpha)nF\eta}{RT}\right) \right] \\ &= i\_0 \left[ \exp\left(\frac{\alpha nF(E - E\_{rv})}{RT}\right) - \exp\left(\frac{(1-\alpha)nF(E - E\_{rv})}{RT}\right) \right] \end{split} \tag{2}$$

where η is the overpotential, i<sup>0</sup> the exchange current density (rate of either the forward or reverse half-cell reaction) at the equilibrium potential Erev, α the transfer coefficient (usually close to 0.5, but must be between 0 and 1), and n the number of electrons transferred.

The graphical representation of the Butler-Volmer equation, as shown in Figure 1, is called the polarization curve.

Electrochemical Techniques for Corrosion and Tribocorrosion Monitoring: Methods… DOI: http://dx.doi.org/10.5772/intechopen.86743

#### Figure 1.

information can be readily found in instruction guidelines manual or standard references [1–17]. The accent is put on the interest and validity of combination techniques to provide a better understanding of the corrosion process and more

The concept of "polarization resistance" has presumably been initiated by Bonhoeffer and Jena in 1951 [18]—a subsequent to Wagner and Traud's works [19, 20]. In their study of the electrochemical behavior of iron samples of different carbon contents, they found that the slope of the polarization curve, i.e., the rate of potential change E with external current i, at the corrosion potential (or opencircuit potential of a mixed electrode), was low for some iron samples and large for others. Defining this slope as "polarization resistance," RP, as a result of Lange's suggestion, it was found that there was an unambiguous correlation between the polarization resistance and the corrosion rate, whereas no correlation was found

Subsequently, Stern and Geary [21] were the first authors to theoretically establish a linear relationship between the polarization resistance and the corrosion rate based on the kinetics of electrochemical reactions (i.e., corrosion current at opencircuit conditions) and the concept of mixed potential theory, first formulated by Wagner and Traud in 1938 (i.e., parameters of the cathodic and anodic E/i relations) [19]. The advantages and limitations of their method have been discussed in a series of published articles [19, 21, 22], and the linearity of the slope of currentpotential plot around the corrosion potential has been verified by experimental evidence, thereby avoiding the problem of large current densities. Their theory has been experimentally supported by other authors [19, 21, 22] for different materials and under a variety of environmental conditions. From the 1960s, plenty of publications [23, 24] reported on the use of the polarization technique, which quickly became one of the main electrochemical techniques routinely adapted to rapid corrosion rate measurements, a condition necessary to its success in industrial

For a system in which electrode processes involve a slow reaction step at the electrode surface, the rate of reaction is limited by activation overvoltage; the relationship between the reaction rate, or net current density i, and the driving force for the reaction, or potential E, is given by the Butler-Volmer equation. This equation relates i, for a single electrode process, such as Eq. (1) to E by the

Fe \$ Fe<sup>2</sup><sup>þ</sup> <sup>þ</sup> <sup>2</sup><sup>e</sup>

� exp ð Þ <sup>1</sup> � <sup>α</sup> nF<sup>η</sup> RT

where η is the overpotential, i<sup>0</sup> the exchange current density (rate of either the forward or reverse half-cell reaction) at the equilibrium potential Erev, α the transfer coefficient (usually close to 0.5, but must be between 0 and 1), and n the number of

The graphical representation of the Butler-Volmer equation, as shown in

� (1)

(2)

� exp ð Þ <sup>1</sup> � <sup>α</sup> nF Eð Þ � Erev RT

reliable predictions.

Corrosion Inhibitors

1.1 Linear polarization resistance (LPR)

between the carbon content and the rate of corrosion.

monitoring corrosion operations.

<sup>i</sup> <sup>¼</sup> <sup>i</sup><sup>0</sup> exp <sup>α</sup>nF<sup>η</sup>

Figure 1, is called the polarization curve.

RT 

RT 

<sup>¼</sup> <sup>i</sup><sup>0</sup> exp <sup>α</sup>nF Eð Þ � Erev

formula (2),

electrons transferred.

168

Current density (i)-overpotential (η) curves for the system O + e \$ R at 25°C. α = 0.5, il,a = �il,c = il. Partial current densities: ia, ic (dashed line), il limit current density (horizontal line), and RP the polarization resistance (circle).

Stern and Geary's theory [21] is based on a simplified corrosion process assuming that only one anodic reaction and one cathodic reaction are involved during the corrosion process. It is therefore inevitable that erroneous results occur when the corrosion process involves more than one anodic or cathodic reaction. To address this problem, Mansfeld and Oldham [25] presented a modification of the Stern-Geary equation by including more than one oxidation and one reduction reaction in a complicated corrosion process. The current-overpotential relationship at electrodes is set by a number of complex physical and chemical phenomena based on experimental conditions. The reactions occurring at the electrode/electrolyte interface are heterogeneous chemical processes that may involve elementary electron-transfer steps (one or more steps) over the electrochemical double layer, ion-transfer, potential independent or chemical steps, etc.

It is well known that the electrochemistry of corroding metals involves two or more half-cell reactions. Suppose there is a simple corrosion system, such as an iron metal (a corroding working electrode) immersed in a sulfuric acid solution, in addition to Eq. (1), the following half-cell reaction (Eq. (3)) also occurs:

$$\text{H}^{2+} + 2\text{e}^- \leftrightarrow \text{H}\_2 \tag{3}$$

The dissolution of Fe takes place in the acid electrolyte. At equilibrium, the total anodic rate is equal to the total cathodic rate. In this case, the net rate of either Fe dissolution or hydrogen evolution can be measured at the electrode potential of the steady-state freely corroding condition. This potential refers to the corrosion potential Ecorr, which lies between the equilibrium potentials of the two individual half-cell reactions. At Ecorr, the net rate corresponds to the uniform corrosion rate, icorr, at free corrosion condition. In such system, the relationship between the overpotential (η, applied potential minus corrosion potential) and the current (flowing between the working electrode and the auxiliary counter electrode) is governed by the fundamental Butler-Volmer equation given as follows:

$$\begin{split} i &= i\_0 \left[ \exp\left(\frac{\alpha n F \eta}{RT}\right) - \exp\left(\frac{(1 - a)nF\eta}{RT}\right) \right] \\ &= i\_0 \left[ \exp\left(\frac{\alpha n F(E - E\_{corr})}{RT}\right) - \exp\left(\frac{(1 - a)nF(E - E\_{corr})}{RT}\right) \right] \end{split} \tag{4}$$

In Figure 1, the linear relationship between the polarization resistance and the corrosion rate can be easily illustrated graphically. In the small region near the corrosion potential, Ecorr, only a very small perturbation potential, usually less than �30 mV (typically �10 mV), is applied above or below the corrosion potential, yielding a linear relationship between the overpotential (η = E � Ecorr) or the polarization from the corrosion potential and the current. Due to this smooth excitation, the LPR technique is not expected to interfere with corrosion reactions. The slope of that linearized curve (i � E) is defined as the polarization resistance, RP, of a corroding electrode (in ohms cm�<sup>2</sup> if the current density is plotted or in ohms if the current is plotted), which is mathematically interpreted as

$$R\_P = \left(\frac{\partial \eta}{\partial \dot{t}}\right)\_{|E - E\_{\text{corr}} = 0} \tag{5}$$

Similarly, in the step pulse method, an applied potential is incremented in steps of 5 or 10 or 20 mV, starting from a negative potential moving to a positive potential through the corrosion potential. The value of Rp is determined from the slope of the plot of the potential-current. Prior to the tests, a steady-state corrosion potential is required. The open-circuit potential of the corrosion system is first measured, typically for 1 hour (during which time the corrosion potential of most

Electrochemical Techniques for Corrosion and Tribocorrosion Monitoring: Methods…

Progress is made through competitive advantages between different measurement techniques, including a rapidity in current measurement (generally rather quickly in a few minutes), where only a lower excitation is required (less than 30 mV, generally 10 mV), so that the corrosion rate would not be affected by corrosion reactions, an easy measurement of low corrosion rates (less than 0.1 mil/ year (2.5 μm/year), and measurements taken repeatedly, the LPR technique can be considered as a nondestructive technique and used for online corrosion monitoring

The main drawback of this technique is that the Tafel parameters must be known in advance in order to convert the polarization resistance into the corrosion rate. To tackle this problem, several numerical methods [8, 9, 26–28] have been proposed to obtain both Tafel parameters and corrosion rate from the same polarization measurement in the vicinity of the corrosion rate. Nevertheless, the success is limited since the Tafel parameters thus determined will not be very accurate, which

may compromise the nondestructive nature of the LPR technique. Another disadvantage of the LPR method lays in the fact that it will not work properly in low conductive media. Basically, the LPR technique can only be used to determine

uniform corrosion rates; it can hardly provide information about localized

1.1.1 Illustrative examples of the application of LPR in corrosion and tribocorrosion

A modified electrochemical noise technique, namely, electrochemical emission spectroscopy (EES) [29], offers one of the most convincing examples of the application of the LPR technique in tribocorrosion [30]. Indeed, the analysis of noise data in a potential-current plane shows the transposition of the statistical resistance due to electrochemical noise to the resistance due to linear polarization. Noise resistance is often considered equivalent to the polarization resistance, RP [31–33]. The noise resistance, RN, calculated using a method proposed by Eden et al. [33], for mild steel passive alloy in 0.05 M H2SO4 (corrosion under activation control), is of the order of 48 Ω without any sliding contact. The LPR measured on this mild steel after EES monitoring is shown in Figure 2a. The comparative value of RP obtained by the LPR technique is 50 Ω. The RN value obtained using the EES technique is therefore very close to the RP obtained by the LPR technique. Under tribocorrosion conditions (5 N normal force, 10 Hz sliding frequency, 200 μm peak-to-peak displacement amplitude), the plane plot of the potential-current data under steadystate wear-corrosion regime shows a best-fit line through the data points with a positive slope of 54 Ω (see Figure 2b), which roughly corresponds to RN (48 Ω) or RP (50 Ω in Figure 2a). Notwithstanding, no attempt has been made to relate these resistance measurements with the breakdown (i.e., depassivation) or the buildup of any kind of passive film (i.e., repassivation) on the mild steel surface subjected to either a mechanical stimuli (e.g., active-passive wear track zone area or metastable pit area) or in the absence of wear (free corrosion), characteristic phenomena of

electrodes is stabilized) or until it reaches a stationary state.

of uniform corrosion rates useful for the field.

DOI: http://dx.doi.org/10.5772/intechopen.86743

corrosion.

systems

localized corrosion.

171

where i is the current density corresponding to a particular value of E.

The corrosion current, Icorr, can be calculated when the overpotential approaches zero and is related to RP as follows:

$$I\_{corr} = \frac{1}{R\_p} \cdot \frac{b\_a b\_c}{2.303(b\_a + b\_c)}\tag{6}$$

where ba and bc are the so-called anodic and cathodic Tafel slopes or Tafel parameters, respectively (cf. infra). The corrosion current density, icorr, can thus be calculated from Eq. (6) if RP and Tafel constants (ba and bc) are known.

ASTM G59 describes an experimental procedure required to carry out polarization resistance measurement [10]. In agreement with this standard, the potential should be scanned from �30 mV to +30 mV of the corrosion potential at a rate of 0.167 mV s�<sup>1</sup> .

Many of the foregoing determined corrosion key parameters are based on empirical observations. As with any empirical method, due to the high number of factors involved in a corrosion or tribocorrosion system (e.g., environmental changes, temperature, pH, reagent as chloride ions, pressure, specimen geometry, test setup configuration, etc.), it is not uncommon to observe that the values of ba, bc, and RP are influenced by these operational parameters and are therefore subject to change. Of significance, the slope generated from the i–E curve around the corrosion potential may not be linear and may or may not be symmetrical in the anodic and cathodic regions. The symmetry of the curve (i–E) at the point of equilibrium or at open-circuit potential is obtained only when ba and bc are equal. These values are required for computing the corrosion current and are usually determined by the Tafel extrapolation method (cf. infra).

It is worthy to note that the measurements of Rp can be derived potentiodynamically or by the method of stepwise potentiostatic polarization or by anodic step pulse method. In the potentiodynamic method, the potential is swept at a constant rate (typically 60 mV/h) from the active (cathodic) direction to the noble (anodic) region passing through the corrosion potential while tracking the current density continuously. More information regarding this method can be found elsewhere [3].

#### Electrochemical Techniques for Corrosion and Tribocorrosion Monitoring: Methods… DOI: http://dx.doi.org/10.5772/intechopen.86743

Similarly, in the step pulse method, an applied potential is incremented in steps of 5 or 10 or 20 mV, starting from a negative potential moving to a positive potential through the corrosion potential. The value of Rp is determined from the slope of the plot of the potential-current. Prior to the tests, a steady-state corrosion potential is required. The open-circuit potential of the corrosion system is first measured, typically for 1 hour (during which time the corrosion potential of most electrodes is stabilized) or until it reaches a stationary state.

Progress is made through competitive advantages between different measurement techniques, including a rapidity in current measurement (generally rather quickly in a few minutes), where only a lower excitation is required (less than 30 mV, generally 10 mV), so that the corrosion rate would not be affected by corrosion reactions, an easy measurement of low corrosion rates (less than 0.1 mil/ year (2.5 μm/year), and measurements taken repeatedly, the LPR technique can be considered as a nondestructive technique and used for online corrosion monitoring of uniform corrosion rates useful for the field.

The main drawback of this technique is that the Tafel parameters must be known in advance in order to convert the polarization resistance into the corrosion rate. To tackle this problem, several numerical methods [8, 9, 26–28] have been proposed to obtain both Tafel parameters and corrosion rate from the same polarization measurement in the vicinity of the corrosion rate. Nevertheless, the success is limited since the Tafel parameters thus determined will not be very accurate, which may compromise the nondestructive nature of the LPR technique. Another disadvantage of the LPR method lays in the fact that it will not work properly in low conductive media. Basically, the LPR technique can only be used to determine uniform corrosion rates; it can hardly provide information about localized corrosion.
