**1. Introduction**

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 [1–4]. 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.

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 selfrepaired 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 *Fe*<sup>2</sup><sup>þ</sup> <sup>þ</sup> <sup>2</sup>*OH*� ! *Fe OH* ð Þ<sup>2</sup> *rusting 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, 7–9]. 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,

*Physical and chemical model that represents the concrete failure by corrosion on the steel reinforcement [6].*

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion…*

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 [11–15].

washers and wires) [10].

**3**

**Figure 1.**

*DOI: http://dx.doi.org/10.5772/intechopen.94470*

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.* anodicoxidation 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 (Ecorr). 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 Ecorr 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 Ecorr. 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 porousoxide 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, SO4 <sup>2</sup> or NO3 <sup>2</sup>. **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 *Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion… DOI: http://dx.doi.org/10.5772/intechopen.94470*

**Figure 1.**

*Physical and chemical model that represents the concrete failure by corrosion on the steel reinforcement [6].*

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 selfrepaired 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 *Fe*<sup>2</sup><sup>þ</sup> <sup>þ</sup> <sup>2</sup>*OH*� ! *Fe OH* ð Þ<sup>2</sup> *rusting 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, 7–9]. 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 [11–15].

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 metalprocessing 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 [16–24]. 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].

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

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion…*

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

process [34].

scaffold for skin cell growth [35].

Cases of *EIS* study applied to steels;

*DOI: http://dx.doi.org/10.5772/intechopen.94470*

• Inhibition using organic molecules.

• Hard-coatings as protection.

**5**

• Steels measured in their received condition.

• Steel corroded at non-stationary condition.

• Kinetic oxidation reaction at different aqueous solutions.

• Corrosion monitor in concrete reinforced materials.

• Inhibition in natural liquids extracted from plants.

• Corrosion monitor in steels used as food containers or beverages.

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,

**1.1 Fundaments of electrochemical impedance spectroscopy (EIS)**

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 [26–33] *EIS* is considered a successful new electrochemical technique with a great evolution in recent years that has become an *Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion… DOI: http://dx.doi.org/10.5772/intechopen.94470*

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;


#### **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 [36–38].

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.

**1.2 Basics aspects of EIS data representation**

*resistance, Cdl is the capacity of the double layer.*

*DOI: http://dx.doi.org/10.5772/intechopen.94470*

function of time *t* is represented as follows;

*<sup>R</sup>* <sup>¼</sup> *<sup>V</sup>*

bellow [8]:

**7**

**Figure 2.**

Electrochemical impedance spectroscopy (EIS) is the analytical method widely used to study the electrochemical systems by applying a small *AC* voltage 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 Rp 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

*Schematic simulation of the electrochemical interface metal/electrolyte (electrical double layer) and its representative equivalent electrical circuit* EEC *model. Rs is the solution resistance, Rct is the charge transfer*

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion…*

*<sup>I</sup>* ð Þ *DC* , *<sup>Z</sup>* <sup>¼</sup> *<sup>E</sup>*

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 ð Þ *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

*<sup>I</sup>* ð Þ *AC* (1)

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 Cdl (ions charge) and the flow of ions through the metal surface is view as a resistance Rct 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.

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion… DOI: http://dx.doi.org/10.5772/intechopen.94470*

#### **Figure 2.**

*Schematic simulation of the electrochemical interface metal/electrolyte (electrical double layer) and its representative equivalent electrical circuit* EEC *model. Rs is the solution resistance, Rct is the charge transfer resistance, Cdl is the capacity of the double layer.*

#### **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 *AC* voltage 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 Rp 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]:

$$R = \frac{V}{I}(DC), Z = \frac{E}{I} \text{ (AC)}\tag{1}$$

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 ð Þ *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 *t* is represented as follows;

**Figure 3.** *Sinusoidal waveform response in linear system showing phase-shift angle that is used to describe the electrochemical reactions at the interfaces [42].*

$$E\_t = E\_o \sin\left(at\right) \tag{2}$$

*Et* ¼ *E*<sup>0</sup> exp ð Þ *jωt* ,*It* ¼ *I*<sup>0</sup> exp ð Þ *jωt* � *ϕ* (6)

*<sup>I</sup>* <sup>¼</sup> *<sup>Z</sup>*<sup>0</sup> exp ð Þ¼ *<sup>j</sup><sup>ϕ</sup> <sup>Z</sup>*0ð Þ *cos<sup>ϕ</sup>* <sup>þ</sup> *jsin<sup>ϕ</sup>* (7)

considering the relationship between the potential and current amplitude, it

*Vector representation of impedance as complex number;* X *capacitive-reactance,* R *resistance, Z' real component*

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion…*

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 (�Zimag vs. Zreal) that represent the real impedance plotted against its imaginary part and also is often used the Bode plots (*log*|Z| vs. *log f*req., *ϕ* vs. *log f*req.) 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

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. Cdl 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. Rct is the resistance of the electron charge transfer, which is the value of the impedance in its real component and Rs is the solution resistance. The combination of these three passive elements provides a simple equivalent electrical circuit (*EEC*) for a uniform

results the total of the impedance as a complex number, as it follows;

*<sup>Z</sup>*ð Þ¼ *<sup>ω</sup> <sup>E</sup>*

**Figure 4.**

*and Z" imaginary part of impedance.*

*DOI: http://dx.doi.org/10.5772/intechopen.94470*

together at both ends of the spectra.

**9**

where *Et* is the potential at time *t*, *E*<sup>0</sup> is the amplitude of the signal and *ω* is the angular frequency (expressed in terms of radians/second). So, the relationship between angular frequency and frequency (*f* in hertz units) is given by;

$$
\omega = 2\mathfrak{x}^{\mathfrak{f}} \tag{3}
$$

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. *It is* the single response of instantaneous current at the maximum amplitude, Φ is the shiftedphase angle and has a different amplitude, *I*<sup>0</sup> as described in Eq. 4;

$$I\_t = I\_o \sin\left(\alpha t + \phi\right) \tag{4}$$

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;

$$Z = \frac{E(t)}{I(t)} = \frac{E\_0 \sin\left(\alpha t\right)}{I\_0 \sin\left(\alpha t + \phi\right)} = Z\_0 \frac{\sin\left(\alpha t\right)}{\sin\left(\alpha t + \phi\right)}\tag{5}$$

then, impedance (*Z*0) 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*<sup>0</sup> ð Þ and the other to the imaginary component *Z*<sup>00</sup> ð Þ. Due to this assumption, *Z*<sup>0</sup> can be expressed in its complex notation by incorporating the complex number *<sup>j</sup>* <sup>¼</sup> ffiffiffiffiffiffi �<sup>1</sup> <sup>p</sup> , where the **Figure 4** shows the complex representation of the impedance as vector concept, *<sup>Z</sup>*ð Þ¼ *<sup>ω</sup> <sup>Z</sup>*<sup>0</sup> <sup>þ</sup> *jZ*<sup>00</sup> and its phase-angle, *tan* ð Þ¼ *<sup>ϕ</sup> <sup>Z</sup>*<sup>00</sup> *<sup>Z</sup>*<sup>0</sup> . Using Euler relationship, the expression of the impedance translates in a complex function like;

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion… DOI: http://dx.doi.org/10.5772/intechopen.94470*

**Figure 4.**

*Vector representation of impedance as complex number;* X *capacitive-reactance,* R *resistance, Z' real component and Z" imaginary part of impedance.*

$$E\_t = E\_0 \exp\left(jat\right), I\_t = I\_0 \exp\left(jat - \phi\right) \tag{6}$$

considering the relationship between the potential and current amplitude, it results the total of the impedance as a complex number, as it follows;

$$Z(\alpha) = \frac{E}{I} = Z\_0 \exp\left(j\phi\right) = Z\_0(\cos\phi + j\sin\phi) \tag{7}$$

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 (�Zimag vs. Zreal) that represent the real impedance plotted against its imaginary part and also is often used the Bode plots (*log*|Z| vs. *log f*req., *ϕ* vs. *log f*req.) 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. Cdl 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. Rct is the resistance of the electron charge transfer, which is the value of the impedance in its real component and Rs 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 *ϕ* 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 *EEC* models 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*ðÞ¼ *Eo* ∗ *Sin*ð Þ *ωt* 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* <sup>¼</sup> *Eo <sup>R</sup>* ), 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.

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, *ϕ* = 0°. Then for this condition in that the phaseangle is equal to zero, the value of impedance module for a pure resistor (*R*) is relatively its reactive or real part (*ZR*ðÞ¼ *t R*), being its imaginary part or the

#### **Figure 5.**

*Representation of a corrosion cell and its equivalent electrical circuit (*EEC*),* WE is the *working electrode,* CE *is the counter electrode and* RE *is the reference electrode.*

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

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

*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*

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion…*

*DOI: http://dx.doi.org/10.5772/intechopen.94470*

**Table 1.**

**Table 2.**

**11**

*6. ion diffusion processes.*

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion… DOI: http://dx.doi.org/10.5772/intechopen.94470*

#### **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.*

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*ðÞ¼� *<sup>t</sup>* <sup>1</sup> *<sup>j</sup>ωC*. 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*ðÞ¼ *t jωL*.

(or polarization resistance), and its capacitance of the double layer Cdl.

value of Cdl is given by the following expression;

*DOI: http://dx.doi.org/10.5772/intechopen.94470*

combination of parallel *RC* in series) *ZT*ðÞ¼ *<sup>t</sup> <sup>R</sup>*<sup>2</sup>

n o <sup>þ</sup> *Ro*

*jωC*<sup>1</sup>

circuits or **Figure 7c** (circuit #4) *ZT*ðÞ¼ *<sup>t</sup> <sup>R</sup>*<sup>2</sup> <sup>þ</sup> <sup>1</sup>

*ZT*ðÞ¼ *<sup>t</sup> <sup>R</sup>*<sup>2</sup>

d as given by;

**Figure 7.**

**13**

<sup>1</sup>þ*jωC*<sup>2</sup> <sup>þ</sup> *<sup>R</sup>*<sup>1</sup> h i<sup>k</sup> <sup>1</sup>

From the Nyquist Plot of **Figure 6b** Cdl is 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 Rct and Rs is obtained by reading the real axis, *Z'*, value at the high frequency intercept. However, considering the maximum angular frequency (ωmax) as the frequency at which the imaginary component of the impedance *Z"* has its largest value and Rct, the

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion…*

*Cdl* <sup>¼</sup> <sup>1</sup>

Two-time constants could be expected in **Figure 7a** (circuit #2 is the

� � as results of applying voltage through the

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

*Impedance data simulation of* EEC *models; a) circuit #2 parallel* RC *elements in series (oxides products), b) circuit #3 parallel* RC *elements in parallel follow by* R *in series (*paint coating) *and c) circuit #4 parallel* RC *elements in series (corrosion mechanism)*. Ro *= 276 Ω,* R1 *= 3.3 kΩ,* C1 = *1 μF,* R2 *=1kΩ,* C1 = *10 μF.*

or **Figure 7b** (circuit #3 is a parallel arrangement in parallel connection

*ωmaxRct*

<sup>1</sup>þð Þ *<sup>j</sup>ωC*2*R*<sup>2</sup> <sup>þ</sup> *<sup>R</sup>*<sup>1</sup>

*jωC*<sup>2</sup> � �k*R*1<sup>k</sup> <sup>1</sup>

� �,

h i <sup>þ</sup> *Ro* � �. These *EEC*

<sup>1</sup>þð Þ *<sup>j</sup>ωC*1*R*<sup>1</sup> <sup>þ</sup> *Ro*

*jωC*<sup>1</sup>

(8)

On the other hand, when two passive components are combined in a *RC* circuit, 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*ðÞ¼� *<sup>t</sup>* <sup>1</sup> *<sup>j</sup>ω<sup>C</sup>* þ *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*ðÞ¼ *<sup>t</sup> <sup>R</sup>*<sup>1</sup> <sup>1</sup>þð Þ *<sup>j</sup>ωC*1*R*<sup>1</sup> <sup>þ</sup> *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 Rs, charge transfer resistance Rct

#### **Figure 6.**

*Impedance data simulation of a simplest EEC model; a)* RC *elements in series (high coating impedance) and b) circuit #1* RC *in parallel follow by* R *in series (simple corrosion undergo by electron charge transfer).* Ro *= 276 Ω,* R1 *= 3.3 kΩ,* C1 = *1 μF.*

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion… DOI: http://dx.doi.org/10.5772/intechopen.94470*

(or polarization resistance), and its capacitance of the double layer Cdl. From the Nyquist Plot of **Figure 6b** Cdl is 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 Rct and Rs is obtained by reading the real axis, *Z'*, value at the high frequency intercept. However, considering the maximum angular frequency (ωmax) as the frequency at which the imaginary component of the impedance *Z"* has its largest value and Rct, the value of Cdl is given by the following expression;

$$\mathbf{C}\_{dl} = \frac{1}{\alpha\_{\text{max}} R\_{ct}} \tag{8}$$

Two-time constants could be expected in **Figure 7a** (circuit #2 is the combination of parallel *RC* in series) *ZT*ðÞ¼ *<sup>t</sup> <sup>R</sup>*<sup>2</sup> <sup>1</sup>þð Þ *<sup>j</sup>ωC*2*R*<sup>2</sup> <sup>þ</sup> *<sup>R</sup>*<sup>1</sup> <sup>1</sup>þð Þ *<sup>j</sup>ωC*1*R*<sup>1</sup> <sup>þ</sup> *Ro* � �, or **Figure 7b** (circuit #3 is a parallel arrangement in parallel connection *ZT*ðÞ¼ *<sup>t</sup> <sup>R</sup>*<sup>2</sup> <sup>1</sup>þ*jωC*<sup>2</sup> <sup>þ</sup> *<sup>R</sup>*<sup>1</sup> h i<sup>k</sup> <sup>1</sup> *jωC*<sup>1</sup> n o <sup>þ</sup> *Ro* � � as results of applying voltage through the circuits or **Figure 7c** (circuit #4) *ZT*ðÞ¼ *<sup>t</sup> <sup>R</sup>*<sup>2</sup> <sup>þ</sup> <sup>1</sup> *jωC*<sup>2</sup> � �k*R*1<sup>k</sup> <sup>1</sup> *jωC*<sup>1</sup> h i <sup>þ</sup> *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;

#### **Figure 7.**

*Impedance data simulation of* EEC *models; a) circuit #2 parallel* RC *elements in series (oxides products), b) circuit #3 parallel* RC *elements in parallel follow by* R *in series (*paint coating) *and c) circuit #4 parallel* RC *elements in series (corrosion mechanism)*. Ro *= 276 Ω,* R1 *= 3.3 kΩ,* C1 = *1 μF,* R2 *=1kΩ,* C1 = *10 μF.*

$$C\_{\varepsilon} = \frac{\epsilon\_o \epsilon A}{d} \tag{9}$$

*<sup>W</sup>* <sup>¼</sup> *σω*�1*=*2 1ð Þ �*<sup>J</sup>* (10)

ð Þ *<sup>j</sup><sup>ω</sup>* <sup>1</sup>�*<sup>α</sup>*

, [47]. To obtain the

*<sup>θ</sup>max:* (11)

In real cases the shape of Nyquist plot does not always show a perfect semicircle

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion…*

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

capacitance value (*Cdl*) from the *CPE*, it is necessary to obtain the maximum frequency of the Nyquist semicircle (ωθmax) 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 dimen-

*Cdl* <sup>¼</sup> *QO* <sup>∗</sup>*ω*ð Þ *<sup>n</sup>*�<sup>1</sup>

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

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

EEC *electrical circuit #1 with a* CPE *to fit de impedance data corresponding to corrosion of pipeline steel*

*,* Rct *= 24.71 Ω-cm2*

*.*

*,* Cdl *= 53.04 μF/cm<sup>2</sup>*

of the metal (carbon steel APIX-52-5 L) in acidic media) HCl1M [20, 47].

useful to represent several electric elements *ZCPE* <sup>¼</sup> *Qo*

*DOI: http://dx.doi.org/10.5772/intechopen.94470*

. Eq. 11 shows the calculation of Cdl:

sions S-sec<sup>n</sup>

**Figure 9.**

**15**

*immersed in HCl 1 M.* Rs *= 1.58 Ω-cm<sup>2</sup>*

Where *<sup>ϵ</sup><sup>o</sup>* is the electrical permittivity constant of free space (8.85 � <sup>10</sup>�<sup>12</sup> 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*ðÞ¼ *<sup>t</sup> <sup>j</sup>ωR*2*<sup>L</sup> <sup>R</sup>*2þ*jω*<sup>L</sup> <sup>þ</sup> *<sup>R</sup>*<sup>1</sup> � �<sup>k</sup> <sup>1</sup> *jωC*<sup>1</sup> h i <sup>þ</sup> *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*ðÞ¼ *<sup>t</sup> <sup>R</sup>*1þ*<sup>W</sup>* <sup>1</sup>þ½ � *<sup>j</sup>ωC*1ð Þ *<sup>R</sup>*1þ*<sup>W</sup> <sup>α</sup>* <sup>þ</sup> *Ro* � � called 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, 43–45]. This is typical for analytical electrochemistry in diffusion controlled (*W*) in corrosion measurements, which is expressed by the Eq. (10), where *σ* is the Warburg coefficient and can be calculated from the slope of the straight line in the complex plane of **Figure 8b**.

#### **Figure 8.**

*Impedance data simulation of* EEC *models; a) circuit #5 parallel* RC *elements in parallel with an inductance* L *(adsorption mechanism) and b) circuit #6 parallel* RC *elements in series with Warburg impedance* W *(diffusion control).* Ro *= 276 Ω,* R1 *= 3.3 kΩ,* C1 = *1 μF,* Wo = *0.001 S-sec0.5.*

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion… DOI: http://dx.doi.org/10.5772/intechopen.94470*

$$\mathcal{W} = \sigma \alpha^{-1/2(1-f)} \tag{10}$$

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* <sup>¼</sup> *Qo* ð Þ *<sup>j</sup><sup>ω</sup>* <sup>1</sup>�*<sup>α</sup>* , [47]. To obtain the capacitance value (*Cdl*) from the *CPE*, it is necessary to obtain the maximum frequency of the Nyquist semicircle (ωθmax) 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-sec<sup>n</sup> . Eq. 11 shows the calculation of Cdl:

$$\mathbf{C}\_{dl} = \mathbf{Q}\_O \ast a^{(n-1)}\_{\theta \max} \tag{11}$$

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

#### **Figure 9.**

EEC *electrical circuit #1 with a* CPE *to fit de impedance data corresponding to corrosion of pipeline steel immersed in HCl 1 M.* Rs *= 1.58 Ω-cm<sup>2</sup> ,* Cdl *= 53.04 μF/cm<sup>2</sup> ,* Rct *= 24.71 Ω-cm2 .*

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:


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.

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

*Typical impedance spectra showing the effects of the amplitude signal in; a)* EEC *model #1 (*Ro *= 276 Ω,*

*Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion…*

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

1M(**Figure 10b**), the metal interface exposed to the acid solution allows the electron transfer rate at the equilibrium potential (Ecorr) 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

presence of a protective oxide layer (passive condition) and can be easily

, which is indicated by a well-defined one time constant due to the

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

and that allows the current to be phase shifted with

potential difference *ZT*ðÞ¼ *<sup>t</sup> <sup>q</sup>*

**Figure 10.**

80 μF/cm<sup>2</sup>

**17**

*C*

R1 *= 3.3 kΩ,* C1 = *1 μF) and b) a stainless steel immersed in HCl 1 M.*

*DOI: http://dx.doi.org/10.5772/intechopen.94470*
