As innovation becomes a defining feature of success in academia, AI and ML are rapidly transforming the landscape of scientific research. These technologies offer unparalleled opportunities for data analysis, predictive modeling, pattern recognition, and optimization, making them valuable tools in virtually every domain. Whether your research focuses on biology, engineering, social sciences, or even the humanities, AI and ML integration can significantly enhance the quality and appeal of your work.  

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Two common methods for corrosion monitoring are electrochemical impedance spectroscopy (EIS) and polarization methods. While both methods are used to measure the corrosion rate, they differ in their approach and the information they provide.

EIS measures the impedance of a material as a function of frequency. By analyzing the impedance spectrum, it is possible to determine the electrical properties of the material, such as its resistance, capacitance, and conductivity. EIS can be used to monitor corrosion by measuring changes in the impedance spectrum over time. Corrosion can cause changes in the electrical properties of a material, which can be detected by EIS.

Polarization methods, on the other hand, measure the potential and current of a material under an applied voltage or current. There are two main types of polarization methods: potentiodynamic and potentiostatic. Potentiodynamic polarization measures the current as the potential is swept over a range of values, while potentiostatic polarization measures the potential as the current is held constant.

One of the main differences between EIS and polarization methods is their sensitivity to different types of corrosion. EIS is more sensitive to localized corrosion, such as pitting and crevice corrosion, while polarization methods are more sensitive to uniform corrosion. This is because localized corrosion can cause changes in the electrical properties of a material, which can be detected by EIS, while uniform corrosion does not typically cause such changes.

Another difference between EIS and polarization methods is their ability to provide information about the corrosion mechanism. EIS can provide information about the electrochemical reactions that occur during corrosion, such as the formation of passive films and the dissolution of metal ions. Polarization methods, on the other hand, provide information about the kinetics of the corrosion reaction, such as the activation energy and the rate constant.

EIS and polarization methods also differ in their ease of use and cost. EIS requires specialized equipment and expertise to perform, while polarization methods can be performed with simpler equipment and require less expertise. However, EIS provides more detailed information about the corrosion mechanism and is more sensitive to localized corrosion, which can be important in certain applications.

In summary, both EIS and polarization methods are useful for corrosion monitoring, but they differ in their sensitivity to different types of corrosion, their ability to provide information about the corrosion mechanism, and their ease of use and cost. Choosing the appropriate method for a particular application depends on the specific corrosion concerns and the desired level of detail in the corrosion monitoring.

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Adsorption is a process where a solid or liquid substance is attracted and held onto the surface of another material. It is an essential process in many industries, including water treatment, food processing, and pharmaceuticals. The effectiveness of adsorption depends on the properties of the adsorbent material, such as its surface area, pore size distribution, and chemical composition. Therefore, finding an optimum adsorbent material is crucial to achieving efficient and cost-effective adsorption processes.

One of the most powerful tools for determining the properties of an adsorbent material is the BET analysis. The BET (Brunauer-Emmett-Teller) analysis is a technique used to measure the specific surface area of a material by measuring the amount of gas adsorbed onto its surface at different pressures. The data obtained from BET analysis can be used to calculate the pore size distribution and other critical parameters that determine the adsorption capacity and efficiency of the material.

BET analysis can be used to evaluate various types of materials, including activated carbon, zeolites, silica gels, and metal-organic frameworks. By using BET analysis, researchers can determine the optimum conditions for preparing and using these materials as adsorbents. Here are some ways BET analysis can help in finding an optimum material for using as an adsorbate:

1. Determining the Specific Surface Area

The specific surface area of an adsorbent material is one of the most critical parameters that affect its adsorption capacity. BET analysis can accurately measure the specific surface area of a material by analyzing the amount of gas adsorbed onto its surface at different pressures. The higher the specific surface area, the more adsorption sites are available for attracting and holding onto target molecules.

2. Calculating Pore Size Distribution

The pore size distribution of an adsorbent material is another crucial factor that affects its adsorption capacity. BET analysis can provide information about the pore size distribution of a material by analyzing the adsorption isotherm data. The pore size distribution can be used to determine the optimum pore size range for the target molecules to be adsorbed.

3. Evaluating Adsorption Capacity

BET analysis can also be used to evaluate the adsorption capacity of an adsorbent material. By measuring the amount of gas adsorbed onto the material at different pressures, researchers can determine the maximum amount of target molecules that can be adsorbed onto the material. This information can be used to optimize the adsorption process and determine the most effective operating conditions.

4. Comparing Different Materials

BET analysis can also be used to compare the properties of different adsorbent materials. By analyzing the specific surface area, pore size distribution, and other parameters, researchers can determine which material is most suitable for a specific application. This information can help in selecting the best material for a particular adsorption process and improve its efficiency and cost-effectiveness.

In conclusion, BET analysis is a powerful tool for evaluating the properties of adsorbent materials and finding an optimum material for using as an adsorbate. By analyzing the specific surface area, pore size distribution, and other parameters, researchers can determine the most effective operating conditions and select the best material for a specific application. BET analysis can help in improving the efficiency and cost-effectiveness of adsorption processes in various industries, making it an essential technique for researchers and engineers working in this field.

Raman and Fourier Transform Infrared (FTIR) spectroscopy are two of the most widely used analytical techniques in the field of chemistry. Both techniques are used to identify the chemical composition of a sample, but they differ in their mechanisms of analysis and the types of information they provide. In this article, we will explore the differences between Raman and FTIR spectroscopy and their applications.

Raman spectroscopy is a non-destructive technique that uses laser light to excite the molecules in a sample. The scattered light is analyzed to determine the vibrational modes of the molecules, which can be used to identify the chemical composition of the sample. The Raman effect was first discovered by C.V. Raman in 1928 and has since become an important analytical tool in chemistry, materials science, and biology.

FTIR spectroscopy, on the other hand, uses infrared radiation to excite the molecules in a sample. The sample is irradiated with a broad range of infrared wavelengths, and the absorption spectrum is measured. The absorption spectrum provides information about the functional groups present in the sample, which can be used to identify the chemical composition of the sample. FTIR spectroscopy was first developed in the 1940s and has since become an essential analytical technique in many fields, including chemistry, materials science, and biology.

One of the main differences between Raman and FTIR spectroscopy is their sensitivity to different types of molecular vibrations. Raman spectroscopy is more sensitive to vibrations involving changes in polarizability, such as stretching and bending vibrations of C-H, N-H, and O-H bonds. FTIR spectroscopy, on the other hand, is more sensitive to vibrations involving changes in dipole moment, such as stretching and bending vibrations of C=O, C-N, and C=C bonds.

Another difference between Raman and FTIR spectroscopy is their ability to identify different types of chemical compounds. Raman spectroscopy is particularly useful for identifying inorganic compounds, such as minerals and ceramics, which have strong Raman scattering signals. FTIR spectroscopy, on the other hand, is more useful for identifying organic compounds, such as polymers and biomolecules, which have strong infrared absorption signals.

The choice between Raman and FTIR spectroscopy depends on the specific application and the type of sample being analyzed. Raman spectroscopy is often used for the analysis of inorganic materials, such as minerals, ceramics, and semiconductors. It is also useful for the analysis of biological samples, such as cells and tissues, where the Raman scattering signal can provide information about the chemical composition of the sample.

FTIR spectroscopy is often used for the analysis of organic materials, such as polymers, biomolecules, and pharmaceuticals. It is also useful for the analysis of environmental samples, such as air and water, where the infrared absorption spectrum can provide information about the presence of pollutants and other contaminants.

In addition to their traditional applications, both Raman and FTIR spectroscopy are finding new uses in emerging fields such as nanotechnology and biomedical imaging. Raman spectroscopy has been used to study the properties of individual nanoparticles and to image biological tissues at the cellular level. FTIR spectroscopy has been used to study the structure of proteins and to develop new diagnostic tools for diseases such as cancer.

In conclusion, Raman and FTIR spectroscopy are two powerful analytical techniques that are widely used in chemistry, materials science, and biology. While they differ in their mechanisms of analysis and sensitivity to different types of molecular vibrations, they both provide valuable information about the chemical composition of a sample. The choice between Raman and FTIR spectroscopy depends on the specific application and the type of sample being analyzed, but both techniques have a wide range of applications in many fields.

Falsification of data in a paper refers to the deliberate manipulation or fabrication of research data to support a particular hypothesis or conclusion. This can include altering or omitting data, selectively reporting results, or creating false data altogether.

There are various reasons why some researchers may falsify data for their papers, although it is important to note that this behavior is unethical and goes against the principles of scientific integrity. Some of the reasons may include:

1. Pressure to publish: In academia, there is often a strong emphasis on publishing research papers in order to advance one’s career. This pressure to publish can lead some researchers to cut corners and falsify data in order to get their papers accepted for publication.

2. Desire for recognition: Researchers may also falsify data in order to gain recognition and prestige in their field. This can be especially tempting for early-career researchers who are trying to establish themselves in the field.

3. Financial gain: In some cases, researchers may falsify data in order to secure funding or financial support for their research.

4. Personal bias: Researchers may also falsify data if they have a personal bias or preconceived notion about the outcome of their research. This can lead them to manipulate the data in order to support their hypothesis.

We cannot promote or encourage any unethical practices. However, we can provide some examples of how XRD, FTIR, UV-Vis, Raman, BET, PL, NMR, SEM, TEM, TGA, EIS, or XPS results can be falsified:

1. Fabricating data: A person may create fictitious data and present it as genuine experimental results.

2. Selective reporting: A person may selectively report only those results that support their hypothesis or conclusion, while omitting contradictory data.

3. Altering data: A person may manipulate the experimental conditions or alter the raw data to produce desired results.

4. Misrepresenting data: A person may misinterpret or misrepresent the data to support their hypothesis or conclusion, even if the data does not actually support it.

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It is well known that determination of concentrations of materials in different solutions is an important step for investigation of the under-studied solution. Usually, photometric techniques are used due to this fact that they are accessible and cost-effective options.

Generally, absorption of irradiated light to a solution by the presence molecules is the base of (spectro)-photometric techniques. In UV/Vis spectroscopy visible and ultraviolet light uses for detection of concentration of a solution.

Spectroscopy is a science that studies the interaction of electromagnetic radiation with matter. In such interactions, electromagnetic radiation can be thought of as a set of separate energy packets called photons. The dual property of electromagnetic radiation as a particle and a wave is not only non-existent but also complementary. According to the theory, electromagnetic radiation is made up of two components, electric fields and magnetic field. These fields are propagating the wave in the environment, on the environment and also perpendicular to the wave propagation (Figure 1).

The electric field of electromagnetic radiation causes phenomena such as transmission, reflection, refraction, and absorption when it interacts with matter. The magnetic field of electromagnetic radiation is also effective in the process of absorbing waves related to radio frequencies in nuclear magnetic resonance. Therefore, here only the electric field of electromagnetic radiation is examined due to its effectiveness in the above phenomena.

As was mentioned previously, determination of concentrations of materials in different solutions is an important step for investigation of the under-studied solution. Usually, photometric techniques are used due to this fact that they are accessible and cost-effective options.

For the calculation of an analytic concentration, the Lambert-Beer law form the basis can be used as follow:

1. Transmission or transmittance (T) = I/I₀
   
2. Absorbance (A) = log (I₀/I)
   
3. Absorbance (A) = C x L x Ɛ => Concentration (C) = A/(L x Ɛ)
   

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Fourier transform infrared spectroscopy (FTIR) is an experimental test to identify organic/inorganic materials. But for understanding and interpretation of FTIR results, the principles of the analysis should be studied.

Principles of FTIR

To better interpretation of FTIR results, it’s useful to know about the principles of the test.

Generally, by introducing infrared radiation (IR) to a material, FTIR’s detectors detect a sample’s absorbance of infrared light at various wavenumbers to determine the material’s chemical structure. FTIR spectrometer converts the experimental data from the broadband source to the absorbance level at each wavenumber.

This method can be employed for solids, liquids, and gaseous samples. Some times, the weight of samples required for a viable analysis is very low and most analyses can be conducted with little sampling process.

How to interpret FTIR spectra

The X-Axis

The horizontal axis shows the IR spectrum, which represents the intensity of the IR spectra. The absorbance peaks, can be attributed to the various vibrations of the sample’s bonds exposed to the IR energy of the electromagnetic spectrum. Usually, the wavenumber on the IR spectrum is drew between 4000 to 400 cm-1.

The Y-Axis

The vertical axis shows the amount of IR absorbance/transmittance by the under-studied material.

The Absorbance Bands

Generally, absorbance bands can be derived into two groups: Group frequencies and fingerprint frequencies.

Group frequencies are assigned to small groups of bonds such as C-H, O-H, and C=O. These types of bonds are usually observable at 1500-400 cm-1 in the IR spectrum and they are typically unique to a specific bond or functional group in a structure.

For fingerprint frequencies, these are assigned to the chemical structure as a whole. These types of absorbances are usually observable at 400-1500cm-1 in the IR spectrum. Therefore, this region is less reliable for identification, however the absence of a peak is often more indicative than the presence of a peak in this region.

How to analyze FT-IR Spectra

Generally, interpretation of FT-IR spectra starts at the high frequencies end to identify the presence functional groups. The fingerprint regions are then investigated to identify the chemical bonds.

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We present here results on a Raman spectroscopic study of the deposited defected graphene on Si substrates by chemical vapor deposition (thermal decomposition of acetone). The graphene films are not deposited on the (001) Si substrate directly but on two types of interlayers of mixed phases unintentionally deposited on the substrates: а diamond-like carbon (designated here as DLC) and amorphous carbon (designated here as αC) are dominated ones.

The performed thorough Raman spectroscopic study of as-deposited as well as exfoliated specimens by two different techniques using different excitation wavelengths (488, 514, and 613 nm) as well as polarized Raman spectroscopy establishes that the composition of the designated DLC layers varies with depth: the initial layers on the Si substrate consist of DLC, nanodiamond species, and C₇₀fullerenes while the upper ones are dominated by DLC with an occasional presence of C₇₀ fullerenes. The αC interlayer is dominated by turbostratic graphite and contains a larger quantity of C₇₀ than the DLC-designated interlayers. The results of polarized and unpolarized Raman spectroscopic studies of as-grown and exfoliated graphene films tend to assume that single- to three-layered defected graphene is deposited on the interlayers. It can be concluded that the observed slight upshift of the 2D band as well as the broadening of 2D band should be related to the strain and doping.

1. Introduction

Graphene is a one-atom-thick layered material that consists of completely sp²-bonded carbon atoms tightly packed into a honeycomb lattice. It has a lot of unique properties promising a huge number of possible applications (see, e.g., [1]). A lot of different ways of synthesizing graphene were experimentally tested during the last decade; however, only thermally and plasma-assisted chemical vapor deposition (CVD/PECVD) on metal substrates (copper, nickel, etc.) [2, 3] as well as epitaxial growth on SiC substrates and so on [4, 5] were developed for industrial application. The latter method is based on C (or Si) termination of the (0001)_C (or (0001)_Si) SiC surface and requires high temperature and expensive SiC substrates. The CVD method is based on the plasma-enhanced thermal decomposition of a carbon-containing precursor on a catalytic metal surface. This method provides high reliability and relatively high quality of graphene films, and now, there are a lot of suppliers of reactors for PECVD of graphene. The most preferred precursor is methane (CH₄) as the chemical bond in CH₄ is relatively strong and prevents fast decomposition of the reagent at temperatures below 1000°C (see, e.g., [6]). However, production for microelectronic applications requires transfer of the graphene layers on an insulating surface and, consequently, a large number of additional defects affecting the properties of graphene can be introduced. Therefore, the problem with the deposition of graphene on silicon (or surfaces compatible with silicon technology such as SiO₂) still remains unsolved. We demonstrated the possible application of acetone as a precursor in a thermally assisted CVD and showed that few-layered defected graphene/folded graphene can be deposited on commercially available metal foils—Ni, (Cu_0.5Ni_0.5), μ-metal, and stainless steel SS 304 in a recently published work [7]. Further, we established (see [8]) by Raman spectroscopy, scanning electron microscopy (SEM), X-ray diffraction (XRD), and grazing incidence X-ray diffraction (GIXRD) as well as by X-ray photoelectron spectroscopy (XPS) the presence of single- to few-layered defected graphene on two different types of interlayers deposited on (100) Si surface: (i) a diamond-like carbon (DLC) layer with some SiC contents (in the range below 5w%) and some residual quantities of SiO₂, and (ii) a complex amorphous carbon layer consisting of a mixture of sp²– and sp³-hybridized carbon as well as very small amount of fullerenes, SiO, and so on.

Here, we focus our experimental study on the Raman spectroscopic characterization of defected as-deposited graphene layers (including polarized spectroscopy) as well as graphene flakes exfoliated from similar specimens by two different ways using 488, 514, and 633 nm excitation laser wavelengths aiming at unambiguous confirmation of the graphene deposition of as well as the identification of the exact composition of the interlayers between the Si substrate and graphene layer/s.

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2. Experimental

2.1. CVD Process

We use 2 inches in diameter (001) Si substrates and a horizontal tube quartz CVD reactor with an internal diameter of approximately 70 mm. The experimental setup also consists of a gas-supply system (inlet and outlet parts), a thermostat with acetone evaporation alert/indication system, a quartz substrate holder, and a resistive heating furnace. The CVD process is based on thermal decomposition of acetone in Ar main gas flow. The deposition temperature was in the range 1150–1160°C. The temperature of the thermostat was kept at 12°C. In order to prevent the supersaturation in the high-temperature zone of the reactor, we used a “pulsed” regime in experiments by alternating the flow of the gas mixture of Ar + C₃H₆O) for 3 min on top of the main flow of pure Ar of about 150–180 cm³/min for 1.5 min for each pulse. The optimal results (predominantly single-layered graphene) were obtained after two deposition pulses.

2.2. Exfoliation

We exfoliated the carbon films deposited on (001) Si substrates by the following two different techniques:(i)The Scotch tape method (see, e.g., [9]): we put tightly the adhesive Scotch tape on the multilayered graphene side of the specimens. After peeling the tape off the specimen, a single- to few-layered graphene remains on the tape’s surface and the interlayer between the upper few layers of graphene and the substrate becomes accessible for spectroscopic examination. Then, we put tightly the Scotch tape with graphene flakes either on 320 nm SiO₂/Si or on glass substrate. About 30–50% of the graphene flakes remain adhered to the SiO₂ or glass substrate after removing the tape due to the Van der Waals force.(ii)We also adhered the multilayered graphene side of the specimens to epoxy resin. After careful cleavage, the most part of the graphene layer/s remains on the surface of the resin. Then, the adhered to the resin graphene film becomes accessible for spectroscopic examination. The Raman spectrum of the epoxy resin does not contain strong peaks around the 2D band of graphene (the area around 2630–2670 cm⁻¹). We established that the 2D band of graphene is clearly distinguishable for graphene regions lying on gas bubbles close to the surface of the resin; otherwise, the 2D band of graphene is weak.

2.3. Characterization

The Raman measurements were carried out in backscattering geometry at a micro-Raman HORIBA Jobin Yvon Labram HR 800 visible spectrometer equipped with a Peltier-cooled CCD detector with a He-Ne (633 nm wavelength and 0.5 mW) laser excitation. The 514 nm (about 23 mW) as well as 488 nm (about 24 mW) lines of an external Ar laser were also used. The laser beam was focused on a spot of about 1 μm in diameter, the spectral resolution being 0.5, 0.7, and 1 cm⁻¹, respectively, or better.

The Raman spectrum of graphene is a clearly established fingerprint of this 2D material (see [10]). The main first-order features in the Raman spectra of graphene and defect-infested graphene excited at 633 nm wavelength are the following:(i)G band (~1582 cm⁻¹) is the only band in graphene allowed by selection rules for first-order Raman effect; it is ascribed to optical (iTO and LO) doubly degenerate phonons of E_2g symmetry at the Γ point (initially described by Tuinstra and Koenig [11]).(ii)D band (~1330 cm⁻¹) is due to breathing-like bands of C hexagonal rings (corresponding to transverse optical phonons near the K point) and requires a defect for its activation via an intervalley double-resonance Raman process (see [12]).(iii)D’ band (at about 1615 cm⁻¹; defect induced similarly to the D band) occurs via an intravalley double-resonance process (see, e.g., [13]).(iv)D” band (at about 1145 cm⁻¹) is resulting from double-resonance intervalley scattering of LA phonons on defects (see [14]). The intensity of this band should be about 100 times lower than that of the D band.

Overtones and combination bands:(i)2D band (historically known from graphite and carbon nanotube-related literature as G’- peak) appears at about 2648–2665 cm⁻¹. It is clearly shown [15–20] that the shape and width of the 2D band can be used for the identification of the mono-, bi-, and three-layered graphene.(ii)The overtone of the D’- peak (2D’) and combination G (phonons), as well as (D+D’) bands, occur around 3230, 2450, and 2930 cm⁻¹, respectively (see [21]).

3. Results and Discussion

Two areas with different surface morphologies are observed by optical microscopy (Figure 1(a)): a clear relief (ridge-like formations) lying along <001> directions covers the first area denoted as DLC while the second area (denoted as αC) is covered by an inhomogeneous film with a constant depth. It should be also mentioned that optical inhomogeneities are observed on the DLC as well as αC-marked areas.
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(e)Figure 1Optical microscopy image of the surface morphology of (a) as-deposited graphene and graphene-related phases on diamond-like carbon (DLC) and amorphous carbon (αC) interlayers. The arrows remarked [100] and [010] directions of the Si substrate. The marker represents 20 μm. (b) The exfoliated and transferred graphene flakes on 320 nm SiO₂. The Raman spectra are taken from “+”-marked positions. The marker represents 30 μm. (c) The layers remaining on the surface of the substrate after exfoliation by Scotch tape. The Raman spectra are taken from the “+”-marked positions near points 1, 2, and 3. The marker represents 30 μm. (d) The exfoliated and transferred graphene flakes on glass substrate. The Raman spectra are taken from the “+”-marked positions near points 1 and 2. The marker represents 20 μm. (e) A graphene flake on air bubble near the epoxy resin surface. The Raman spectra are taken from the square-marked position. The marker represents 20 μm.

It should be recalled that the Raman spectrum (excited at 633 nm laser wavelength) taken from αC- and DLC-denoted areas (see [8]) contains all features typical for graphene: symmetric and clearly pronounced 2D band with full width at a half maximum (FWHM) of 40–56 cm⁻¹, I_2D/I_G ratio between 2 and 3.5, and I_2D/I_D ratio between 2 and 4. However, the 2D band appears at about 2660–2668 cm⁻¹ (for single- and bilayered graphene, respectively), that is, it is blueshifted by about 20 cm⁻¹ relative to the results presented in [15, 22, 23].

Due to the double-resonance origin of most of the monitored spectral features, we perform a Raman spectroscopy examination of as-deposited defected graphene at 488, 514, and 633 nm excitation wavelengths and the results are presented in Figure 2. The 2D bands are blueshifted by about 20 cm⁻¹ and can be typically deconvoluted into (a) a single Lorentzian with FWHM of about 40-41 cm⁻¹ (see Figure 3(a)); (b) four Lorentzians (FWHM of 22 (±1) cm⁻¹) for 2D band with total width of 45–56 cm⁻¹ (see Figure 3(b)); and (c) six Lorentzians (Figure 3(c)) for 2D band with total width larger than 56 cm⁻¹. The results of the deconvolution indicate the presence of single-, bi-, and three-layered defected graphene, respectively (see [15–20]). We did not establish a clear difference between the graphene layers deposited on αC and DLC interlayers; however, bi- and three-layered areas were more frequently observed on DLC interlayers. The results for predominantly single-layered (SL) and bilayered (BL) defected graphene (according to the deconvolution of 2D bands) are summarized in Table 1.

Figure 2Raman spectra taken from as-grown films excited at 633 nm (red trace), 514 nm (blue trace), and 488 nm (green trace) laser wavelengths.
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(c)Figure 3Deconvolution of 2D band identified as coming from single-layered (a), bilayered (b), and three-layered defected graphene deposited on αC. The spectrum is excited at 633 nm laser wavelength.Table 1Summarized results of Raman spectroscopy examination of as-deposited defected graphene films.

In order to access the interlayers as well as graphene flakes for Raman examination, the so-called Scotch tape method was initially used for exfoliation. The Raman spectra of the graphene flakes exfoliated in this way with some occasional amorphous (αC) interlayers transferred to Si/SiO₂ (300 nm) or glass substrate are shown in Figures 4 and 5, respectively.

Figure 4The Raman spectrum of defected 1-2-layered graphene transferred on 320 nm SiO₂. The 2D band is symmetric and appears at 2658-2659 cm⁻¹ with FWHM of 38–40 cm⁻¹ (measured in point 2) and 40–42 cm⁻¹ (measured in point 1).

Figure 5The Raman spectrum of the interlayer (point 1, Figure 1(c)) of αC after exfoliation by Scotch tape. The features observed at about 1450 and 1530 cm⁻¹ are typical for C₇₀ fullerenes.

A lot of flakes (of the order of 10²) were transferred on Si/SiO₂ and examined by Raman spectroscopy. The Raman spectra are enhanced due to interference effects caused by the SiO₂ 300 nm layer over the Si substrate, and I_2D/I_G varies in the range 3.5-6.0. However, it was impossible to isolate single-layered graphene flake (or to obtain clear Raman response of single-layered graphene) in this way. The exfoliated flakes were never transparent (see point 1 in Figure 1(b)). The best spectra were recorded from the points in a darker contrast (point 2 in Figure 1(b)), but the FWHM of 2D Raman band remains >35 cm⁻¹. Moreover, the D” band slightly overlaps with the second order of Si substrate when the spectrum is excited at 514 as well as 488 nm laser wavelengths.

After peeling the tape off the specimen, the interlayer between the upper flake and the substrate is accessed. The remaining interlayers have different optical contrasts (see Figure 1(c)) and Raman spectra: the spectrum of typically retained interlayer (point 1 in Figure 1(c)) in Figure 5 is very similar to that of turbostratic graphite (see [24]), but weak peaks of C₇₀ fullerenes (the features observed at about 1450 and 1530 cm⁻¹ (see [25, 26])) are also clearly distinguished (Figure 5). The strong modes of fullerenes C₇₀ at about 1180 and 1568 cm⁻¹ are merged with D” and G bands.

The Raman spectra (Figure 6) taken from points 2 and 3 (Figure 1(c)) are similar as they contain the most prominent modes of C₇₀ peaks at 1160, 1220, 1454, 1526, and 1565 cm⁻¹ [25, 26], nanodiamond (Nd) peaks at 1330 and 1620 cm⁻¹ (see [27]), and turbostratic graphite. The D, G, and D’ bands are found at 1335, 1590, and 1612 cm⁻¹, respectively, but in a different proportion: the spectrum from point 3 is dominated by the peaks of C₇₀ and Nd while the spectrum from point 2 is dominated by turbostratic graphite (see Figure 6). It should be also remarked that features of C₆₀ fullerenes (see, e.g., [25, 26]) were not observed.

Figure 6Raman spectra of the interlayer that remains on the substrate after exfoliation by the Scotch tape method taken from points 2 and 3 (Figure 1(c)).

As it was mentioned above, the D” band overlaps with the second-order band of Si substrate especially when the spectrum is excited at 488 and 514 nm laser wavelengths. In order to distinguish the dispersion of the D” band of several Scotch tape methods, exfoliated flakes were transferred on glass substrates. The flakes have very similar surface morphology to those transferred on SiO₂/Si substrates (Figure 1(d)). The Raman spectrum of such flakes is not significantly different from that of the as-deposited layers (Figure 7); however, the D” band appears at 1096 (for 488 nm excitation) and at 1135 cm⁻¹ (for 633 nm excitation), respectively, that is, they coincide with the data of Herziger et al. [14].

Figure 7The Raman spectra of as-grown graphene on αC excited at 488 nm (green trace) and 633 nm (black trace) wavelengths. The similar spectra of exfoliated graphene transferred on a glass substrate excited at 488 nm (blue trace) and 633 nm (red trace). The inset: magnified part of the region 900–1200 cm⁻¹.

According to the above results, we conclude that the exfoliation by the Scotch tape method does not enable splitting up between the defected graphene and the interlayers (especially the αC-designated one). Another way for exfoliation was probed (by exfoliation on epoxy resin), and the optical micrograph image of the area of the edge of a resin bubble and the Raman spectrum taken from this area (excited at 633 nm) are shown in Figures 1(e) and 8, respectively. The Raman spectrum of epoxy resin does not contain any features in the 2D region of graphene (upper trace in Figure 8); hence, 2D bands of a single- and bilayered graphene were identified at the edge of a lot of bubbles on the surface of the resin (Figure 1(e)). It should be clearly remarked that the measured FWHM of the 2D band of such single-layered graphene is about 27–29 cm⁻¹, but it is situated at 2654–2656 cm⁻¹, that is, it remains upshifted with about 10–15 cm⁻¹.

Figure 8Raman spectra of graphene films situated on air bubbles/cavities. The 2D band is situated at 2655 cm⁻¹ and has FWHM ~28 cm⁻¹ (i.e., it corresponds to single-layered graphene—blue trace).

Recently, Li et al. [28] established that the intensity of 2D band varies as a cosine to the fourth power when the laser propagation direction is parallel to the graphene layer and the polarization is rotated around it. They also derived the orientation distribution function of monolayered graphene as well as that of graphene paper and highly oriented pyrolytic graphite. We perform similar measurements in X(Y_φY_φ)X geometry, φ being the angle between the incident laser beam polarization and the graphene layer plane; Z is the axis perpendicular to the graphene plane, and the laser beam propagates transversely to the graphene layer along the X direction (see Figure 9(a)). The excitation laser beam was focused in a manner to comprise no more than 30% of the edge of the Si substrate and graphene film (Figure 9(a)). The parallel scattering geometry was used. The measurements were performed starting from φ = 0° (corresponding to X(YY)X in Porto notations) and finished at φ = 180°. The preliminary results of these rotational angle-dependent Raman measurements of as-deposited specimen are presented in Figure 9. The signal significantly drops upon changing the angle from 0° to 90° and increases again in the interval between 90 and 180° which resembles indeed the cos⁴ law. At 90° (corresponding to X(ZZ)X in Porto notations), the Raman signal is very weak but still observable (Figure 9), and the rotational angle-independent features of C₇₀ fullerenes and nanodiamond (Nd) dominate the spectrum. The residual features in the Raman spectra taken at φ = 90° point out that the measured polarized Raman spectra are taken from graphene deposited on DLC interlayer. The measurements in this scattering geometry (X(YY)X in Porto notations) access measurements of the interlayer/s without exfoliation. On the other hand, the polarized Raman study confirms the deposition of graphene because the intensities of the most prominent Raman features of graphite (D, G, and 2D bands) show similar behavior in similar conditions as those of graphene. However, the intensity of the Raman features of graphene decreases significantly slower than those of graphene as it is shown in [28].
(a)
(b)
(a)
(b)Figure 9(a) Optical photography of the specimen in X(YY)X geometry (in Porto notations). The inset: optical photography of the specimen in Z(YY)Z geometry (in Porto notations). The arrow-remarked laser spots are eye guide showing the real area of the laser spot during measurements. The marker represents 10 μm. (b) Spatially resolved Raman spectra of as-deposited defected graphene at 633 nm excitation.

It is worth noting that the 2D band from the single-layered graphene regions is symmetric and strong, but it is somewhat broadened with FWHM of about 40–42 cm⁻¹and is blueshifted by 15–20 cm⁻¹ in as-grown specimens. It is well known that such behavior is usually related to strain (see [29–32]) and doping [33]. Moreover, Lee et al. [34] and Bouhafs et al. [35] experimentally studied the influence of these parameters on the position and FWHM of G and 2D bands in single- and bi-/multilayered graphene, respectively. The deduced simple plot of the 2D versus G band positions enables distinguishing the influence of doping and strain on the positions of G and 2D bands. In our single-layered specimens, the G band is slightly uphifted by 1-2 cm⁻¹ while the 2D band is more significantly blueshifted and broadened by 10–20 cm⁻¹. Therefore it can be assumed that the 2D band blueshift and broadening are due to the lattice strain predominantly as well as to the doping. It can be suggested that the lattice strain is due to the bonding between graphene and the interlayers while the doping should be related to charge transfer from the interlayers/interfaces to graphene as well as to different intrinsic (grain boundaries, etc.) and extrinsic (trapped nitrogen, oxygen, and impurities during the deposition) defects, that is, it can be related to the influence of the interlayers/substrates as well as of the deposition process.

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4. Conclusions

We extended the analysis of defected graphene deposited by CVD as well as the two types of interlayers between the defected graphene layer/s and Si substrates by both unpolarized and polarized Raman spectroscopy. The performed Raman spectroscopy examination of as-deposited defected graphene at 488, 514, and 633 nm excitation wavelengths enables the most of the monitored spectral features of double-resonance origin (D, D”, and 2D bands). The Raman studies of exfoliation by the so-called Scotch tape method revealed that (a) the composition of the designated DLC interlayers varies with depth: the initial layers on the Si substrate consist of a mixed phase of turbostratic graphite, nanodiamond/diamond-like carbon, and C₇₀ fullerenes while the upper ones are dominated by diamond-like carbon and some C₇₀ fullerenes and (b) the amorphous carbon interlayer is dominated by turbostratic graphite and contains a larger quantity of C₇₀ than the DLC-designated interlayers. Single- and bilayered defected graphene flakes were exfoliated on epoxy resin. The preliminary results of polarized Raman experiments show that the intensity of the 2D band varies as a cosine to the fourth power when the laser propagation direction is parallel to the graphene layer and the polarization is rotated around it which is an additional indication of the deposition of single-layered graphene. The results of Raman spectroscopic studies of as-grown and exfoliated graphene films tend to assume that the observed slight upshift of the 2D band as well as the broadening of 2D band is due to the strain and can be related to the bonding between the graphene and the interlayers, that is, it could be regarded as an influence of the interlayers between the defected graphene and the Si substrates.

Conflicts of Interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

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Authors: T. I. Milenov,¹ E. Valcheva,² and V. N. Popov²

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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

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Most metallic corrosion occurs via electrochemical reactions at the interface between the metal and an electrolyte solution. For example, a thin film of moisture on a metal surface forms the electrolyte for atmospheric corrosion. A second example is when wet concrete is the electrolyte for reinforcing rod corrosion in bridges. Although most corrosion takes place in water, corrosion in non-aqueous systems is not unknown.

Corrosion normally occurs at a rate determined by an equilibrium between opposing electrochemical reactions. One reaction is the anodic reaction, in which a metal is oxidized, releasing electrons into the metal. The other is the cathodic reaction, in which a solution species (often O₂ or H⁺) is reduced, removing electrons from the metal. When these two reactions are in equilibrium, the flow of electrons from each reaction is balanced, and no net electron flow (electrical current) occurs. The two reactions can take place on one metal or on two dissimilar metals (or metal sites) that are electrically connected.

Figure 1 sketches this process. The vertical axis is electrical potential and the horizontal axis is the logarithm of absolute current. The theoretical current for the anodic and cathodic reactions is represented as straight lines. The curved line is the total current: the sum of the anodic and cathodic currents. This is the current that you measure when you sweep the potential of the metal with your potentiostat. The sharp point in the curve is actually the point where the current reverses polarity as the reaction changes from anodic to cathodic, or vice versa. The sharp point is caused by plotting along a logarithmic axis. The use of a logarithmic axis is necessary because of the wide range of current values that must be recorded during a corrosion experiment. Because of the phenomenon of passivity, the current often change by six orders of magnitude during a corrosion experiment.

Figure 1. Corrosion process showing anodic and cathodic components of current.

The potential of the metal is the means by which the anodic and cathodic reactions are kept in balance. Refer to Figure 1. Notice that the current from each half reaction depends on the electrochemical potential of the metal. Suppose that the anodic reaction releases too many electrons into the metal. Excess electrons thus shift the potential of the metal more negative, which slows the anodic reaction and speeds up the cathodic reaction. This counteracts the initial perturbation of the system. 

The equilibrium potential assumed by the metal in the absence of electrical connections to the metal is called the open-circuit potential, E_oc. In most electrochemical corrosion experiments, the first step is the measurement of E_oc. 

The value of either the anodic or cathodic current at E_oc is called the corrosion current, I_corr. If we could measure I_corr, we could use it to calculate the corrosion rate of the metal. Unfortunately, I_corr cannot be measured directly. However, it can be estimated using electrochemical techniques. In any real system, I_corr and corrosion rate are a function of many system parameters, including type of metal, composition of the solution, temperature, movement of the solution, metal history, and many others.

The above description of the corrosion process does not say anything about the state of the metal surface. In practice, many metals form an oxide layer on their surface as they corrode. If the oxide layer inhibits further corrosion, the metal is said to passivate. In some cases, local areas of the passive film break down, allowing significant metal corrosion to occur in a small area. This phenomenon is called pitting corrosion or simply pitting.

Because corrosion occurs via electrochemical reactions, electrochemical techniques are ideal for the study of the corrosion processes. In electrochemical studies, a metal sample with a surface area of a few square centimeters is used to model the metal in a corroding system. The metal sample is immersed in a solution typical of the metal’s environment in the system being studied. Additional electrodes are immersed in the solution, and all the electrodes are connected to a device called a potentiostat. A potentiostat allows you to change the potential of the metal sample in a controlled manner and measure the current that flows as a function of applied potential.

Both controlled-potential (potentiostatic) and controlled-current (galvanostatic) polarization are useful. When the polarization is done potentiostatically, current is measured, and when it is done galvanostatically, potential is measured. This discussion will concentrate on controlled-potential methods, which are much more common than galvanostatic methods. With the exception of open-circuit potential versus time, electrochemical noise, galvanic corrosion, and a few others, potentiostatic mode is used to perturb the equilibrium corrosion process. When the potential of a metal sample in solution is forced away from E_oc, it is referred to as polarizing the sample. The response (that is, resulting current) of the metal sample is measured as it is polarized. The response is used to develop a model of the sample’s corrosion behavior. 

Quantitative Corrosion Theory

In the previous section we pointed out that I_corr cannot be measured directly. In many cases, you can estimate it from current-versus-voltage data. You can measure a logarithmic current versus potential curve over a range of about one half volt. The voltage scan is centered on E_oc. You then fit the measured data to a theoretical model of the corrosion process.

The model we use for the corrosion process assumes that the rates of both the anodic and cathodic processes are controlled by the kinetics of the electron-transfer reaction at the metal surface. This is generally the case for corrosion reactions. An electrochemical reaction under kinetic control obeys Eq. 1, the Tafel equation.

                                 In this equation,

The Tafel equation describes the behavior of one isolated reaction. In a corrosion system, we have two opposing reactions: anodic and cathodic.

The Tafel equations for the anodic and cathodic reactions in a corrosion system can be combined to generate the Butler-Volmer equation (Eq. 2).

where

What does Eq. 2 predict about the current-versus-voltage curve? At E_corr, each exponential term equals one. The cell current is therefore zero, as you would expect. Near E_corr, both exponential terms contribute to the overall current. Finally, as the potential is driven far from E_corrby the potentiostat, one exponential term predominates and the other term can be ignored. When this occurs, a plot of logarithmic current versus potential becomes a straight line. 

A plot of log I versus E is called a Tafel plot. The Tafel plot in Figure 1 was generated directly from the Butler-Volmer equation. Notice the linear sections of the cell current curve.

In practice, many corrosion systems are kinetically controlled and thus obey Eq. 2. A curve of logarithmic current versus potential that is linear on both sides of E_corr is indicative of kinetic control for the system being studied. However, there can be complications, such as:

• Concentration polarization, where the rate of a reaction is controlled by the rate at which reactants arrive at the metal surface. Often cathodic reactions show concentration polarization at higher currents, when diffusion of oxygen or hydrogen ion is not fast enough to sustain the kinetically controlled rate. 
• Oxide formation, which may or may not lead to passivation. This process can alter the surface of the sample being tested. The original surface and the altered surface may have different values for the constants in Eq. 2.
• Other effects that alter the surface, such as preferential dissolution of one component of an alloy, can also cause problems.
• A mixed control process where more than one cathodic, or anodic, reaction occurs simultaneously may complicate the model. An example of mixed control is the simultaneous reduction of oxygen and hydrogen ion.
• Finally, potential drop as a result of cell current flowing through the resistance of your cell solution causes errors in the kinetic model. This last effect, if it is not too severe, may be correctable via IR-compensation in the potentiostat. 

In most cases, complications like those listed above cause non-linearities in the Tafel plot. Use with caution the results derived from a Tafel plot without a well-defined linear region.

Classic Tafel analysis is performed by extrapolating the linear portions of a logarithmic current versus potential plot back to their intersection. See Figure 2 (which is Figure 1 reprinted with annotations that demonstrate the analysis). The value of either the anodic or the cathodic current at the intersection is I_corr. Unfortunately, many real-world corrosion systems do not provide a sufficient linear region to permit accurate extrapolation. Most modern corrosion test software., performs a more sophisticated numerical fit to the Butler-Volmer equation. The measured data are fit to Eq. 2 by adjusting the values of E_corr, I_corr, β_a, and β_c. The curve-fitting method has the advantage that it does not require a fully developed linear portion of the curve.

Figure 2. Classic Tafel analysis.

Polarization Resistance

Eq. 2 can be further simplified by restricting the potential to be very near to E_corr. Close to E_corr, the current-versus-voltage curve approximates a straight line. The slope of this line has the units of resistance (Ω).  The slope is, therefore, called the polarization resistance, R_p. An R_p value can be combined with an estimate of the β coefficients to yield an estimate of the corrosion current.

If we approximate the exponential terms in Eq. 2 with the first two terms of a power-series expansion ( ) and simplify, we get one form of the Stern-Geary equation:

In a polarization resistance experiment, you record a curve of current versus voltage as the cell voltage is swept over a small range of potential that is very near to E_oc (generally ±10 mV). A numerical fit of the curve yields a value for the polarization resistance, R_p. Polarization resistance data do not provide any information about the values for the β coefficients. Therefore, to use Eq. 3, you must provide β values. These can be obtained from a Tafel plot, or estimated from your experience with the system you are testing.

Calculation of Corrosion Rate from Corrosion Current

The numerical result obtained by fitting corrosion data to a model is generally the corrosion current. We are interested in corrosion rates in the more useful units of rate of penetration, such as millimeters per year. How is corrosion current used to generate a corrosion rate? Assume an electrolytic dissolution reaction involving a chemical species, S:

            S   ®  Sⁿ⁺ +   n^e–

You can relate current flow to mass via Faraday’s Law.

Q = nFM           Eq. 4

where

A more useful form of Eq. 4 requires the concept of equivalent weight. The equivalent weight (EW) is the mass of species S that will react with one Faraday of charge. For an atomic species, EW = AW/n (where AW is the atomic weight of the species). 

Recalling that M = m/AW and substituting into Eq. 4 we get:

where m is the mass of species S that has reacted.

In cases where the corrosion occurs uniformly across a metal surface, the corrosion rate can be calculated in units of distance per year. Be careful: this calculation is only valid for uniform corrosion; it dramatically underestimates the problem when localized corrosion occurs! 

For a complex alloy that undergoes uniform dissolution, the equivalent weight is a weighted average of the equivalent weights of the alloy components. Mole fraction, not mass fraction, is used as the weighting factor. If the dissolution is not uniform, you may have to measure the corrosion products to calculate EW.

Conversion from a weight loss to a corrosion rate (CR) is straightforward. We need to know the density, d, and the sample area, A. Charge is given by Q = It, where t is the time in seconds and I is a current. We can substitute in the value of Faraday’s constant. Modifying Eq. 5,

where

Table 1. Corrosion Rate Constants

IR Compensation

When you pass current between two electrodes in a conductive solution, there are always regions of different potentials in the solution. Much of the overall change in potential occurs very close to the surface of the electrodes. Here the potential gradients are largely caused by ionic concentration gradients set up near the metal surfaces. Also, there is always a potential difference (a potential drop) caused by current flow through the resistance in the bulk of the solution.

In an electrochemical experiment, the potential that you wish to control or measure is the potential of a metal specimen (called the Working Electrode) versus a Reference Electrode.  We are normally not interested in the potential drops caused by solution resistances because they are negligible in typical electrolyte solutions such as 1 M H₂SO₄ or 5% NaCl. 

Gamry Instruments potentiostats, like all modern electrochemical instruments, are three-electrode potentiostats. They measure and control the potential difference between a non-current-carrying Reference Electrode and one of the two current-carrying electrodes (the Working Electrode). The potential drop near the other current-carrying electrode (the Counter Electrode) does not matter when a three-electrode potentiostat is used. 

Careful placement of the Reference Electrode can compensate for some of the IR-drop resulting from the cell current, I, flowing through the solution resistance, R.  You can think of the Reference Electrode as sampling the potential somewhere along the solution resistance. The closer it is to the Working Electrode, the closer you are to measuring a potential free from IR errors.  However, complete IR compensation cannot be achieved in practice through placement of the reference electrode, because of the finite physical size of the electrode. The portion of the cell resistance that remains after placing the Reference Electrode is called the uncompensated resistance, R_u. 

Gamry potentiostats can use current-interrupt or positive-feedback IR compensation to dynamically correct uncompensated resistance errors. In the current-interrupt technique, the cell current is periodically turned off for a very short time. With no current flowing through the solution resistance, its IR drop disappears instantly. The potential drop at the electrode surface remains constant on a rapid time scale.  The difference in potential with the current flowing and without is a measure of the uncompensated IR drop.

The potentiostat makes a current-interrupt measurement immediately after it acquires each data point. The potentiostat actually takes three potential readings: E₁ before the current is turned off, and E₂ and E₃ while it is off (see Figure 3). Normally, the latter two are used to extrapolate the potential difference, ∆E, back to the exact moment when the current was interrupted. The timing of the interrupt depends on the cell current. The interrupt time is 40 µs on the higher current ranges. On lower current ranges, the interrupt lasts longer.

Figure 3. Current-interrupt potential versus time.

In controlled potential modes, the applied potential can be dynamically corrected for the measured IR error in one of several ways. In the simplest of these, the IR error from the previous point is applied as a correction to the applied potential. For example, if an IR free potential of 1 V is desired, and the measured IR error is 0.2 V, the potentiostat applies 1.2 V. The correction is always one point behind, for the IR error from one point is applied to correct the applied potential for the next point. In addition to this normal mode, a Gamry Instruments potentiostat offers more-complex feedback modes in which the two points on the decay curve are averaged.

By default in the controlled potential modes, the potential error measured via current-interrupt is used to correct the applied potential. In the controlled current modes, no correction is required. If IR compensation is selected, the measured IR error is subtracted from the measured potential. All reported potentials are therefore free from IR error.

For a detailed theoretical discussion of uncompensated resistance, see Keith B. Oldham, et al., Analytical Chemistry, 72 (2000), 3972 and 3981.

Current and Voltage Conventions

Current polarities in electrochemical measurements can be inconsistent. A current value of –1.2 mA can mean different things to workers in different branches of electrochemistry or in different countries or even to different potentiostats. To an analytical electrochemist it represents 1.2 mA of anodic current. To a corrosion scientist it represents 1.2 mA of cathodic current. A Gamry Instruments potentiostat in default mode follows the corrosion convention for current in which positive currents are anodic and negative currents are cathodic. For the convenience of our users around the world, Gamry Instruments potentiostats can provide the current polarity as per your preference with a simple software command.

The polarity of the potential can also be a source of confusion. In electrochemical corrosion measurement, the equilibrium potential assumed by the metal in the absence of electrical connections to the metal is called the open-circuit potential, E_oc. We use the term corrosion potential, E_corr, for the potential in an electrochemical experiment at which no current flows, as determined by a numerical fit of current-versus-potential data. In an ideal case, the values for E_oc and E_corr are identical. One reason the two voltages may differ is that changes have occurred to the electrode surface during the scan.

With most modern potentiostats, all potentials are specified or reported as the potential of the working electrode with respect to either the reference electrode or the open-circuit potential. The former is always labeled as “vs. E_ref” and the latter as “vs. E_oc”. The equations to convert from one form of potential to the other are:

            E vs. E_oc = (E vs. E_ref) – E_oc

            E vs. E_ref = (E vs. E_oc) + E_oc

Regardless of whether potentials are versus E_ref or versus E_oc, one sign convention is used. The more positive a potential, the more anodic it is. More anodic potentials accelerate oxidation at the Working Electrode. Conversely, a negative potential accelerates reduction at the Working Electrode.

Some References on Corrosion Theory and Electrochemical Corrosion Tests

DC Electrochemical Test Methods, N.G. Thompson and J.H. Payer, National Association of Corrosion Engineers. ISBN: 1-877914-63-0.

Principles and Prevention of Corrosion, Denny A. Jones, Prentice-Hall, 1996. ISBN 0-13-359993-0.

Polarization Resistance Method for Determination of Instantaneous Corrosion Rates, J.R. Scully, Corrosion, 56 (2000), 199.

Several electrochemical corrosion techniques are approved by the ASTM (American Society for Testing and Materials, 100 Barr Harbor Drive, West Conshohocken, PA 19428. They may be found in Volume 3.02 of the ASTM Standards:

G 5: Potentiostatic and Potentiodynamic Anodic Polarization Measurements

G 59: Polarization Resistance Measurements

G 61: Cyclic Polarization Measurements for Localized Corrosion Susceptibility of Iron-, Nickel-, and Cobalt-Based Alloys

G 100: Cyclic Galvanostaircase Polarization

G 106: Verification of Algorithm and Equipment for Electrochemical Impedance Measurements

G 108: Electrochemical Potentiokinetic Reactivation (EPR) for Detecting Sensitization

G 150: Electrochemical Critical Pitting Temperature Testing of Stainless Steels

Electrochemical Techniques in Corrosion Engineering, National Association of Corrosion Engineers, 1986.

Corrosion Testing and Evaluation, STP 1000, Ed. R. Baboian and S.W. Dean, American Society for Testing and Materials, West Conshohocken, PA, 1991. ISBN 0-8031-1406-0.

Electrochemical Corrosion Testing, STP 727, Ed. F. Mansfeld and U. Bertocci, American Society for Testing and Materials, West Conshohocken, PA, 1979.

Corrosion and Corrosion Control, 3rd ed., Herbert H. Uhlig, John Wiley and Sons, New York, 1985.