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The corrosion mechanism taking place in an aqueous phase with or without mechanical contact is electrochemical in nature. The electrochemical signal is one of the primary sources of information that relates to behavior in potential, current, and electrical charge of a corroding electrode. It arises from processes that cause corrosion and other electrochemical reactions. In a sliding contact in an ionic electrolyte medium, electrochemistry is more likely to interfere with the tribological behavior of tribocorrosion systems. In recent years, attempts by researchers have been made to control the material loss by electrochemical methods for various engineering systems.

Applied online for monitoring in-situ uniform, localized, galvanic, or more forms of corrosion, such techniques are very convenient means to measure corrosion rate of materials. Such methods can also be used in different ways to evaluate their ability to protect materials (as inhibitors, protective layers, coatings). In this chapter, theoretical and experimental applications, fundamental aspects, limits of the electrochemical techniques for corrosion, and tribocorrosion monitoring are presented. Standards developed, so far, by various standardization organizations are reported. Fundamentals of traditional and advanced corrosion methods are described, focusing on their advantages, i.e. sensitivity to low corrosion rates, short experimental duration, and well-established theoretical understanding.

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, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 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 open-circuit potential of a mixed electrode), was low for some iron samples and large for others. Defining this slope as “polarization resistance,” R_P, 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 open-circuit 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 current-potential 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),Fe↔Fe2++2e−Fe↔Fe2++2e− E1i=i0[exp(αnFηRT)−exp((1−α)nFηRT)]=i0[exp(αnF(E−Erev)RT)−exp((1−α)nF(E−Erev)RT)]i=i0expαnFηRT−exp1−αnFηRT=i0expαnFE−ErevRT−exp1−αnFE−ErevRT E2

where η is the overpotential, i₀ the exchange current density (rate of either the forward or reverse half-cell reaction) at the equilibrium potential E_rev, αthe 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.

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:H2++2e−↔H2H2++2e−↔H2 E3

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 E_corr, which lies between the equilibrium potentials of the two individual half-cell reactions. At E_corr, the net rate corresponds to the uniform corrosion rate, i_corr, 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:i=i0[exp(αnFηRT)−exp((1−α)nFηRT)]=i0[exp(αnF(E−Ecorr)RT)−exp((1−α)nF(E−Ecorr)RT)]i=i0expαnFηRT−exp1−αnFηRT=i0expαnFE−EcorrRT−exp1−αnFE−EcorrRT E4

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, E_corr, 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 − E_corr) 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, R_P, of a corroding electrode (in ohms cm⁻² if the current density is plotted or in ohms if the current is plotted), which is mathematically interpreted asRP=(∂η∂i)|E−Ecorr=0RP=∂η∂iE−Ecorr=0 E5

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

The corrosion current, I_corr, can be calculated when the overpotential approaches zero and is related to R_P as follows:Icorr=1Rp.babc2.303(ba+bc)Icorr=1Rp.babc2.303ba+bc E6

where b_a and b_c are the so-called anodic and cathodic Tafel slopes or Tafel parameters, respectively (cf. infra). The corrosion current density, i_corr, can thus be calculated from Eq. (6) if R_P and Tafel constants (b_a and b_c) 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⁻¹.

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 b_a, b_c, and R_P 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 b_a and b_c 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 R_p 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]. 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 R_p 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, 27, 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.

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

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, R_P [31, 32, 33]. The noise resistance, R_N, 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 R_P obtained by the LPR technique is 50 Ω. The R_Nvalue obtained using the EES technique is therefore very close to the R_Pobtained 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 steady-state 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 R_N (48 Ω) or R_P (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 localized corrosion.

1.2. Tafel extrapolation method

In 1905, Julius Tafel [34] presented the experimental relationship between the current, I, and the overpotential, η, during an electrocatalytic test of the reduction reaction of hydrogen (i.e., protons to form molecular hydrogen) on a number of electrode metals such as Hg, Sn, Bi, Au, Cu, Ni, and so on:η=a+blogIη=a+blogI E7

where the overpotential η is defined as the difference between the potential of the working electrode, E, and the equilibrium potential.

The existence of a linear relationship between E and log I has been demonstrated when the electrode is polarized at sufficiently large potentials, and far away from the corrosion potential both in anodic and cathodic directions [34], as can be seen in the polarization curve depicted in Figure 3. The portions in which such relationships prevail are called Tafel portions or Tafel regions.

This can be mathematically expressed asI=Icorr[exp(2.303ηba)−exp(−2.303ηbc)]=Icorr[exp(2.303(E−Ecorr)ba)−exp(−2.303(E−Ecorr)bc)]I=Icorrexp2.303ηba−exp−2.303ηbc=Icorrexp2.303E−Ecorrba−exp−2.303E−Ecorrbc E8

where E_corr is the corrosion potential, E the applied potential, η the overpotential (difference between E and E_corr), I the current, I_corr the corrosion current, and b_a and b_c are the Tafel constants or Tafel parameters derived from E − log I plots as the anodic and cathodic slopes in the Tafel regions, respectively.

Extrapolating from the Tafel portions of either anodic or cathodic or both, an intersection point is obtained at E_corr, from which I_corr is readily available from the log I axis. Therefore, it is possible to obtain simultaneously the corrosion current, I_corr, and the Tafel parameters (i.e., b_a and b_c) from this method.

In order to obtain the Tafel portions in the anodic and cathodic regions, the electrode has to be polarized far away from its corrosion potential, e.g., ±250 mV away from E_corr. Eq. (8) can be rearranged, as appropriate, to choose one single polarization direction, either anodic or cathodic way.

At sufficiently larger values of η (100 mV ≤ η ≤ 500 mV), in the anodic direction (i.e., η = η_a), Eq. (8) can be rearranged as,ηa=balogIIcorrηa=balogIIcorr E9

Likewise, at sufficiently larger values of η, in the cathodic direction (i.e., η = η_c), Eq. (8) can be modified as,ηc=−bclogIIcorrηc=−bclogIIcorr E10

The polarization curve can be measured either dynamically or statically (either in the potential-controlled mode or in the current-controlled mode). The dynamic polarization techniques can be carried out relatively fast, but the drawback is that the Tafel parameters are scanning rate dependent. The static polarization techniques may produce better Tafel parameters, but they are very time-consuming.

Tafel extrapolation measurements can be performed either by the potentiodynamic method or by the stepwise potentiostatic polarization method [35]. As in R_P measurements, in both methods, corrosion potential is first measured, typically for 1 h (during which time corrosion potentials of most electrodes are stabilized) or until it stabilizes. After that, the potential step—at increments of ±25 or ± 50 or ± 100 mV, every 5 min, recording the current at the end of each 5-min period—is applied (potential-step method), or the potential is scanned at a constant rate (typically 0.6 V/h) (potentiodynamic method). In both methods, the experiment is started at the corrosion potential, and the cathodic polarization is first conducted by applying an overpotential of approximately 500 mV or until gas evolution (e.g., hydrogen) occurs at the electrode, at a constant rate of 0.6 V/h. Following, the corrosion potential is measured again (typically for 1 h), and then anodic polarization is conducted by applying an overpotential so that the potential at the end of the anodic polarization reaches +1.6 V versus SCE. Tafel plots are generated by plotting both anodic and cathodic data in a semilog paper as E-log I. From the plot, three values are determined: the anodic Tafel slope, the cathodic Tafel slope, and I_corr (from back-extrapolation of both anodic and cathode curves to E_corr). The main advantage of this method is that it provides a simple, straightforward method to determine Tafel parameters, namely, b_a and b_c.

The disadvantage of the Tafel technique is that large current densities are often required to generate the complete Tafel plots. The use of large current densities can alter the surface conditions of the specimen (e.g., permanent change or surface damage), thereby distorting the results and increasing complications due to mass transport and uncompensated electrolyte resistance. The measurement of current density over a wide potential range may also distort the results if the adsorption of some species is potential dependent. Since this method applies a large overpotential to the metal surface (e.g., anodic polarization), therefore, the technique is rather destructive and can hardly be used for online corrosion monitoring purposes and in particular in the field. An ASTM G5 standard provides a procedure for constructing an anodic polarization plot [36]. However, it does not supply a method to construct a cathodic polarization plot nor a procedure to determine the corrosion current by the Tafel extrapolation method.

1.3. Corrosion rate determination by electrochemical noise analysis (ENA)

Many of the electrochemical techniques, among those described earlier, measure the electrochemical response of the corrosion system following the application of an external disturbance. In the last 50 decades, an original concept has emerged where it was possible to use the inherent noise of the electrochemical system as a stimulus to measure both potential and current changes [31, 32, 37, 38, 39, 40, 41, 42, 43]. Broadly, measured inconsistently in corrosion experiments, the electrochemical noise was first considered an unwanted or undesirable artifact that comes from measuring instruments or pickups from the environment. This is why this misleading name was cast. This sort of noise can be easily observed during corrosion potential measurements because the measured corrosion potential always fluctuates slightly, usually randomly. Random fluctuations result from stochastic processes [44], and, considering each chemical process is stochastic in nature, it generates noise.

Since the pioneer work of Iverson [45], who has reported a relation between the frequency or amplitude of the electrochemical noise and the inhibiting power of the environment for a number of metals and alloys (e.g., aluminum alloys, magnesium, mild steel, etc.), there has been a growing interest toward the measurement of electrochemical noise and its peculiar relationship with localized corrosion [11, 12, 31, 32, 41, 46, 47, 48, 49, 50, 51]. In this respect, electrochemical noise measurements obtained from the analysis of corrosion potential or current fluctuations provide a new approach to the study of corrosion processes in reactive environments such as aqueous media or hot aggressive gases or even under the effect of mechanical stimuli, e.g., tribocorrosion. Indeed, mechanical friction of solids in contact with a corrosive environment is likely to generate (i) noise due to stochastic contact between randomly distributed surface asperities and (ii) noise due to the synergy of wear-corrosion processes resulting from the activity of the surfaces and controlled by the response of potential-current transients and the configuration of the wear track area, coordinated by the coupling effects of wear and corrosion in the tribo-electrochemical cell. Among the possibilities offered by the measurement of electrochemical noise sources during an electrochemical or a tribo-electrochemical system, the following can be retained: adsorption–desorption processes, e.g., formation and detachment of gas bubbles; fluctuations in the mass transport rate and in temperature; interfacial nucleation and growth processes; degradation processes due dielectric film disruption; kinetics of atom exchange at the surface sites, e.g., Johnson’s noise in the interfacial impedance; and so on.

While multiple case studies on electrochemical noise have been regularly reported in recent years, even greater progress is possible, with the scope for increased breakthrough in science and technology (e.g., novel materials, precision tools on macro-to-nanoscopic scales, availability and intelligent use of these materials and tools, and so on). In particular, the main focus of these investigations is to promptly obtain in situ mechanistic information on the repassivation and breakdown of passive films and to monitor any process associated with confined corrosion and/or tribo- or bio-tribocorrosion [46, 47, 51]. It has been, indeed, suggested that the noise is caused by film breakdown and repassivation processes, and given the dynamic competition between these two processes, pitting will initiate. However, the foundation for using electrochemical noise analysis for determining the corrosion rate of an electrode is still a subject of debate within the scientific community. Indeed, the fundamental approach is not as robust as that of other techniques. On the other hand, the advantage of the noise analysis is that it is not necessary to apply any external polarization and the system is in natural corrosion conditions. This renders the technique as nondestructive and nonintrusive, capable of monitoring basic changes in an electrochemically active system. This makes it particularly suitable for online corrosion monitoring in the laboratory, especially for localized corrosion monitoring, detection of general corrosion, crevice investigation, stress corrosion cracking [12, 52, 53], fretting corrosion, or be used in the assessment of anti-corrosive organic coatings, and other surface inhomogeneity case studies [43, 46, 47]. Several approaches extend the use of electrochemical noise measurements in both pilot plant and field facilities, its use is not merely limited to the foregoing phenomena, but its development is justified especially when measurements are performed in systems with very low conductivity, where, for e.g., the impedance technique fails because of the loss of signal in the high resistance of the solution (cf. infra).

1.3.1. Instrumentation for electrochemical noise measurements in corrosion and tribocorrosion systems

Electrochemical noise is a generic term used to describe the naturally occurring fluctuations in potential and current, which is due to spontaneous changes in electrode kinetics and mechanisms [33]. When applied to corrosion studies, electrochemical noise may be redefined as the spontaneous fluctuations observed in potential and current at the free corrosion potential. The electrochemical noise can thus be classified into potential noise and current noise. There are three major possible modes for measuring potential and current noise in a corrosion system, but the most common mode uses two nominally identical working electrodes, WE₁ and WE₂ (WE₁ as the corroding metal and WE₂ as a counter electrode), and a noise-free reference noble electrode, RE [33] (see Figure 4a). The current flowing between the two working electrodes is measured by a zero-resistance ammeter (ZRA), and their potential is monitored versus the reference electrode through a voltmeter (V) under free corrosion conditions. The two other leftover modes are two identical working electrodes WE₁ and WE₂ with a bias potential [54] (not shown here) and one WE coupled to a micro-counter electrode (MC, e.g., Pt wire tip) [29, 46, 47, 55] (see Figure 4b). This last mode of electrochemical noise analysis seems to be a promising way to obtain unambiguous estimates of the rate of chemical wear in a tribocorrosion experiment as evidenced by some recent investigations [46, 47, 51] but also to predict the corrosion rate of localized corrosion in a free corroding system [29, 31, 32, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 56].

1.3.2. Electrochemical noise data management process

The overall approach to analyzing noise data is the assessment of mechanistic information from either time-domain analysis, frequency-domain analysis, or both, using statistical methods [44, 57, 58]. If the information in the time-domain records is evident, time-domain analysis is sufficient to distinguish different processes (e.g., different forms of corrosion).

In what follows, one assumes that all various types of noise are excluded from this description, with the exception of the thermal noise. Except for the last noise, all other noise sources can be minimized or eliminated using careful strategy within reasonable limits of materiality. Effective and convenient ways include the removal of unwanted environmental and instrumental noise from the electrochemical noise, e.g., by shielding electrical connections/wires for coupling the electrodes to the experimental apparatus, by using a Faraday cage to exclude electrostatic/electromagnetic influences, even by implementing analogue/digital filters to eliminate systematic noise at frequencies different than the frequency of interest, and so on. Guidelines for the calibration of noise measuring device can be found elsewhere [13, 59].

1.3.3. Noise resistance

The basic quantitative approach is the time-domain analysis of the noise signal. The noise resistance, R_N, is defined as the ratio of the standard deviations of potential/current noise signal time dependent, σ(t):RN=σE(t)σI(t)RN=σEtσIt E11

Eq. (11) implies that in the case where a low-driving force noise produces a high current density noise between the two electrodes (WE₁ and WE₂), the yielding noise resistance will be low. Noise resistance, R_N, has been shown to correlate well with the polarization resistance, R_P, as determined by EIS for certain corrosion systems. This latter being directly related to the corrosion current [14, 29, 60] is using the Stern-Geary equation and Tafel slopes. Notwithstanding, much work has been devoted trying to best match R_N or the normalized R_N (per unit of exposed surface area) to the corrosion resistance or the corrosion rate [5, 14, 31, 32, 37, 38, 39, 40, 41, 42, 43, 44, 45, 48, 49, 50, 60]. Although signal analysis in the time domain is well established, an approach based on spectral analysis is gaining more and more importance in research laboratories. It consists of transforming the potential and current noise fluctuations recorded in the frequency domain using the Fast Fourier Transform (FFT) method [61].

The frequency range for which the FFT is commonly performed extends from 1 mHz up to 1 Hz. The spectral noise plots are similar to those of impedance plots. The spectral noise resistance, R_SN, is given by the ratio of the potential and current FFTs at each frequency, and the limiting value, R_SN⁰, can be used as a measure of the corrosion resistance:RSN(f)=(EFFT(f)IFFT(f))RSNf=EFFTfIFFTf E12

The log–log plot of R_SN versus f is similar to the impedance plot, and the spectral noise resistance limit R_SN⁰ is given byR0SN=limf→0RSN(f)RSN0=limf→0RSNf E13

Another approach would be to examine the spectral noise response in terms of power spectral densities (PSD). These latter are calculated from the FFT or using the maximum entropy method (MEM) [62]. R_SN is determined from the PSDs by the relation (14):RSN(f)=(EPSD(f)IPSD(f))1/2RSNf=EPSDfIPSDf1/2 E14

It has been shown that the use of a single data set of potential and current noise [32] would yield identical values of R_SN as calculated by either Eqs. (13) or (14). In some cases, R_SN⁰ is bound to R_N or R_P as,RN=RSN(0)=RPRN=RSN0=RP E15

effective if the impedance of the two electrodes is identical and much higher than the resistance of the test solution between them [5, 32, 63]. Experiments have validated this relationship for several systems [5, 31, 63]. Nonetheless, there is no agreement on the fundamental basis for the relationship between noise resistance and corrosion rate.

1.3.4. Illustrative examples of the application of electrochemical noise in tribocorrosion systems

Investigations into electrochemical kinetics make common point research between tribocorrosion and corrosion. The study of localized phenomena of depassivation and repassivation is essential to understand the mechanisms of corrosion-wear as well as to reduce the material loss. The possibility of using the electrochemical noise detection technique as a promising tool to study the electrochemical properties of well-controlled damaged surfaces has been widely considered due to its nondestructive nature and its potential in online corrosion monitoring applications. Time-spatially resolved measurements should provide more reliable data on the electrochemical part of tribocorrosion. The noise analysis in relation to depassivation-repassivation events randomly distributed in time and space can be traced back to Oltra et al. [64]. The power spectral density (PSD) of the noise under the impact of the jet particles was related to the Fourier transform of individual repassivation transients obeying a Poisson distribution. Later, the application of electrochemical noise analysis to tribocorrosion was reviewed. Investigations involving PSD noise analyses on various tribo-electrochemical cells for passivating materials were conducted by Ponthiaux et al. [65], by Déforge et al. [51], and in more details by Berradja et al. [46, 66]. In this latter work, the noise spectra were measured on AISI 304 L stainless steel versus corundum in a Ringer’s solution in a pin-on-disk tribometer under stationary sliding-corrosion regime conditions, either at open-circuit potential or at a controlled potential. The PSD of the current noise has been interpreted as resulting from the overlap of the large number of discrete repassivation transients at the contact junctions, including the double-layer charge and the strong dependence of depassivation and repassivation kinetic rates of the oxide surface film on the sliding frequency. This was consistent with the shift in the PSD plots of the current noise fluctuations by about a decade when the sliding frequency was varied from 0.1 to 1 Hz (see Figure 5). Similar findings were obtained via Déforge et al. [51] by dividing open-circuit potential fluctuations to the impedance of the electrode. A 1/f low-frequency noise is explained by a long-term drift of the surface conditions. Only a minor influence of the applied normal load was observed on the PSD plots, recommending reaching the limit rate of the depassivation of the oxide surface film.

Application of the noise analysis to tribocorrosion offers the feasibility to record in parallel the PSD of normal and tangential force fluctuations and their tie-in with the current noise data (see Figure 6). Force fluctuations show an almost flat spectrum (white noise) as expected following short random mechanical interactions between colliding asperities, whereas the current noise is consistent with finite time-constant transient responses to the depassivation events.

1.4. Corrosion forecast by electrochemical impedance spectroscopy (EIS)

The EIS has matured greatly over the past 25 years as a tool in corrosion protection research and has proven to be one of the most useful electrochemical characterization techniques presently available. In practice, EIS has become a standardized research tool for corrosion prediction [15] and found wide applications in both fundamental and applied laboratory researches [67]. Recent applications in tribocorrosion reflect the steady progress of the EIS method in terms of research and development [62]. Compared with the LPR technique, the EIS technique is considered more advanced, since it has the ability to study high-impedance systems, in which the conventional LPR technique has failed, such as coatings and linings [16, 68], high pure water, and organic coating/metal systems [69] or corrosion in a low conductive solution [70]. This technique is especially useful for evaluating corrosion inhibitors [24, 71], analyzing the corrosion mechanisms [72, 73], and so on.

A significant number of tutorials have been addressed on the EIS experimental setup, the measurement methodology, and data analysis methods [27, 74, 75, 76, 77, 78]. The technique has been of a great deal of concern to the extent that an ASTM standard, i.e., ASTM G106-89, has been produced to provide the practitioner with a test method to verify that the electronic equipment, the electrochemical cell, and the spectrum generation algorithm impedance work properly [15].

1.4.1. Principle of the EIS technique

The EIS technique normally uses a typical three-electrode cell system controlled by a potentiostat, similar to that used in the LPR technique. Unlike the previous time-resolved techniques, where the current system response is either the consequence of a large voltage perturbation from the steady-state condition (case of Tafel extrapolation) or from a smaller perturbation (case of LPR method), in the EIS approach, however, by applying a small varying perturbation over a range of frequency, it is possible to probe the full response of the electrochemical system, and not just the resistive components. In that respect, a small AC signal, i.e., alternating potential or voltage V(ω) typically a sine wave of amplitude ±10 mV of the corrosion potential, is applied over a wide range of frequency (typically from 10⁵ down to 10⁻² or 10⁻³ Hz) at a number of discrete frequencies (typically 5–10 frequencies per decade), and the alternating current response, i(ω), is measured at each frequency, ω (i.e., the ac polarization or angular frequency, ω = 2πf). For a linear system, the current response signal will be a sine wave of the same frequency as the excitation signal (voltage) but shifted in phase. This is transmitted to a frequency response analyzer or a lock-in amplifier to calculate the impedance and phase shift. Full frequency sweeps provide phase-shift information that can be used in combination with equivalent circuit models to gain valuable information from the complex interface of the corrosion system. The frequency-dependent impedance is determined by the relation: Z(ω)=V(ω)/i(ω)Zω=Vω/iω .

1.4.2. Electrode/electrolyte electrochemical interface circuit

Basically, the electrode/electrolyte interface is characterized by a separation of charges resulting in the creation of parallel planes of electrical charges whose behavior is similar to a circuit consisting of a capacitor and a resistor in parallel and certainly not to a perfect capacitor. Indeed, the current flowing in a perfect capacitor would cease when the latter would be fully charged, hence the need to add a resistor in parallel to let a weak current flow. An electrochemical interface can be viewed as an electrical circuit, or called the equivalent circuit, composed of a number of elements such as resistances (R), capacitances (C), and inductances (L) [26]. Explanations of the EIS results are usually based on the equivalent circuit used. Many software programs and packages are now available for fitting the impedance spectra to analogous circuits [15], a strategy often used to analyze data. Further information on the EIS measurements and instrumentation can be found elsewhere [15, 17, 79, 80].

Not all the available proposed equivalent circuits to model electrochemical interfaces can actually satisfy what is applied to a freely corroding system. In most cases, the impedance corresponding to a simple corrosion process, under activation control, can be represented by the well-known Randles’ [81] equivalent circuit (RC circuit) which allows to describe the behavior of many electrochemical electrode/electrolyte interfaces. A typical example is shown in Figure 7, where R_S, R_CT, and C_DL represent labels for the solution resistor, the Faradaic charge transfer resistor, and the double-layer capacitance, respectively. The capacity is associated with the separation of charges at the electrode/electrolyte interface as in the case of a working electrode having a surface film (e.g., AISI 304 stainless steel immersed in a 0.5 M H₂SO₄ electrolyte), in which case the capacity of the equivalent circuit can be associated with the capacity of the passive oxide surface film and the resistor in parallel with the capacitor is considered as the charge transfer resistance, R_CT (or the polarization resistance, R_P, under EIS-free corrosion conditions), while the ohmic resistance in solution, R_S, between the working electrode and the reference electrode is in series with the parallel resistor and the capacitor. If the amplitude of the perturbation signal is small enough (e.g., a voltage less than 20 mV), R_CT can be regarded as equivalent to the linear polarization resistance (R_P).

The behavior of such an electrochemical interface can be described by Eq. (16):Z(ω)=Rs+Rp1+(jωRPCDL)βZω=Rs+Rp1+jωRPCDLβ E16

R_CT or R_P can be determined in several ways. A convenient way is to use the Nyquist diagram. For the simple Randles-type equivalent circuit as shown in Figure 7, the corresponding Nyquist diagram is displayed in Figure 8, in which a perfect semicircle is observed. The high-frequency response is used to determine the component of R_S involved in the measurement. R_S can be read directly from the abscissa when the angular frequency ω (ω = 2πf) tends to be infinite (f_max or f → ∞). The total resistance (R_P + R_S) can also be read from the abscissa when ω approaches zero (f_min or f → 0). So, R_P can be determined by subtracting the R_S value from the low-frequency measurement. The conversion of the polarization resistance into a corrosion rate requires an independent empirical measurement of the Tafel slopes using a potentiodynamic polarization method and/or harmonic distortion analysis or otherwise taken from the literature. The double-layer capacitance, C_DL, can also be determined for a system exhibiting a behavior similar to that of a perfect RC circuit from the values of R_P and the maximum frequency, f_max, that corresponds to the frequency of the point at which the imaginary component has a maximum value, viz.:

CDL=12πfmaxRpCDL=12πfmaxRp E17

It is worth of note that in practice, f cannot really go as high as infinite; it is inevitable that some extrapolation has to be made. Extrapolation at the high-frequency limit usually presents few issues because the impedance becomes nonreactive at frequencies as low as 10 kHz in most cases [82]. On the other hand, reactance is still commonly observed at frequencies as low as 10⁻³ Hz [82]. Therefore, special precautions must be taken to obtain reliable data and to avoid possible artifacts [17, 83]. Furthermore, the measurement cycle time depends on the frequency range used, in particular the low frequencies. For instance, a single-frequency cycle at 10⁻³ Hz needs about 15 min of testing time. A high-to-low-frequency analysis moving down to 10⁻³ Hz frequency likely requires more than 2 hours of scan time. In order to perform a normal standard corrosion monitoring with the EIS technique, assistance is needed to optimize the use of the high-frequency data and reduce measurement time. There is a constant need to improve data processing and analysis in order to minimize uncertainties and to allow the EIS technique becoming user-friendly for corrosion monitoring in both laboratory and field facilities, though it must be emphasized that the need for an easy-to-deploy field instrument has always been an obstacle to online corrosion monitoring with the EIS technique.

An alternative to the impedance model in the Nyquist diagram involves the conversion of the impedance into a complex number. The impedance can thus be designated by an amplitude, |Z|, and a phase shift, ϕ, or by the sum of the real (Z′) and imaginary (Z″) components, such that,Z(ω)=Z'(ω)+jZ”(ω)Zω=Z′ω+jZ”ω E18

Both the log|Z| data and the phase angle ϕ are plotted against the angular frequency, log ω, of the excitation signal, a format which substitutes for the Nyquist diagram, i.e., the so-called Bode diagram. Figure 9 shows how the same data (Nyquist plot) appears in a Bode plot format with respect to the equivalent circuit of Figure 7.

Highest (ω_H) and lowest frequencies (ω_L) can be readily determined. As shown in Figure 9, Z is independent of the frequency at ω_H and ω_L, limit values represented by horizontal lines. From these lines, values of R_S and (R_S + R_CT) can be measured. This analysis forms the basis of the corrosion monitoring as proposed by Tsuru et al. [74] to allow the determination of |Z| at each frequency in the horizontal portions of the Bode diagram.

Sometimes, it is not convenient to perform impedance measurements at very low frequencies (as in DC techniques such as linear polarization). However, it is still possible to extrapolate the polarization resistance, R_P, from the Bode diagram. In Figure 9, the low- and high-frequency breakpoints (i.e., ω_L and ω_H, respectively) can be determined from the 45° phase angle Bode diagram (see the pseudo-Gaussian curve). The intersection point A can be determined from the log ω_H and R_S. By extrapolating from A toward the central linear portion of the |Z| curve, a linear line can be determined. On this line, point B is obtained at log ω_L.With the projection of point B to the log|Z| axis, the total resistance (R_S + R_CT) can be measured. In this way, R_P can be determined. At intermediate frequencies, the capacitor affects the response of the overall RC circuit.

The situation struggles when diffusion processes govern the corrosion behavior. A convenient way to deal with this complication is to add a Warburg impedance. The latter describes the impedance of the concentration and diffusion processes in the equivalent circuit as shown in Figure 10.

The Warburg impedance, Z_W, is given by the equationZW=σwω√−jσwω√ZW=σwω−jσwω E19

where σ_w is the Warburg coefficient.

Eq. (19) implies that, whatever the frequency, the real and imaginary parts of the Warburg impedance are equal and inversely proportional to σ_w^½. In the Nyquist plot, this impedance will result in a straight line at a constant phase angle at 45°, as shown in Figure 10. However, the effect of the Warburg impedance can complicate the correct estimate of the R_P value in certain cases. Therefore, the impedance data must be numerically adjusted to fit with the correct model to facilitate the extraction of the total resistance (R_S + R_P) from the abscissa or by using an appropriate modeling software. However, the situation can readily become more complicated if other effects, such as time-constant dispersion, adsorption processes, and so on, are taken into account; the time-constant dispersion, which can be caused by inhomogeneities in the corroded surface, results in a depression of the semicircle [75, 76]. Adsorption, on the other hand, can reveal a second semicircle at low frequencies [77]. All these effects can occur simultaneously [27], making the interpretation of impedance data rather more difficult [78, 84] (Figure 11).

There is a need for an appropriate model equivalent circuit beyond the existing model standards to remedy that shortcoming. An “appropriate” model is understood not only as a good fit of the impedance data but also as a rational explanation of the underlying corrosion mechanism. Moreover, the requirement of sophisticated AC frequency generator and analyzer and the time needed to acquire the complete impedance diagram (particularly in the range of low frequency) impose a serious limitation in real-time corrosion monitoring applications. Other disadvantages include a priori knowledge of the Tafel parameters in order to convert the polarization resistance into a corrosion rate and the fact that it is too difficult to detect and monitor localized corrosion, even if such applications have been explored [85, 86].

1.4.3. Illustrative examples of the application of EIS in corrosion and tribocorrosion systems

Attempts were made to use the EIS technique in corrosion and corrosion-wear monitoring of Fe-31% Ni electrode immersed in 0.5 M H₂SO₄ [87]. The corresponding Nyquist impedance diagrams were recorded at an anodic potential of −675 mV/SSE (+100 mV/open-circuit potential) before and during sliding-corrosion as shown in Figure 12. At this potential, the prevailing reaction is dissolution. At high frequency, under free corrosion and unloaded conditions, the capacitive arc reveals the influence of the dielectric properties of the electrochemical double layer and the charge transfer due to electrochemical reactions. Under sliding conditions, the size of the capacitive arc increases, suggesting an increase in the transfer resistance and a decrease in the reactivity of the surface, consistent with the effect of mechanical straining of the worn surface. At low frequency, however, the inductive arc indicates the relaxation of the surface concentration of adsorbed intermediate species involved in the dissolution mechanism. Under corrosion-wear conditions, the kinetics of the dissolution process is apparently modified, as revealed by the second inductive loop in the diagram. Given that not all of these investigations have been concluded, a detailed explanation is not straightforward, and further research is recommended. Although these impedance measurements provide a convenient way to study the mechanism of electrochemical reactions involved in tribocorrosion processes, still the interpretation of impedance records during sliding-corrosion experiments is rather difficult because of the heterogeneous surface-state condition. Actually, a nonuniform distribution of the electrochemical impedance on the steel surface must be taken into account. The action of friction can be analyzed thoroughly if this distribution is known. Equivalent electrical circuit models or finite element models could be used to obtain impedance distributions and to calculate the overall impedance.

2. Comparison of the techniques for the assessment of corrosion rate

The transposition of the foregoing electrochemical techniques to corrosion situations is illustrated in [63] for the assessment of corrosion rate. The results presented in Table 1 summarize the data generated by the different techniques for Fe electrodes in 0.5 M H₂SO₄ under well-controlled conditions and their corresponding corrosion current densities, resistances, and required parameters which determined those data.

Table 1.

Data outcomes determined by different electrochemical techniques on Fe in 0.5 M H₂SO₄.

Reproduced from [63] with permission from Wiley Online Library.

All these techniques monitor the electrode response following the stimulation by a potential variation in time or frequency domain with the exception of the electrochemical noise analysis technique. The extent of the potential stimulation and the current response decreases in the order from Tafel extrapolation method, linear polarization, EIS, to electrochemical noise. Each of these techniques provides the necessary information for a given corroding system, and there are trade-offs involved in the comparative decision of which is the best to use.

Author: Abdenacer Berradja

1. EIS Spectrum Analyser

EIS Spectrum Analyser is a standalone program for analysis and simulation of impedance spectra. The analyser routine is based on algorithms of the PDEIS spectrometer. In the original (potentiodynamic) version the impedance data analysis is applied on a 3D spectrum and gives dependences of the ac response components on electrode potential.

This standalone program has been adapted to solve a wide range of tasks in the common (stationary) impedance spectroscopy. In addition to data fitting to equivalent circuits with resistors, capacitors, inductors, constant phase, Warburg (3 types), user-defined and Gerischer elements, the EIS Spectrum Analyser provides various tests for data consistency and quality of fit. It has also a built-in impedance spectra simulation routine, tools for impedance data processing (subtraction of circuit elements and subcircuits, normalisation for electrode surface area) and plotting in various formats. The program is free for noncommercial use.

See: http://www.abc.chemistry.bsu.by/vi/analyser/

2. ZsimpWin

ZSimpWin is a EIS Data Analysis program that does not require user-input on initial values. ZSimpWin is an Electrochemical Impedance Spectroscopy (EIS) Data Analysis Software integrated with the 
VersaStudio software to provide straightforward and versatile equivalent circuit model fitting.  Innovative concepts have been implemented to achieve the following performance:

• Minimal user input: The user specifies a job by selecting a model for an impedance data set, and simply requests execution to ZSimpWin.  
• Automatic analysis: Parameters associated with the selected model are determined automatically. ZSimpWin assigns an initial guess of these parameters (default = Auto Setup option), starts computation using the initial guess, finds results, improves these results a number of times until desired results are obtained, and then saves the final results. 
• Batch Analysis: Setup a batch by including multiple jobs and process in sequence.  
• Output results in various forms: Results consist of plots, estimated parameters, and historical records of computation process.  Each or several combinations can be printed or copied to Windows clipboard. 
  
• Requires only mouse button clicks:  The whole process requires no entry of numbers or character strings.                                                                
• Compatible with Windows 10, 8 , 7 and XP.

See: https://www.ameteksi.com/products/software/zsimpwin

3. Zview

ZView software from Scribner Associates offers best-in-class equivalent circuit modeling. Fit common circuits instantly, generate publication-quality graphs quickly. ZView integrates easily with SAI measurement softwares, and supports testing hardware from Solartron, PAR, and others. Increase your data processing efficiency quickly and easily with ZView.

See: https://sai-zview1.software.informer.com/3.4/

Introduction of EIS

Electrochemical impedance spectroscopy (EIS) is one of the most powerful methods in the study of corrosion. The EIS method can be used to measure the rate or rate of corrosion, monitor corrosion, determine coating integrity, and study the mechanism of reactions. In this article, which is a compilation, translation and purification of references [1] and [2], the applications, limitations and benefits of this method are introduced. EIS is usually performed by applying an AC current signal to a state-steady electrochemical system and then measuring the current response. Because the amount of disturbance applied, the AC signal, is a small excitation signal, EIS is essentially a non-destructive technique. To apply this method requires a geometrically corroded cell that includes a reference electrode, as well as equipment capable of measuring and recording the electrical response of an electrochemical cell over a wide range of applied AC frequencies. When a small sine voltage is applied to an electrochemical system according to Equation 9, a sine current response in the form of Equation 2 will be observed. Due to the lack of rapid response of relaxation processes or the release of dipoles, the rotation of bipolar components in response to the applied alternating electric field results in a phase change.

Typical measurements in EIS are usually made in a three-electrode system, as shown in Figure 9. The entire set includes an electrochemical cell, a frequency generator, a frequency response analyzer (FRA), and a computer that is used to control experiments and store information. A potentiostat is used to control the electrode potential. The FRA is the heart of the system that calculates the imaginary and real parts of impedance. The frequency studied is usually in the cell range. 0.01–100,000 Hz (cycles / s) Electrochemical, the test material is embedded as an electrode working. Electrode counters, which must be neutral and not involved in the electrochemical reaction, are usually made of Pt, gold, or graphite. Reference electrodes are usually conventional saturated calomel electrodes (SCE) or AgCl / Ag electrodes. However, in many applications, such as thin electrolyte layers or in high temperature environments, conventional reference electrodes do not work properly. In these cases, systems without conventional reference electrodes should be used. As an example, we can refer to the two-electrode system, which usually consists of two identical electrodes consisting of test materials (Figure 2-a) and is widely used in atmospheric corrosion monitoring [5. [Figure 2-b) Indicates that it is used to monitor high-corrosion corrosion. , Multi-electrode array (Figure 2-c) can be used for EIS monitoring.

An uncompensated electrolyte resistance (Rs), a specific capacitance value related to the coating applied to the metal surface (Cc), a hole resistance in the coating of resistance pathways (pore solution resistance) (Rcp) in the coating where ions are transported, a The specific capacitance corresponding to the double layer in the solution / metal (Cdl) and a resistance (Rp) which is the resistance of the charge transfer process (ie corrosion), and in other words, the resistance to polarization at the solution / metal interface. In Beaunier rectified circuits, usually other additional components, such as the constant phase element (CPE), the phase component of the inductance or induction coefficient (L) and the resistor (W (Warburg,) replace the resistor or capacitor. Special capacitance, accuracy and quality of experimental data fitting with these circuits are improved, but the physical interpretation of the results will be ambiguous, this is because the CPE module can not be easily obtained with capacitor capacitance, and the capacity power calculation is calculated. Capacitor from CPE parameters requires accurate knowledge of the physical reasons for CPE behavior [7.] An example of a Nyquist diagram and its equivalent wind diagram in doubt ل 4 is given. The position of the equivalent circuit components in these diagrams is given on each diagram. In addition to common, simple equivalent circuit models, more complex physical models are sometimes used to interpret EIS data obtained from more complex systems. An example is the line transmission model (TML), which was first used by Levie de in his research on porous electrodes [11] [TML model and its modified models for analyzing EIS data on atmospheric corrosion under electrolyte layers Thin [5] as well as stress corrosion [12] have been used.

Atmospheric corrosion is an electrochemical process that usually occurs beneath a thin electrolyte surface layer, in the presence or absence of salt contaminants and dissolved gases in these layers. It has been shown that the atmospheric corrosion rate of metals depends on the thickness of the electrolyte thin film. The thickness of the electrolyte layer affects the rate of oxygen transfer through the electrolyte layer and the dissolution of corrosion products. The rate of oxygen transfer determines the rate of cathodic reaction (in neutral and alkaline solutions) and the dissolution of corrosion products determines the anodic process. Monitoring or corrosion of thin electrolytic films using conventional electrochemical methods is challenging The electrolyte is thin, very high, leading to a sharp drop in ohmic potential and a non-uniform current distribution that makes it difficult to measure the corrosion rate [5. The solution resistance is estimated from the impedance measured in the high frequency range of the EIS spectrum, and the sum of the resistivity (Rp) and the solution resistance (RS) from the impedance in the low frequency range. Figure 4b: The calculated resistive palliation is then converted to the corrosion rate of the metal. To study atmospheric corrosion of the metal surface under thin electrolytic layers (100010-1000 ~) by EIS, it is possible to expose the corrosion cell to the atmosphere. weather Use outside or use laboratory-drier simulation cycles [19–13,10,9,5. Used in epoxy resin (Figure 2-A) to make cells. The study can be done in two ways: either the impedance spectrum is recorded over a wide range of applied frequencies or the impedance value is checked continuously at two constant frequencies. The study of EIS spectrum in a wide frequency range has shown that a one-dimensional equivalent circuit model called TML can be used to model the corrosion rate in these systems [5. Palrization is calculated from the impedance difference measured at the above two frequencies. The corrosion rate is then calculated using the polarization resistance [5]. Nishikata et al. [5] also used shoulder-shaped electrodes to study atmospheric corrosion to EIS. Impedance information was monitored at 10 mHz and 10 kHz. The results showed that the inverse of the mean impedance at low frequency completely corresponds to the corrosion rate obtained by gravimetry. Wetting of Time also occurs when the amount of solution conductivity or high frequency impedance image (Rs image) exceeds a threshold value. One of the disadvantages of this method in the study of atmospheric corrosion is that if the metal surface is covered with a thick layer of corrosion products, the low frequency impedance can not be equated to the polarization resistance. Finally, Ma et al. [20] used a complex multi-electrode system to study atmospheric corrosion and found the results to be more accurate than two-electrode systems. 3.2 Corrosion of reinforced concrete Rebar (in concrete is the main reason for reducing the life of reinforced concrete structures that are exposed to strong corrosive environments) such as marine environment. Therefore, reinforcement corrosion monitoring is very important to assess the health status of reinforced concrete. Various methods are used to evaluate corrosion in reinforced concrete, and electrochemical methods are among the most common. Among these, EIS is an attractive technique because, as mentioned earlier, it is almost a non-destructive method. In addition, EIS is suitable for environments with very high strength, such as concrete, because it is essentially a transient method and does not require the system to be in a stable state [21. [In steel systems (reinforcement) / Concrete, information Various parameters such as the presence of surface films, concrete properties, joint joint corrosion and mass transfer phenomena can be obtained from the EIS method [21. [22] [In addition, the high-frequency impedance of information in Moore Provides dielectric properties of concrete, and low-frequency impedance information on the properties of passive films (surface oxide layers) on steel. Studies that began three decades ago have proven the validity of EIS as a technique for studying rebar corrosion in concrete, both experimentally and theoretically. John et al. (9189) monitored corrosion of rebar in high porosity concrete using EIS. They obtained both the corrosion rate of the steel rebars and the information on the steel surface layers. Later, more fundamental work was done by McDonald et al. To establish the application of EIS in the detection of rebar corrosion in concrete [3]. In this work, the rebar was simulated as a one-dimensional electrical transmission line. Their results show that imaginary and real components of impedance and phase angle can be used to detect corrosion of rebar embedded in concrete, but this is only possible at very low frequencies (for example, 1 mHz). It was also found that monitoring the peak voltage at the concrete surface just above the rebar helps to fully detect corrosion.

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Electrochemical Impedance Spectroscopy (EIS) is a powerful tool enabling the study of processes that occur at the interface of an electrode.

In EIS a periodic signal is applied in current or voltage at several frequencies. The periodic signal is traditionally built with a sinus.
The transfer function H of the system is defined as:

H(s)=L[Output(t)]L[Input(t)]H(s)=ℒ[Output(t)]ℒ[Input(t)] (1)

ℒ  being the Laplace transform

Measurements as a function of the frequency of the perturbation give an impedance, Z,  (or admittance) diagram. The impedance is given in Ohm as it is the ratio of the voltage vs. the current and is a complex number.

To be valid, the system under study has to be:

• Linear: The response (output) of the cell has to be directly proportional to the input. The small perturbation of the electrode state has the advantage that the solutions of relevant mathematical equations used are transformed in linear forms.
• Time invariant: The state of the cell must not change during the measurements.
• Causal: The output has to be correlated directly with the input.

The modulus Z and phase Phi are the parameters of interest, so the impedance data can be plotted in Bode plot (Z and Phi vs frequency), but in electrochemistry, the most common plot is the Nyquist plot -Im(Z) vs Re(Z).

As the periodical perturbation is performed at several frequencies, EIS is capable of characterizing processes that have different time constants i.e. fast process at high frequency (> 10 kHz) and low process such as diffusion at low frequencies (<100 mHz).

Consider Ohm’s law, which describes the relationship of voltage to a direct current passing through a resistor:

E=IRE=IR

Impedance is, very simply, extends the concept of resistance to an alternating current circuit, and generally represented as ZZ. So you can think of it, simply, like this:

E=IZZE=IZZ

We’ll come back to this in a moment. For now, it should be clear that a measurement of impedance, therefore, can be made by made simply by applying an oscillating voltage, and measuring the (oscillating) current response. We can write down an equation for the oscillating voltage we apply like so:

E(t)=|E|sin(ωt)E(t)=|E|sin⁡(ωt)

where |E||E| is the amplitude of the voltage signal, and ω=2πfω=2πf (the angular frequency). The response will be a current with an amplitude |I||I|, which is also shifted in phase from the applied signal:

I(t)=|I|sin(ωt+θ)I(t)=|I|sin⁡(ωt+θ)

The current is shifted in phase because of reactance (e.g., a capacitance or inductance) in addition to the resistance (which changes the amplitude). The impedance can therefore be expressed like this:

ZZ=E(t)I(t)=|E|sin(ωt)|I|sin(ωt+θ)=|Z|sin(ωt)sin(ωt+θ)ZZ=E(t)I(t)=|E|sin⁡(ωt)|I|sin⁡(ωt+θ)=|Z|sin⁡(ωt)sin⁡(ωt+θ)

Have a look at the animation below. The ‘current’, I, is 72° out of phase with the ‘voltage’. The graph on the right is known as a Lissajous curve, showing the relationship between I and E. In the past, impedance spectroscopy was done by obtaining these curves on an oscilloscope and analysing them. Thankfully, it’s all a bit easier nowadays.

Complex representation

Ok, complex maths time. Without going into too much detail, via Euler’s formula:

ejx=cos(x)+jsin(x)ejx=cos⁡(x)+jsin⁡(x)

we can re-write all of the above using complex numbers:

ZZ=|Z|ejθ=|E|ejωt|I|ejωt+θZZ=|Z|ejθ=|E|ejωt|I|ejωt+θ

or simply:

EE=IZZ=I|Z|ejθEE=IZZ=I|Z|ejθ

Note that jj is the imaginary unit, i.e., j=√−1j=−1, which we use instead of ii to avoid confusion with the symbol for electrical current. You can see from the above equation that the ratio of an oscillating voltage to an oscillating current is the impedance, which has a magnitude |Z||Z| and a phase angle θθ. You can think of this as a polar coordinate representation. More commonly for impedance spectroscopy, however, we generally use the Cartesian complex plane representation, dividing the complex impedance into the real and imaginary parts:

ZZ=Z′+jZ′′ZZ=Z′+jZ″

Z′Z′ and Z′′Z″ are the resistive and reactive parts of the impedance respectively. You’ll see this more clearly on the page about the impedance of simple RC circuits.

We can represent any ZZZZ on an Argand diagram, as in the graph below. This is the basis for the Nyquist plot, which is the plot of the real and imaginary parts of the impedance that you’ll come across most often. An impedance measurement for a single frequency is a single point on a Nyquist plot. An impedance spectrum is therefore a series of points, where each point is a different frequency.

These plots are visually useful, because the characteristic shapes that can appear in the plots as you’ll see later can give you a rough idea of what you’re looking at. The downside, though, is that you can’t know what the frequency associated with a particular point is from looking at the Nyquist plot alone, and so the plot doesn’t contain all the information you need. This is why the alternative Bode plot – plots of logZ′log⁡Z′ and logZ′′log⁡Z″ vs logflog⁡f, or log|Z|log⁡|Z| and θθ vs logflog⁡f – are still important.

Nyquist plot

I’ll finish up this page by briefly introducing a typical Nyquist representation of an impedance spectrum itself. The plot below is data I acquired from a Li-ion test battery, and fitted to a model myself. The frequency range the points represents is between 100 kHz and 100 mHz. This is fairly typical for most systems, although depending on what you want to measure you might go up to 1 MHz or more, or as low as 1 mHz. So how do you make sense of this plot? Well, there are three things I’ll note for now.

First, the impedance is always lowest (i.e., smallest values of |Z||Z| at the highest frequency, so you can see that the frequency decreases if we follow the curve from the points near the origin to the points in the top-right corner. Secondly, you’ll note (as in the Argand diagram above) that the values of Z′′Z″ are negative (plotted as −Z′′−Z″). This will become clearer later, but by convention capacitance is a negative reactance, so impedance spectra will in most cases only have positive Z′Z′ values and negative Z′′Z″ values.

Lastly, you’ll note the shape of the spectrum, particularly the semi-circle part. The shapes you see in the Nyquist plots can be characteristic of certain elements or combinations of elements, so they are (often, but not always) visually useful for quickly understanding something about the system you’re measuring. Because of this I was able to take this relatively good quality data, think of a reasonable model, guess a few of the parameters and then fit the entire spectrum relatively quickly. In the following pages you’ll read about the experimental technique I used to get this data as well as the elements of the model I’ve fitted the data to, and hopefully you’ll be able to see how it all fits together.

Orthonormal scales should be used for Nyquist impedance plots. The length from 0 to 1 along the imaginary axis should be equal to the length from 0 to 1 along the real axis. Otherwise, semicircle graphs are not semicircles (Fig. 1) and it becomes difficult to measure angles (Fig. 2). We present here two examples: the impedance for a Tafelian redox system (Fig. 1) and the Randles circuit with Warburg impedance (Fig. 2). Orthonormal and non-orthonormal plots are compared: non-orthonormal scales are indicated by a sad face and the orthonormal scale is indicated by a happy face. More details in the corresponding Mathematica Demonstration [1].

EIS accuracy contour plots must be used to interpret errors made during EIS measurements and identify the best frequencies possible to be used for a given impedance range. The aim of Fig. 1 is to demonstrate how to read and understand EIS accuracy contour plots provided with each potentiostat .

Fig 1: Superimposition of EIS accuracy contour plot and modulus
Bode diagram of R1+R2/C2  electrical circuit (left) and Nyquist diagram
of the same circuit (right).

The different colored areas show different ranges of impedances that can be measured at various frequencies within a specified error in magnitude (%) and in phase (°).

The accuracy contour plot is an image of the capability of the instrument and is only valid for a given set of conditions (input amplitude, temperature, data averaging, etc).

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Corrosion of steels represents worldwide, one of the most costly problems that several industries are challenged every day due to the aggressive conditions during the manufacturing process of the steel parts or the premature failure of steel tools by stress corrosion cracking (SCC) as well as deterioration of steel components from equipment and machinery in a certain service. The construction industry is an example in where steel is essential, which requires durable and strong structures for the build of bridges, tunnels, towers, buildings, airports, roads, plants and railways. Many of these constructions are usually outdoors, exposed to the atmosphere conditions, additionally, the surrounding environment where these steels are placed for their service is often highly polluted, that it often degrades the steel structure at a considerable corrosion rate.

Some of those steels are also design to be used in the; mining industry, pipeline transport of fluids, shipbuilding, agriculture equipment and heavy machinery, among others. During their usage, steels are also severely damaged by one type of corrosion mechanism [1, 2, 3, 4]. According to Zaki Ahmad [5] the concept of corrosion must be defined taking into account the environment in which the metal-materials are place to serve for long periods of exposure time, thus, all the environments are considered corrosive to some degree of damage as follows; i) air humidity, ii) fresh, distilled, salt and marine water, iii) natural urban, marine and industrial atmospheres, iv) steam and gases, v) ammonia and hydrogen sulfide, vi) sulfur dioxide and oxides of nitrogen, vii) fuel gases, acids, alkalis and soils.

Therefore, the concept of corrosion in steels is then define as a natural electrochemical process that destroys the integrity of the metal structure in the presence of any environment containing moisture and oxygen. This process involves two electrode reactions that can occur in a spontaneously way at the interface between the metal and the aqueous environment according to the thermodynamic’s Law; One, is the reaction of metal-base with chemical species from the environment (i.e. anodic-oxidation reaction, which discharge electrons from the metal substrate) and the second is the reduction reaction of an oxidizing agent (i.e. cathodic reaction, which restores the electron deficiency with reduction of protons from the metal surface). The exchange of electrons between anodic and cathodic reactions produces an electronic current flow across the metal interface, which is known as corrosion potential (E_corr). This means the value at which the two-coupled reactions are in equilibrium, some effects can be caused by imposing an electrical potential on the metal surface as much greater than the E_corr to favored the metal dissolution reaction as a soluble species that diffuses into the aqueous solution [4, 5]. This suggests that Fe contained in steel as a base component is oxidized and depends on the free energy like a driving force of E_corr. The transfer of the charge (ions/electrons) through the metal interface, react with the oxygen from the steel surface, with the subsequent growth of an unstable corrosion product in the form of a thick porous-oxide layer (also known as rust), which occupies more volume than the original material. However, hydrated iron oxides are not considered as a protective layer on steels in presence of negative ions, Cl⁻, SO₄²⁻ or NO₃²⁻. Figure 1 shows a typical example of the degradation mechanism of concrete structures due to corrosion of the steel reinforcement embedded in it; i) initially, the pores of the concrete structure are the access pathway of negative ions that come from the environment, ii) then, corrosion reduces the cross-sectional area of the steel bar, iii) it produces oxides (hydrated ferric oxide-rust) with a larger volume that cause tensile stress in surrounding concrete areas, which results in cracking and subsequent structural failure of the concrete [6].

In other conditions, a thin oxide film can grow on metal-base to provide the protection against corrosion attack, that steels require in order to be useful when they are exposed to severe atmospheric conditions during their usage. This passive film is so thin that it is invisible to the naked eye; however, this film can be self-repaired immediately, when it is suddenly scratched or intentionally removed. An example of this outstanding property is the existence of several types of stainless steels that usually contains a significant proportion of chromium (12 to 25 wt.% Cr) with nickel and molybdenum to prevent the formation of ferrous hydroxide (Fe2++2OH−→Fe(OH)2rusting product)Fe2++2OH−→FeOH2rusting product by the presence of Cr in the Fe-base alloy, which reacts with oxygen from the environment to form a passive adherent oxide-layer (Cr₂O₃), thus, given a remarkably resistance to corrosion attack of the underlying metal, additionally, this oxide layer, can be regenerated by itself in the presence of oxygen [4, 7, 8, 9]. Based on the fundamental concepts, one of the advantages of using stainless steel is its high corrosion resistance, but in combination with other alloying elements can provide good mechanical strength, making the steel an appropriate material to be used in diverse applications that, in many cases, offers the only alternative for its high durability in aggressive environments; its use can be seen in domestic (cutlery, blades, household appliances and electronics), architectural (structures, handrails, concrete reinforcing bars, building components, cables for bridges and coastal works), transport (automotive exhaust system, ship containers, waste trucks and tankers for chemicals), chemical (pressure vessels, chemical containers, pipes, chemical plants, waste-water treatment), oil/gas (platform structures, machinery, storage tanks and pipelines), medical (surgical instruments, implants, equipment, dental inserts, wire and brackets in orthodontics), and other common uses (food containers, beverage bottles, springs, fasteners, bolts, nuts, washers and wires) [10].

For conventional steels produced by casting process, the most useful steel products are those that contain small amounts of alloying elements such as plain carbon steels (Mn, Si, S, P), alloyed steels (Cu, Ni, Cr or Al) and tool or machinery steels (W, Mo, Co, B and V). This alloying provides mechanical strength, ductility, machinability, and a substantial corrosion resistance. Although, these steels do not have the same ability of corrosion protection as the stainless steel does; the oxide film formed on the surface has only a few micrometers thick with microporous or growth defects, so it is possible to inferred that this oxide layer does not protect the metal from corrosion attack, this means a temporally low passivity is considered. However, in aggressive aqueous solutions the porous oxide layer can dissolve or break-down at least some areas of the film, therefore, leading to the Fe-base to a further localized attack. In industrial applications, the surface properties of the steel have a significant impact on their service life and performance. Among the several surface treatments to provide protection through a thick hard layer, diffusion techniques are using such as powder pack, gaseous atmosphere, plasma, ion beam and salt baths, that depends on the diffusion time and atmosphere concentration, these being a high effective treatment and less expensive. Additionally, carburizing, nitriding or boriding, are also well-known as thermochemical surface treatments [11, 12, 13, 14, 15].

Acid solutions are frequently used in many applications concerning industrial processes and are considered as the most corrosive media for steels. Acids like HCl, H₂SO₄, HNO₃, H₃PO₄, H₂CrO₃, and some alkalis such NH₃ are frequently used for surface cleaning, removal of rust deposits, pickling processes, chemical attack, metal surface treatments, and wastewater systems. Other relevant uses are metal-processing equipment, chemical processing, pipelines, food processing, chemical and petrochemical plants. Therefore, printed research works report several cases of using organic molecules compounds (imidazole, 2mercapto-benzimidazole, pyridine, thidiazole, pyrrolidine, triazole, among others) that have provided a significant corrosion inhibition property for steels during their exposure to acid media [16, 17, 18, 19, 20, 21, 22, 23, 24]. These molecules must contain in their structure functional electronegative groups, π electrons, heteroatoms or heteroatoms of nitrogen, sulfur and oxygen with aromatic and heterocyclic rings. These reports generally indicate that the molecules are dissolved in an ethanol-water solution and then added in small concentrations (ppm) to the acid media, in all the cases, a barrier layer of organic molecules is formed onto the metal surface by an adsorption mechanism, thus giving corrosion protection on steels under-service at aggressive conditions [16, 18, 20, 24].

According to Florian B. Mansfeld (1988) in his research (Do not be afraid of electrochemical techniques —But use them with care) [25] comments that corrosion is fortunately a problem that can be tracked by means of electronic devices (i.e. potentiostats) that applies an electrical signal (V or I) to measure and control the electrical charge transfer; in pursuance of evaluating the reaction kinetic and mechanism of corrosion process that takes place at the metal interface. Meanwhile, the constant improvement of measuring instruments and the availability of commercial software, makes possible an easy performance of the electrochemical tests for the evaluation of corrosion progress and its control in an experimental way. These achievements caught the attention of chemical, petrochemical, food processing and steel manufacture industries, as well as research laboratories and higher education faculties that have encouraged and certified the success of the use of electrochemical techniques to monitoring corrosion on steels. The application of electrochemical techniques, such as linear polarization, polarization resistance and potentiodynamic polarization, have often been used for several decades in evaluating successfully some basic phenomena as oxide passivity, effects of alloying elements, reaction kinetics and the use of inhibitors to control the corrosion behavior, among others. However, it is important to consider the limitations of the polarization techniques that use Direct Current (DC), to perturb the equilibrium of the interface between the metal and electrolyte solution, is the ohmic-droop that is often ignored, this occurs when the current flows through the resistance of the test solution and the resistance of the connecting cables to electrochemical cell electrodes (i.e. uncompensated resistance, IR) [25]. The effects of IR can cause severe distortions of polarization curves, leading in the erroneous estimation of corrosion rates and misinformation of the kinetic model that represents the potentiodynamic curves. Given this limitation, through the last decade, another electrochemical technique appears to be more suitable for corrosion studies, this is the Electrochemical Impedance Spectroscopy (EIS) that uses a small amplitude of alternate current (AC) in a certain frequency domain applied to the corrosion system under study. Usually, EIS data is collected through a potentiostat/galvanostat apparatus, and then it is fitted to an equivalent electrical circuit (EEC) model for its interpretation and analysis, fundamentally seeking a meaningful physical interpretation. In correspondence with several studies [26, 27, 28, 29, 30, 31, 32, 33] EIS is considered a successful new electrochemical technique with a great evolution in recent years that has become an essential analytical tool in the research of materials science. For its detailed information, versatility and sensitivity that makes possible to be used widely in; corrosion studies and corrosion control, monitoring of properties of electronic and ionic conducting polymers or ceramics, colloids and coatings, measurements in semiconductors and solid electrolytes, studies of electrochemical kinetics at electrode-media interfaces, determination of conducting or diffusion mechanism, reactions and process [34].

The practical estimation of EIS technique could be difficult to understand by non-specialist because of the lack of comprehensive and explanation about the theory’s basic aspects in conjunction with the experimental measurements. Nevertheless, it is possible to attain a logical interpretation and analysis of acquired impedance data for a certain practical system, such as those studied in this chapter that will be shown later. In this sense, to avoid uncertainties and misinterpretation of impedance data, analytical co-relationship of physical, chemical and manufacture parameters must be established with an equivalent electrical circuit (EEC) model, thus given a common sense to the impedance response. Therefore, this review considers a wide variety of practical electrochemical impedance cases for the study of corrosion mechanism on steels based on the basic aspects of EIS theory and its experimental interpretation. This chapter serves as a support for postgraduate students to have a criterion in deciding through their own experiences when using the electrochemical impedance technique. The practical cases discussed here are part of the research experienced by Dr. Héctor Herrera Hernández known in the scientific community as DR.3H. Recently, DR.3H and his students & research group are dedicated to their experience in electrochemical impedance knowledge in medical applications as bone replacement or PVDF-based membranes as an appropriate scaffold for skin cell growth [35].

Cases of EIS study applied to steels;

• Steels measured in their received condition.
• Kinetic oxidation reaction at different aqueous solutions.
• Steel corroded at non-stationary condition.
• Corrosion monitor in concrete reinforced materials.
• Inhibition using organic molecules.
• Inhibition in natural liquids extracted from plants.
• Hard-coatings as protection.
• Corrosion monitor in steels used as food containers or beverages.

1.1 Fundaments of electrochemical impedance spectroscopy (EIS)

Since the middle of the 18th century, the Impedance Spectroscopy (IS) technique has been established as a popular theoretical approach to study the electrical properties of conducting materials and their interfaces. However, in the last quarter-century, IS becomes a practical tool that is successfully applied in electrochemistry as an analytical method widely used in many disciplines such as materials science, corrosion technology, semiconductors, conducting polymers, ceramics, coatings, energy storage, and solid-state. Electrochemical Impedance Spectroscopy (EIS) is considered as a new technique with astounding advantages [36, 37, 38].

The concept of impedance in electronic devices is generally treated as a purely complex phenomenological amount and is considered as one of the most important physical characteristics that concerns the resistance that the medium opposes to the propagation of sound (acoustic impedance, Z) through it and therefore it is equivalent to the electrical impedance. In this sense, acoustic impedance is the ratio of the sound pressure of the wave (P) to its volume speed (U) in a material medium [39, 40]. This concept becomes a similar analogous meaning to the electric approach, because an electrical impulse (V or I) is applied to the conducting electrodes and a characteristic electrical response is resulted, known as impedance, Z. Therefore, impedance is then defined as the measure of the ability of a certain circuit to resist the flow of electrical current. The electrochemistry impedance is the relationship between a potential energy difference and the flow of electrons generated by a wave signal applied in an aqueous media. EIS technique is characterized by using an alternating current (AC) signal as driving force, which is applied to a conductive electrode, thus obtaining a characteristic response from the system interface. One of the attractive aspects that makes EIS as a suitable tool for investigating the electrochemical properties of materials during their exposure to aqueous solutions, is the simulation of the system behavior by means of an idealized circuit model. This consists of an arrangement of passive electrical components (i.e. resistors R, capacitors C and inductances L), which are the physical representation of the electrochemical processes occurring at the system interface under study.

Another quality of EIS is its high measurement sensitivity, which makes the technique an attractive advantage for detailed information that can be obtained from the system in study. For example, EIS was used to evaluate the properties of thin oxide films formed on metals, monitoring superficial degradation of polymer layers or paint coatings due to swelling process (coatings damaged by water uptake). Surface changes due to ion adsorption at the interface can also be detected, knowing the kinetics reaction on metals under corrosion process; all this, due to the advantages of this technique to perform measurements using a very small amplitude signal at variable frequency range. As result of the advantages mention above, EIS has attracted the interest of many scientist and engineers from different areas of application, for example: corrosion technology, electrochemistry, metallurgy, hydrodynamic, chemistry, biology, physics, mechanical, and medicine. According to organic chemistry a molecule is a group of non-electrically charged particles that have two or more atoms chemically bonded. They are components of the matter lying on earth (minerals, atmosphere, gaseous substances, organic and inorganic compounds, liquids, among others) [41]. Molecules can be measured with a small AC amplitude of voltage as a function of the frequency without altering their properties. Some systems leading to the formation of interfaces with the materials for example; a solid–solution interface allows the ion charge transfer, conduction and electron flow that is governed by the free energy of the chemical reactions occurring at the interface region (named double layer), as is shown in the model of Figure 2. The electrical properties of the double layer can be measured by an electrical equivalent circuit, considering that the double layer behave as pure capacitor C_dl (ions charge) and the flow of ions through the metal surface is view as a resistance R_ct of current, in according to Ohm’s law. In general, EIS allows separating the contribution response of different components in terms of the resistance of electron charge transfer, double layer capacitance, solution resistance, inductance, and other parameters, where several electrochemical processes are proceeding at a different reaction rate.

1.2 Basics aspects of EIS data representation

Electrochemical impedance spectroscopy (EIS) is the analytical method widely used to study the electrochemical systems by applying a small ACvoltage signal as a function of frequency of the amplitude signal. In potentiostatic mode as that of direct current (DC) techniques, like Linear Polarization Resistance (LPR) or Polarization Potentiodynamic, the basic measurement parameter is the polarization resistance R_p that is equal to the impedance (Z) in alternate current (AC) mode. This can be represented according to the Ohm’s Law equation as denote bellow [8]:R=VI(DC),Z=EI(AC)R=VIDC,Z=EIACE1

where R is the resistor (Ω), V is the voltage (volts) and I is the current (amps) for direct current and E is the potential (volts) and Z is the impedance (Ω) for alternating current. To understand how the theory supports the EIS technique, it is necessary to consider two periodic waves; one is the current signal (I) and the other is related to potential signal (E). These waves behave as that shown in Figure 3, in which both signals oscillate at the same frequency and intensity, because one wave causes the other. However, there is an important effect that is the constant time shift between the two waves at certain angle, this is called the phase-angle shift (ϕ)ϕ and can vary from 0 to 90. Its unit is degrees (°), because usually waves are considered vectors in a polar coordinate system or in a sine function. Figure 3 shows the relation between waves E, I and the phase-angle shift. The applied sinusoidal perturbation can be a potential signal (E), thus given the measurement response in current (I) at a certain frequency domain. The excitation signal as a function of time ttis represented as follows;

Et=Eosin(ωt)Et=EosinωtE2

where EtEt is the potential at time tt, E0E0 is the amplitude of the signal and ωω is the angular frequency (expressed in terms of radians/second). So, the relationship between angular frequency and frequency (ffin hertz units) is given by;ω=2πfω=2πfE3

in order to preserve the linear behavior in electrochemical systems, a small amplitude of AC voltage of about 5 to 10 mV is usually applied. ItisItisthe single response of instantaneous current at the maximum amplitude, Φ is the shifted-phase angle and has a different amplitude, I0I0 as described in Eq. 4;It=Iosin(ωt+ϕ)It=Iosinωt+ϕE4

taking into account the electrical parameters of E and I as a function of angular frequency in the time domain, as well as the shifted-phase angle is possible to rearranged the Eq. 2 and 4 into Ohm’s Law as DC current, this relationship enables to calculate the impedance of the system under study as follows;Z=E(t)I(t)=E0sin(ωt)I0sin(ωt+ϕ)=Z0sin(ωt)sin(ωt+ϕ)Z=EtIt=E0sinωtI0sinωt+ϕ=Z0sinωtsinωt+ϕE5

then, impedance (Z0Z0) is defined as the ratio of applied voltage (E) divided by current (I) and represents an opposition to the flow of electrons or current in an AC circuit due to the presence of resistors, capacitors and inductors. Among of variety of passive electrical components, only resistors and capacitors or inductors contribute manly to impedance; one is related to the real component (Z′)Z′ and the other to the imaginary component (Z′’)Z′′. Due to this assumption, Z0Z0 can be expressed in its complex notation by incorporating the complex number j=−1−−−√j=−1, where the Figure 4 shows the complex representation of the impedance as vector concept, Z(ω)=Z′+jZ”Zω=Z′+jZ′′ and its phase-angle, tan(ϕ)=Z”Z′tanϕ=Z′′Z′. Using Euler relationship, the expression of the impedance translates in a complex function like;

Et=E0exp(jωt),It=I0exp(jωt−ϕ)Et=E0expjωt,It=I0expjωt−ϕE6

considering the relationship between the potential and current amplitude, it results the total of the impedance as a complex number, as it follows;Z(ω)=EI=Z0exp(jϕ)=Z0(cosϕ+jsinϕ)Zω=EI=Z0expjϕ=Z0cosϕ+jsinϕE7

however, the use of the current as a perturbation signal is also designed for certain electrochemical applications. Once the experimental data are collected, a series of potential-time and current-time are obtained, which correspond to the impedance at each frequency studied. The representation of the EIS data ​​is by means of Impedance Spectra known as Nyquist Plots (−Z_imag vs. Z_real) that represent the real impedance plotted against its imaginary part and also is often used the Bode plots (log|Z| vs. log freq., ϕϕ vs. log freq.) that is the graphical representation of the modulus of the impedance and its phase-angle, as a function of the frequency domain) [43, 44]. However, Mansfeld [25] is his reports suggest that Bode plots is more appropriate to represent the impedance data because most of the measuring points are completely displayed at the entire frequency domain of the spectra. Thus, allowing a quick diagnosis of the behavior due to the sensitive of the phase-angle to small changes as a function of frequency variation, expecting time constants. While, Nyquist’s diagrams are not recommendable since most of the data is grouped together at both ends of the spectra.

Experimentally speaking, when an EIS analysis is chosen to study the corrosion behavior of a piece of metal (WE-working electrode) that is immersed in an aqueous solution for a certain period of exposure time, which its equilibrium is perturbed by a low amplitude sinusoidal signal as function of frequency in the presence of a polarizable counter electrode (CE) and a reference electrode (RE), it is necessary to consider some electrical parameters (i.e. dielectric constant, permittivity, conductivity, resistivity and capacity charge) that will allow to interpret and deduce the corrosion behavior and its reactions mechanism by modeling the EIS data to an electrical RC circuit. These RC circuits are assembled with capacitors (C) and resistors (R) in parallel or series. C_dl is used to represent the electrical charge transfer at the metal/electrolyte interface known as the capacitance of a double layer (in farads), and that is present in all corroding aqueous systems. R_ct is the resistance of the electron charge transfer, which is the value of the impedance in its real component and R_s is the solution resistance. The combination of these three passive elements provides a simple equivalent electrical circuit (EEC) for a uniform corroding metal. The experimental contribution of each parameter mentioned above is like that shown in Figure 5.

1.3 Analysis and interpretation of EIS spectra

As mention above, EIS data is usually represented by Bode plots in which the |Z| module and phase angle ϕϕ are fuctions of frequency domain, sustained by its complex plane form that relates to Zreal with the imaginary part Zim, and are usually interpreted by a mathematical correlation to a certain physico-electrical model known as equivalent electrical circuit (EEC), which is designed by an arrangement of ideal components (resistors R, capacitors C and inductors L) connected in series or parallel in order to reproduced the experimental EIS spectra. The impedance values of these elements are associated to the electrochemical processes of real systems such as electron charge transfer, diffusion processes, determination of the capacitance of the electrochemical double layer, mechanism of ions adsorption, mass transfer kinetic, characterization of coatings integrity, electrical resistance of the electrolyte, corrosion detection, conductivity, electrochemical reactions, among others, Table 1 shows different EECmodels that were designed to simulate & interpreted in particular some of the most common electrochemical processes, which will help to understand and describe the EIS spectra obtained during an experimental procedure. For example, If an alternating voltage E(t)=Eo∗Sin(ωt)Et=Eo∗Sinωt of about 10 mV at 1 Hz is applied to the RC circuits that are shown in Table 1 as the perturbation energy of the models to carrier electrons through their passive components, this results in a signal that has a sinusoidal behavior and varies as a function on time (i.e. current intensity Io=EoRIo=EoR), this waveform moves in the same direction and frequency as the supplied potential. However, to simplify the use of sinusoidal signals and their effect on different electrical components such as R (resistor), C (capacitor) and L (inductor), the typical sinusoidal response of the RC components is like that are shown in Table 2, and also it shows their relation to the shifted phase-angle value, the impedance as a function of time-frequency and their relationship to the electrochemical processes.

Table 1.

EEC models used to describe the electrochemical processes most studied by EIS. 1. Electrochemical interface (electron transfer), 2 and 3 oxide products and coatings, 4. corrosion mechanism, 5. adsorption and 6. ion diffusion processes.

Table 2.

Impedance and phase shift angle response for the passive RC electrical components.

A single RC circuit is first considered to have only one ohmic resistance of 3.3 kΩ connected to a power source, in this case, the current intensity flows constantly through the resistor without any phase difference with respect to the potential that originates the waveform signal, ϕϕ = 0°. Then for this condition in that the phase-angle is equal to zero, the value of impedance module for a pure resistor (R) is relatively its reactive or real part (ZR(t)=RZRt=R), being its imaginary part or the reactance X equal to zero, so it is suggested that this behaves as a resistive component. The impedance diagram for a resistive component shows a single straight line on its real axis that tends to infinity as dependent on time and frequency domain. In the case of a pure capacitor (C) the sinusoidal response of voltage is retroceded at least by −90° allowing the imaginary component to be the variable dependent on time and frequency domain, so its value of ZC(t)=−1jωCZCt=−1jωC. In the opposite case, it happens for an inductor (L) in which the current waveform signal is advanced near to 90°, which gives the expression ZC(t)=jωLZCt=jωL.

On the other hand, when two passive components are combined in a RCcircuit, for example, one resistor of about 276 Ω and a capacitor of 1 μF which are connected together in series, a small electrical AC signal of 10 mV is supplied to flow electrons through the closed circuit as dependence of frequency domain from 1 MHz to 1 mHz, the impedance is given by ZT(t)=−1jωC+RoZTt=−1jωC+Ro, and depending on the resistance and capacitor values can be considered as capacitive or resistive behavior. The Bode and Nyquist plots of Figure 6a show the experimental simulation of impedance response for these RC components connected both in series, which behave like a capacitive. Circuit model #1 shows the simplest arrangement of series and parallel, in which a resistor of 3.3 kΩ is connected in parallel to a capacitor of 1 μF and then in series with other resistance of 276 Ω, its impedance response could be described as a function of frequency according to the following equation (ZT(t)=R11+(jωC1R1)+Ro)ZTt=R11+jωC1R1+Ro, see Figure 6b the corresponding impedance spectra. So, circuit #1 is known as Randles circuit and is the typical electrical model used to described as analogy form the physical phenomenon of metal under corrosion attack [45, 46] by electron charge-transfer at the interface metal/electrolyte, and also to simulate uniform corrosion on homogeneous surface, which it has been the most used along the decades on researches. The information data of the impedance spectra is clearly visible in Figure 6b, because it is possible to obtain the value of the frequencies corresponding to the solution resistance R_s, charge transfer resistance R_ct (or polarization resistance), and its capacitance of the double layer C_dl. From the Nyquist Plot of Figure 6b C_dlis clearly observed as a well-defined semicircle (a single time constant) in the entire frequency domain as results from the electrical circuit #1, which is the diameter of this semicircle is equal to R_ct and R_s is obtained by reading the real axis, Z’, value at the high frequency intercept. However, considering the maximum angular frequency (ω_max) as the frequency at which the imaginary component of the impedance Z” has its largest value and R_ct, the value of C_dl is given by the following expression;

Cdl=1ωmaxRctCdl=1ωmaxRctE8

Two-time constants could be expected in Figure 7a (circuit #2 is the combination of parallel RC in series)(ZT(t)=R21+(jωC2R2)+R11+(jωC1R1)+Ro)ZTt=R21+jωC2R2+R11+jωC1R1+Ro, or Figure 7b (circuit #3 is a parallel arrangement in parallel connection (ZT(t)={[R21+jωC2+R1]∥∥1jωC1}+Ro)ZTt=R21+jωC2+R1‖1jωC1+Ro as results of applying voltage through the circuits or Figure 7c (circuit #4) (ZT(t)=[(R2+1jωC2)∥∥R1∥∥1jωC1]+Ro)ZTt=R2+1jωC2‖R1‖1jωC1+Ro. These EEC models are used to describe the impedance spectra for oxide products forming by corrosion reactions on the metal surface, or anodizing coatings, or for paint-coated metals after exposed to corrosive electrolytes. Where C1 is the capacitance of oxide film connected in parallel to R1 that is the oxide resistance, both connected in series to RC parallel that contributes the electrical response of inner barrier layer or the double layer interface (oxide/metal matrix). The capacitance value of coating is measured in Farads [F], which depends on its dielectric constant ε and its thickness d as given by;

Cc=ϵoϵAdCc=ϵoϵAdE9

Where ϵoϵo is the electrical permittivity constant of free space (8.85 × 10⁻¹² F/m) and A is the exposure area of the coated electrode. So, it is expected that the capacitance of coating increases with the exposure time due to water up-take by the coating through ionically conducting paths called pores. Changes in pores resistance and capacitance can be used to estimate the corroding metal.

Other types of impedance spectra commonly observed in the printed research works, are similar to that reproduced with the simulation using circuit #5 or #6. Circuit #5 is the similar arrangement of circuit #3, in which the ideal capacitor C is replaced by a magnetic coil (inductor) L(ZT(t)=[(jωR2LR2+jωL+R1)∥∥1jωC1]+Ro)ZTt=jωR2LR2+jωL+R1‖1jωC1+Ro. In this sense the impedance diagram in Figure 8 shows a semicircle very well defined by its diameter throughout the frequency range (charge transfer process) but is accompanied by a second inductance response below the semicircle at low frequencies, that means adsorption ion mechanism. This impedance response is commonly observed in electrochemical systems where chemical species, ion or any molecule is physically adsorbed at the interface of the electrochemical double layer with a given electrical charge motion. While circuit #7 is derived from the simplest circuit #1 in which its resistor is replaced by another electrical element Zw(ZT(t)=R1+W1+[jωC1(R1+W)]α+Ro)ZTt=R1+W1+jωC1R1+Wα+Rocalled Warburg impedance and related to the diffusion control of the species this can happen when the surface concentration of an electrochemically active species changes during the AC cycle. Thus, it must consider the impedance of a cathodic reaction, such as the reduction of oxygen that is common in corrosion systems. The general shape of a Warburg impedance is shown in Figure 8b. Two regions are clearly seen; a semicircle response is due to the charge transfer reaction and straight line with a 45° angle to the abscissa means to the diffusion of reactants [6, 43, 44, 45]. This is typical for analytical electrochemistry in diffusion controlled (W) in corrosion measurements, which is expressed by the Eq. (10), where σσ is the Warburg coefficient and can be calculated from the slope of the straight line in the complex plane of Figure 8b.

W=σω−1/2(1−J)W=σω−1/21−JE10

In real cases the shape of Nyquist plot does not always show a perfect semicircle as it is observed for pure capacitor, it is necessary to replace capacitor (C) by a Constant Phase Element (CPE) in order to compensate the depression of the semicircle of frequency dispersion resulting of an experimental system due to the surface inhomogeneity, surface roughness, electrode porosity, surface disorder, geometric irregularities, and others. The CPE is a mathematical expression that is useful to represent several electric elements (ZCPE=Qo(jω)1−α)ZCPE=Qojω1−α, [47]. To obtain the capacitance value ​​(Cdl) from the CPE, it is necessary to obtain the maximum frequency of the Nyquist semicircle (ω_θmax) as well as the n exponent, this exponent can have values between 0.7 to 0.9, which can be used to describe the experimental data and a physical meaning is not yet clear, Qo is a constant element with dimensions S-secⁿ. Eq. 11 shows the calculation of C_dl:Cdl=QO∗ω(n−1)θmax.Cdl=QO∗ωθmax.n−1E11

In Figure 9 is shown the configuration of EEC for a Nyquist Plot obtained experimentally from a corrosion system, the use of CPE was useful to adjust the experimental data to a mathematical fit in order to obtain the corrosion behavior of the metal (carbon steel APIX-52-5 L) in acidic media) HCl1M [20, 47].

The validation of the parameters obtained through an analogous EEC model can be evaluated through the Kramers-Kroning Transformations (KKT), this is done in order to evaluate and understand the mechanisms that occur in the system interface. KKT are mathematical relationships between the real and the imaginary parts of the impedance that must be obeyed by valid impedance data. Therefore, meaning that when imaginary impedance Z´´ is known for all frequencies, it is possible to calculate the real impedance Z´ at all frequencies [48, 49]. The general conditions on which KKT are based are show bellow:

1. Causality. The response of the system is due only to the perturbation applied and does not contain significant components from spurious sources.
2. Linearity. The perturbation and response of the system are linearly related i.e. the impedance is independent of the amplitude of the perturbation signal.
3. Stability. The system must be stable in the sense that it returns to its original state after the perturbation is removed.
4. The impedance must be finite-valued at ω→ω→0 and atω→ω→∞ and must be continuous and finite-valued function at all intermediate frequencies.

It has been shown that when a corroding system obeys the just mentioned four criteria the impedance data will converse correctly. However, the inverse is not always true. It is still possible to have a correct KKT when impedance data are nonlinear. In the case of our impedance measurements we are mainly concerned about the stability of the system and for this case the KKT is an excellent tool for data validation.

2. EIS applied to metal corrosion

2.1 Analysis of effects of a voltage stimulus applied to corroded metals

One of the principal applications of EIS is in the study of electrolyte/electrode interfaces which is widely used in the evaluation of corrosion mechanism in metals at different environments conditions, but it has also been very useful in the performance of coatings [50, 51, 52, 53, 54, 55] and in the failure detection of materials by stress corrosion cracking, similarly according to recent publications EIS also appears to be applied in ceramics materials [56, 57, 58]. In this sense, most of literature indicates that when applying a periodic signal of potential with amplitude from 5 to 10 mV in a given frequency domain, it is possible to detect the transitory current to obtain a change in the phase angle between I–V and the |Z| data, which progress over time in order to predict metal corrosion phenomena or a possible electrochemical reactions at the metal interface. It should be noted that using a known electrical circuit it is possible to characterize the impedance spectra for each system under study as it shown before. The device that allows applying a programmed potential and detected the current is a potentiostat. Therefore, in this study a galvanostat-potentiostat PARSTAT-4000 was used to evaluate the effect of the voltage applied to the two-electrode interface. In which a periodic constant signal at 1 kHz of frequency was applied over a voltage range of 1 to 1000 mV as a function of frequency domain (1 MHz to 1 mHz). For this study it was considered the following systems; i) An ideal system like circuit #1, which is designed by RC components, a pure capacitor of 1 μF is connected in parallel to a resistor of 3 kΩ and then connected together in series with a resistor of 200 Ω and ii) a 3 cm² of stainless steel plate were used as working electrode (WE) after being exposed to an aqueous solution of HCl 1 M, then the WE was perturbed by a sinusoidal potential at different amplitude from 1 to 1000 mV, the corresponding impedance data for each of the cases that are displayed in Figure 10.

The results show that when an alternate electrical pulse V(t) of 1 kHz fluctuates from 1 to 1000 mV through an ideal circuit like EEC model #1 as that shown in Figure 10a, a uniform current I(t) flows as a function of frequency domain, this signal produces a well-defined time constant in the entire frequency range. During the pulse at a time t the capacitor stores electrical energy causing an increase in potential difference (ZT(t)=qC)ZTt=qCand that allows the current to be phase shifted with respect to the voltage of about 60°, meanwhile the resistor R1 connected in parallel does not allow the passage of the current, instead of it decreases gradually to zero according to the Ohm’s Law, that is why the capacitor stops charging load. Finally, when the period of the capacitor’s transient load ends, the potential difference in the circuit must be zero when the stored load has been exhausted, i.e. the circuit has been returned to its equilibrium state. Due to the characteristics of the capacitor, which is composed by a parallel polished metal plates separated with a dielectric at a distance of d, and due to the transient events of charging rate and discharging rate during the continuous passage of the potential at different intensities of the signal amplitude does not cause changes in the interface of the plates, so the impedance data in bode representation are overlaid showing the same behavior for all data. That is, the load capacity or capacitance of 1 μF remains constant as the amplitude of the sinusoidal signal increases from 1 to 1000 mV as is shown in Figure 11.

The same behavior is observed for stainless steel SS316 plate immersed in HCl 1 M (Figure 10b), the metal interface exposed to the acid solution allows the electron transfer rate at the equilibrium potential (E_corr) after applying lower amplitudes of the stimulus signal (between 1 to 20 mV), the impedance diagrams for this conditions do not show changes caused by the current flows into the system. In this sense the metal interface working similar as the ideal capacitor allowing ions loading charging such as Cl⁻ and OH⁻ with capacitances ranging between 40 to 80 μF/cm², which is indicated by a well-defined one time constant due to the presence of a protective oxide layer (passive condition) and can be easily represented by the EEC model #1. Notable effects can be caused by applying high current, as is clearly seen in the distortion of the shape of EIS diagrams during increasing the amplitude of the stimulus signal from 50 to 1000 mV, the impedance value |Z| gradually down several orders of magnitude and severe changes in phase angle less than 20° are observed, this mean that two time constants are obvious seen and are related to the corroded interface, i.e. dissolution of the chrome protective film and manifestation of the pitting corrosion process that occurs after 200 mV, for this case an increase in the interface charge of electrons is expected with capacitances over 434.40 mF/cm², like that as shown in Figure 11. It can conclude that it is possible to carry out experimental tests with amplitude signals ranging from 1 to 20 mV at the steady-state of corrosion potential without surface damage by the current applied, which is in according to the literature that reports an amplitude signal of 5 to 10 mv.

2.2 Kinetic oxidation reaction of steels tested in their received condition at different aqueous solutions

Figure 12 shows the typical impedance behavior of a steel with specification of AISI 8620 (0.20 wt.%C, 0.90 wt.%Mn, 0.35 wt.%Si, 0.60 wt.%Cr, 0.70 wt.%Ni, 0.25 wt.%Mo) in its received condition after exposed to different aqueous solutions such as distilled water, NaCl 0.5 M, HCl 1 M, H₂SO₄ 1 M. The supplied voltage signal has an amplitude of 10 mV that fluctuating around the corrosion potential (−654 mV) in the frequency range of 1 MHz to 1 mHz, the response obtained is represented in Bode diagrams in which the impedance module and the phase angle serve as functions of the Log frequency, these diagrams indicate the sensitivity of the EIS technique to evaluate the presence of growth of a natural oxide on the steel surface, this is observed for the case of corrosion test in distilled water. Two well-defined time constants are observed in the evaluated frequency domain, one time constant at higher frequencies is related to the presence of an oxide layer, however, the intensity of the phase angle signal of 85° gives information about the oxide thickness and its adherence, however micro-cracks, closed porosity or growth defects are always present in many kinds of oxide layers that serve as conducting pathways of ions coming from the aqueous electrolyte, allowing electron charge transfer. This causes the phase-shifted continuously to zero degrees at frequencies between 80.7 kHz to 61.5 Hz, suggesting that the system behaves like a resistive component with a low flow of current near 10.3 μA/cm², i.e. the current signal oscillates with the same phase as the potential does. In this frequency range an adsorptive process is carried out in which ions passing through the oxide layer defects, this mechanism is shown by the inductive response of the Figure 13. However, at lower frequencies over 8.59 Hz, an increase in the phase angle to 40° (56.6 mHz) is observed as if it were a capacitor in which the steel interface is charged by OH⁻ molecules, it is worth mentioning that this response is not related to the corrosion process, but this is a typical response to a passive system with a magnitude of impedance about 10³Ω -cm².

On the other hand, when the pH of the aqueous solution decreases to an acidified stage by the presence of ions such as Na⁺, Cl⁻, OH⁻, SO₄⁻, H⁺, the shape of the impedance diagrams has been change, for example, for NaCl solution, a slightly acidified substance breaks-out almost the integrity of the natural oxide layer that covers the metal matrix and the response related to ion charge transfer to the metal interface is observed at lower frequencies. In addition to, an increase in current is also observed of about 34.479 μA/cm²and a |Z| of 10²Ω -cm². Whereas, the same steel exposed to a more corrosive electrolyte such as HCl or H₂SO₄ at 1 M, the EIS response shows a single time constant that corresponding to the reaction’s oxidation and reduction on the steel interface. That means, transient electrical charge events occur on the electrochemical double layer with ions, and is characterized by an increase of the current from 43.58 and 198.25 μA-cm², respectively and the decrease of one order of magnitude of the impedance module 10¹Ω -cm², that is, less resistivity. The results in Table 3 indicates the simulation of impedance parameters with an appropriate electrical circuit that have been describe before, these data suggest that a higher current passing and large electrical charging at the interface of the steel increases the susceptible to attack by corrosion, that is, the internal energy of the aqueous solution has the ability to degrade freely the steel by pitting corrosion.

Table 3.

EIS parameters of simulated data to equivalent electrical circuit (EEC) for the steel 8620 during its exposure to different electrolytes.

Same behavior was observed for impedance-monitored corrosion tests for a 316 stainless steel plate (18.24 wt.%Cr, 8.07 wt.%Ni, 1.76 wt.%Mn, 0.5 wt.%Si, 0.27 wt.%Mo as principal alloying elements) after exposure to different aqueous solutions such as distilled water, 0.5 N NaCl, 0.5 N KCL, 1 M HCl or 0.5 M H₂SO₄, Table 4 shows the dissolution reaction. The impedance spectra that is shown in Figure 14 indicates one of the advantages of the EIS technique to evaluate the performance of metal interface in full immersed to aggressiveness conditions of different electrolytes. In this sense the natural film of chromium oxide that protects stainless steel against corrosion is remarkable in distilled water by the presence of one time constant at higher frequencies with an impedance value near to 1 MΩ-cm². Meanwhile, the presence of Cl⁻ ions (NaCl or KCl salt) alters the coating interface, which is electrically charged by ions causing the passivity state of stainless steel broken-down due to the dissolution of the oxide film, it is assumed that the steel is susceptible to corrosion by pitting. This is also seen through the presence of a time constant in the frequency domain studied. Similarly, the experimental tests in stronger acid media (HCl or H₂SO₄) indicate that stainless steel is seriously corroded in these conditions as a decrease in the impedance value below 1 mΩ-cm².

Table 4.

Capacitance of electrical double layer for the stainless steel SS316 during its exposure to different electrolytes.

2.3 Steel corroded at non-stationary solution (rotating disk electrode, RDE condition)

Other application of the EIS technique is like that shown in Figure 15, which is the evaluation of the effect on hydrodynamic conditions on the corrosion process in steels. This particular study has an interest to show the behavior of a pipeline steel (API-5 L-X70) that is used for transportation of hydrocarbon fluid. This steel was immersed in HCl 1 M solution at a different rotation speed of the working electrode (WE) from 0 to 1500 rpm, i.e. from static conditions 0 rpm, laminar flow 1 to 200 rpm and to turbulent flow 300 to 1500 rpm. Figure 15 shows the EIS response in the representation of Bode and Nyquist for the steel interface during its exposure to a corrosive media at different flow rates.

At the steady-state conditions, without rotation, the impedance response is related to electrons flow from the aqueous media to the metal interface allowing the formation of an interfacial layer over the metal surface, called an electrical double layer or a thin oxide film, which is indicated by the distortion of the semicircle presenting two time constants not very well-defined, besides in the diagram of bode two changes of slopes are shown for the impedance module. When applying rotation from 20 to 200 rpm an increase in the magnitude of the Z_real and Z_imag is observed due to the reaction kinetics at which the interfacial layer is forming at instantaneous rate and is controlled by electron charge and mass transfer mechanism. However, at turbulent conditions (>500 rpm) it does not allow the ions adsorption at the metal interface to maintain the presence of the double electrochemical layer or oxide film allowing only transients of electron transfer as a function of time, which promote the interfacial degradation of the steel. Therefore, the impedance diagrams show that under equilibrium conditions there is a corrosion rate controlled by the presence of a natural oxide on the steel surface, but this increased by the hydrodynamic conditions at turbulent flow, which is what is seen in real cases of application. But at moderate rotation speed the mass transport toward to the metal surface is carried out, giving opportunity to adsorption of molecules that come from the aqueous solution, which is consistent with the review literature [59].

2.4 Corrosion monitor in concrete reinforced materials

EIS technique can also be used for monitoring the evolution of the carbonation progress on concrete and the corrosion of the steel that serves as reinforcement. Carbonation results in a decrease in the pH of the cementation matrix when CO_2(g) from the environment diffuses into the concrete structure, that can cause the loss of the passivity condition on the reinforcing steel surface and leads to an early failure of concrete by corrosion attack. Change in electrical resistance (R_po) and capacitance (C_po) of the concrete bulk is measured by a semicircle at high frequency region, which is the typical response of EIS diagram as that shown in Figure 16. More details are available in the research of H. Herrera in 2019 [6]. The corrosion test of this study was carried out on a fresh cross section of concrete sample after 7, 14, 21, 42, 61, 84, 106 and 120 days of artificially CO_2(g) exposure periods (carbonation process). The characteristic impedance diagrams (EIS) of the concrete specimens after carbonation process at different ages of CO_2(g) exposure during immersion in tap water are shown in Figure 16.

The EIS spectra is displayed in the Nyquist plots (Z_real vs. Z_imaginary), these results show a single capacitive well-defined semicircle at higher frequencies followed by a straight line for 7 to 84 days of carbonation, which indicates the specific resistance of the concrete that could be controlled by charge transfer process; while the straight line indicates a diffusion mechanism of ions through the pores. It is observed that the semicircle amplitude for the reference sample [REF.-0d, non-carbonated] is shorter than the carbonated samples at 7 or 120 days, this suggest that its resistance to the ions diffusion through the porous structure is much lower (a favorable condition for the ions coming from the aqueous solution driven easily into the porous structure of the concrete, resulting in the faster flow of electrons with chemical reactions and molecules adsorption processes around the vicinity of the steel interface), in addition to this, a typical signal describes a passive stage of the concrete. However, notable changes in the semicircle amplitude of the EIS spectra are observed, these changes are associated to the increase in electrical resistance (R) value of the concrete from 23.62 to 101.54 kΩ·cm²as the carbonation progress until to 84 days of CO_2(g) exposure, this resulted to the blockade of the concrete pores by a calcium carbonate products, this reduces de alkalinity condition of the concrete matrix. However, the EIS diagrams for 106 days of exposure the resistance value decreases of about 58.26 kΩ·cm², the carbonation is almost complete, but after 120 days the resistivity still remains lower than 84 days of CO_2(g) exposure (65.59 kΩ·cm²) and the EIS spectra show remarkable changes in the low frequency domain. The changes registered by the EIS data for carbonated samples for 7 to 84 days are well-defined by one semicircle located at high frequencies (concrete porous resistance) with an infinite linear response at low frequencies (diffusion mechanism) only seen in the frequency domain of about >10⁶ to 10⁻³ Hz by imposing a small amplitude of AC signal perturbation to the concrete/steel reinforcement system, this linear response was then modified by a second depressed semicircle with an inductive loop at lower frequencies in the domain of 10⁻⁶ Hz, using the EEC model #6 represents this behavior. The characteristic behavior of a second semicircle formed at lower frequencies for 106 or 120 days indicates that a process of corrosion may occur on the steel bar surface. The EIS parameters effectively demonstrate that after 106 days of exposure the carbonation is almost complete and corrosion damage is clearly progress on the steel bar. Carbonation progress was monitored by a significant increase in the diameter of the semicircle, thus demonstrating the increase in resistivity of ions transmission due to blockade of pores by precipitation of CaCO₃compounds. Finally, the EIS technique results a practical tool for evaluating the carbonation progress on reinforced concrete structures without causing structural damage, and its sensitivity to predict the activation of the reinforcing steel to be corroded.

2.5 Inhibition in organic molecules or natural liquids extracted from plants

Particularly, the Mexican’s oil-industry still uses tubular steel pipes for the specific purpose of transporting hydrocarbons or natural gas. Most of the lines are buried, so the national network extends over quite large distances, crossing varied terrains conditions some with rivers, others with salt-laden marshes, or polluted industrial or urban zones alike; the ambient temperatures and load pressure for the buried-pipelines network vary widely, to put it simply vulnerable to corrosion attack. Steel pipes are corroded as a result of iron oxidation during its exposure of longer service periods. Therefore, corrosion problems are directly related to ever-present economical and production losses, as well as environment affectations, though human losses also happen. Providing effective inhibiting substances that are added to processing fluids may reduce internal corrosion problems; there are a wide variety of organic substances known to act as corrosion inhibitors. Figure 16 have demonstrated that small inhibitor quantities of organic molecules (2-Mercaptobenzimidazole, MBI or 5-Nitro-2-Mercaptobenzimidazole NMBI can be added to the media to diminish its inherent aggressiveness toward the steel surfaces [18, 60, 61]. It becomes evident that testing with the largest 2MBI concentration, namely 200 ppm, there began to appear two-time constants, which suggests that two different processes are involved during the perturbation. One is related to a molecular adsorption mechanism of the organic compound over the polished metal surface, thus giving rise to multilayers, while the second constant is related to infiltration of the corrosive species through assorted passages formed during self-assembly and rearrangement of the organic molecules, very probably due to the diversity of interactive forces operating on the electrode system. This second time constant that operates at intermediate frequencies can be interpreted as a resistance to charge transfer. The 2MBI inhibitor gave inhibiting efficiencies over 96% after adding only 20 ppm covering the metal surface exposed to the acid medium 1 M HCl. Therefore, the heterocyclic organic molecule 2MBI was an efficient inhibitor in H₂SO₄ at 25 ppm. The plot of log Z vs. log f, shown in Figure 17, reveals that as the inhibitor concentration increases, so does the impedance, which is also related to the charge transfer resistance, R_ct. This value was obtained through fitting a RCelectrical circuit model #3 to the experimental data. The |Z| increment is explained by the excess of inhibitor’s molecules in the solution, which as being bipolar it tends to adhere to the metal surface, also interacting among them thus forming a multilayered assembly, capable of blocking the electron charge transfer, refer to Figure 17, to appreciate more clearly the said |Z| increase.

Furthermore, Natural liquid-extracts like Morinda citrifolia has been used as corrosion inhibitor for steels (AISI-1045) exposed to acidic environments of HCl. Both the organic and inorganic compounds commonly used in the industry to inhibit the corrosion process of metals and its alloys are mostly composed by highly toxic chemicals, in addition to being more expensive. In this research sugar-components derived from the Morinda citrifolia (MC) leaves have been extracted in aqueous solutions to perform a natural inhibitor capable to control de corrosion damage, which can replace the traditional inhibitors, being environmentally friendly [62, 63]. The experimental results indicate that this compound has shown excellent performance as corrosion inhibitor, reaching inhibition efficiency (EI), values up to 90% at inhibitor concentrations ranging 0.8 to 2 g/L and immersion times of about 1 to 4 h. It has been found that the inhibition process takes place by the adsorption of the molecules on the surface of the metal (AISI 1045), by a physisorption mechanism. See Figure 18.

2.6 Hard-coatings as protection; borided treatment

Other attractive uses of the EIS technique are its application to evaluate the integrity and coating performance during its exposure in corrosive environments as a function of time. Actually, EIS is used as a quality control to evaluate the process of surface finishing treatments in many industries. In this sense, the results of Figure 19 show the characteristic impedance spectra that indicate the quality properties and corrosion resistance of a Fe₂B/FeB hard coating formed by boron atomic diffusion on the steel surface of a 1045 and 304 stainless steel during the boriding thermochemical treatment. Boriding is recognized as a thermochemical surface treatment in which boron diffuses into the ferrous substrate and reacts with Fe atoms of the bulk material to form a single (Fe₂B) or double-phase (Fe₂B/FeB) layer with a well-define thickness and composition [14]. The thickness of each layer has considerable effects on the mechanical behavior and corrosion behavior of the borided steels. However, the quality of the hard boride coatings depends essentially on the boriding temperature, treatment time, chemical composition of the steel substrate and the amount of boron atoms available around the sample surface to be coated.

In this study, in particular a powder-pack boriding was used on AISI-SAE 1045 steel and SS316 stainless steel as surface thermochemical treatment to improve hardness and wear resistance to the steel samples, due to its low cost of hard coating processing. Boriding can also enhance the corrosion resistance of ferrous materials as shown in Figure 19. The results indicate that a single boride layer of Fe₂B is formed on the 1045 steel surface, its morphology consisting a deep saw-tooth derived from the existence of diffusion paths (porosity and micro-cracks) in the surface of the steel matrix, in which the boron atoms are interstitial inserted to the surface forming a stable phase. For the borided stainless steel SS304 at the same conditions forms two-well defined layers on the surface, the columnar phase that was growth on the 1045 steel is less intense for SS304, this is due to the high concentration of chromium and nickel on the substrate surface, so the diffusion of boron stops by reacting immediately to form interstitial compounds of CrB, Cr₂B or Ni₃B in combination with FeB and Fe₂B. EIS for the borided 1045 steel were recorded over 72 days of exposure to HCl 1 M solution, which the hard coating degrades slowly due to the defects on the coating structure that allow Cl⁻ ions infiltrate, this is denote by changing the EIS spectra shape from one time constant to two time constant with a clearly phase-angle shifted and loss of impedance value, that means pitting corrosion initiation. No-corrosion damage was observed for the borided SS304 during its exposure in HCl 1 M solution for at least 170 days. Three times constants were observed after 44 days that’s reveal the presence of the FeB layer, after Fe₂B layer and the diffusion layer.

2.7 Steels used as beverages container

Steel-can containers are manufactured from thin metal plates and are commonly used for the distribution or storage of food or beverages. Most conventional steel beverage cans have bent to form a tube and then welding both sides leaving a firm seam, then joining the bottom end to the tube, finally, the steel can is filling-out with the content. However, it is necessary to mention that the steels cans have an internal polymer coating or have been treated by electroplating to coated internally with a thin layer of tin in order to prevent any oxidizing or electrochemical corrosion during the steel exposure to the liquid product that it contains, which could be carbonated soft drinks, alcoholic drinks, fruit juices, teas, herbal teas, energy drinks and others [64, 65]. Despite of this internal coating having the good quality, it may fracture during storage or dissolve in small amounts in the liquid product, which depends on certain factors such as temperature, stowage load and handling of the products during their storage, as well as the chemical composition of the liquid and steel. Due to this, efforts have been managed to replace tin-based coatings by chemical compounds derived from epoxy resins or polymers. Nevertheless, the set-up of the factors mention above may situate the metal container (e.g. steel cans) at a potential risk to develop internal corrosion.

On the other hand, the sale of beverages storage in steel cans are committed to their handling in warehouse, in this way, there is a predisposition of the people who buy drink-cans, they think if cans are struck or bent the coating has been damaged and could be associated that the liquid product is contaminated with Fe⁺ ions. The impedance diagrams of Figure 20 show that the EIS technique can be applied to assess the corrosion resistance of the internal coating in a specific beverage can.

In this case experimental corrosion tests on laboratory conditions were performed in a metal container used for the distribution of orange juice in Mexico. This can is made of steel with internally coated by a higher density polymer. Three particular cases are studied as denoted in the scheme of Figure 20; EIS spectra shown the behavior for a) with the coating, b) when the coating is mechanically damaged by a scratch and c) absence of coating, measured in HCl 1 M as a function of AC amplitude signal from 5 to 1000 mV. The bode diagrams indicate the presence of two well-defined time constants in the entire frequency domain for 5 and 10 mV of signal, the first one is related to the polymer coating with a resistance of electron -ion transfer of about 10⁸Ω -cm² with a micro-porous net (conducting paths) inside the coating as indicated by the second time constant. However as increasing the amplitude of signal voltage the |Z| value drops below 10⁴ Ω-cm², this response is associated with local stain-spots on the coating, which is indicted by a third time constant a low frequency. In the condition for the coating damaged by a localized defect such as a scratch or fracture, the impedance value decreases severely to 10⁵ to 10² Ω-cm² as increased the ACsignal, one time constant indicates the electron charge transfer processes through the defect that cause ions to be diffused below the coating until its failure. Finally, for the condition in the absence of the coating on the steel plate, the impedance diagrams show the corrosion process of the steel at different AC signal amplitudes, which shows severe corrosion after 200 mV showing 10¹ Ω-cm² of |Z| value.

3. Conclusions

This review study is related to the basic aspects of EIS to understand the corrosion mechanism of industrial steels that serve at different corrosive conditions, which has a great interest on giving an educational orientation and practical teaching guide of how to use the outstanding Electrochemical Impedance Spectroscopy (EIS) technique in metal corrosion technology. Therefore, this review considers a wide variety of practical electrochemical impedance cases based on the fundamental and qualities aspects of EIS theory and its experimental interpretation. This book chapter also serves as a support for postgraduate students to have a criterion in deciding through their own experiences when using the electrochemical impedance technique. The practical cases discussed here are part of the research experienced of Dr. Héctor Herrera Hernández (DR.3H) and his students & research group. It is worth to mention that EIS has been extended to various disciplines of science and technology, thus demonstrating great efficiency in evaluating the performance and integrity of metallic materials as can be seen in detail in the practical examples presented in this review work. So, EIS is not only applied to stationary conditions, but also more complex variables can be monitored such as: flow parameters, variable that undoubtedly represents the real conditions and could be an interesting challenge for analyzing and interpreting these phenomena by means of EIS data. The fitting EIS data using a mathematical model such as an equivalent electrical circuit is a critical process in the analysis and validation of EIS data for the acquisition of the system’s electrical parameters that can be related to the corrosion rate of the material under study and also gives information of its capacity of electrons charge. Finally, EIS seeks to obtain information on the system and its evolution with time by applying a sinusoidal voltage as a function of frequency range, in order to determine the properties and feasibility of materials that serve under severe service conditions, such as industrial steels as is this case of the reviewed book chapter.

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Electrochemical Impedance Spectroscopy (EIS) can be a useful tool for differentiating today’s high-performance coating systems.  These advanced coatings with their improved barrier properties perform longer in-service environments that are notoriously challenging. The use of accelerated weathering/corrosion testing in the laboratory to differentiate coating performance is still viable, but can take a year or longer, versus 3-4 months that were used just a decade or so ago, which creates longer lead times to market and increased testing costs. 

In order to discriminate between the performance of these coatings, new testing methods such as EIS have been developed to detect signs of deterioration before visible deterioration is evident. EIS measurements are relatively quick and non-destructive to the test surface, which is an advantage since the coated samples can be evaluated at designated intervals and the testing continued. The ability to repeat the testing on the same panels provides consistency in the data and is an improvement over other commonly used methods of evaluation that often require replicate panels so that destructive evaluations can be performed at each designated test interval.

The mathematical and theoretical basis of EIS is complex and beyond the scope of this article. Interested readers are referred to publications by MacDonald[1] and Orzem[2] for in depth discussion of these topics.  An EIS analysis consists of measuring the alternating current that results from application of an oscillating voltage to an electrode (i.e. the sample). Ohm’s law (Voltage = Current / Resistance) explains the relationship between voltage, direct current and electrical resistance. When examining electrochemical reactions such as corrosion, the alternating current equivalent to resistance, impedance is used because the chemical and physical processes of interest do not completely follow Ohm’s Law.  The impedance can be measured over a range of frequencies to assess different electrochemical parameters such as the charge transfer resistance and the coating capacitance. The impedance magnitude (|Z|) is frequently used as the metric for assessing coating performance.

Application of EIS to Coating Performance

The reason that EIS is effective in evaluating coating performance is that the degradation mechanism causes the coating material to become less resistant to moisture permeation (i.e., loses barrier properties).  The EIS procedure involves placing an electrolyte (usually dilute sodium chloride) solution on the surface of the coating.  Most methods require a contact time of at least 2 hours, with some requiring a minimum contact time of 24 hours.  If there is degradation (loss of barrier properties) of the coating, a change in the permeation of the salt solution is signified by a decrease in the impedance measurement.  While an individual data point does not provide enough information to make a judgement on the condition of the coating material, by obtaining a baseline reading and intermittent impedance values of the weathered or stressed coating, useful information on the barrier properties of the coating can be revealed.  The more similar the simulated test environment is to the actual service environment, the more useful the information will be for projecting the service life of the coating. Most of the EIS methods reference ISO 16773 “Paints and Varnishes – Electrochemical Impedance Spectroscopy (EIS) on High-Impedance Coated Specimens” for the testing of coatings.

A tightly cross-linked or thick industrial coating with good barrier properties is expected to have low permeability at the start of the testing, which translates to a value of 10⁹ ohms at 0.1 Hz or higher with most equipment limited to a reading of 10⁹ ohms (giga-ohms); although some equipment can obtain data to 10¹² ohms.  A change (decrease) in the exponent number is the indication that the coating is degrading.  As the exposure continues, some specifications list a maximum reduction of two units in the exponent value (e.g., a coating’s barrier properties starting value of 10⁹ would be suspect at a value of 10⁷).

EIS has also been used to examine other systems. In this article, the application of this method in applications related to oil and gas, microbial corrosion and stress corrosion is discussed. Method limitations in these specific applications are also described. In the oil and gas industry, EIS is used to study various corrosion phenomena, which include the following: 9) corrosion of carbon steel in a solution of saline water by carbon dioxide, and 2) corrosion of pipes buried in the soil. In the study of carbon dioxide corrosion, EIS is used to continuously monitor the formation and growth of corrosion products (mainly carbonate) on the steel surface. Different equivalent circuits are used to fit EIS information due to the multi-stage process. The multistage nature of the process is that the formation layer is non-uniform at the beginning of the corrosion and then completes over time. [93.] Therefore, equivalent circuits are similar to corrosion in solutions. For example, Choi et al. [96–94] used the equivalent circuit of Figure 3-b to fit the EIS spectrum in the early stages of corrosion when the rust layer on the metal has not yet formed. The rust layer had two time constants in the spectrum and therefore the model in Figure 3 should have been used. Microbial corrosion has also been investigated by the EIS. Biofilms are created on the metal surface. Because this process is a bio-sieving process. It is trochemical, electrochemical measurements such as EIS can be used to momentarily monitor this type of corrosion. However, recent studies [97] have shown that the application of this method can lead to delays in biofilm formation and lead to erroneous observations. Therefore, the use of complementary methods such as electrochemical noise is recommended. Finally, the EIS method has been used to study stress corrosion; However, the information obtained from the method will contain errors due to the existence of several phenomena in these phenomena. For example, Petit et al. [97] observed a shift or transmission at specific frequencies of the EIS spectrum, which they attributed to crack formation. Bosch [98] proposed a model for the presence of cracks in impedance information, a stress corrosion process, and suggested that phase change at specific frequencies is related to the length of the cracks. In addition, it is noted that this phase shift can be much smaller than systems detection.
S Among the many electrochemical methods used in corrosion monitoring, S is one of the least degraded due to the very low voltage range applied. The AC properties of this method also make it ideal for studying high resistance systems. These advantages have led to the widespread and successful application of the EIS method in corrosion monitoring. In this paper, EIS method is used to study and monitor atmospheric corrosion, corrosion in concrete, performance of coatings and thin films, performance of inhibitors, corrosion corrosion, corrosion in oil and gas industry, microbial corrosion and stress corrosion and configuration of different electrode systems. Explained in different contexts. Finally, it should be noted that although this method is relatively easy to use, analyzing and fitting EIS information is usually a complex task and therefore great care must be taken in selecting the appropriate equivalent circuit models for data analysis and mathematical models based on the actual physical properties of systems. , Be offered.