current value via cell.As we are knowing the concept of electrical resistance, it can be defined as the ability of a circuit element to resist the flow of electrical current. So as per Ohm’s law, electrical resistance can be defined as the ratio between voltage, E, and current, I. Consider on application of sinusoidal potential excitation, we can get an AC current signal. This obtained current signal can be summed up as sinusoidal functions or Fourier series. The electrochemical impedance is specifically measured applying a modest excitation signal to get cell’s response in a pseudo‐linear manner as shown in Figure 2.4.If the excitation signal is expressed as a function of time (t), the equation takes form like,Here, in equation, Et is the obtained potential at time t, Eo is the amplitude of the signal, and ω is designated as the radial frequency. The interrelationship between radial frequency (ω) who is with unit of radians/second and frequency (f), which is expressed in hertz, is:For a linear system, the response signal for current, It, is shifted in phase (Φ) and has a different amplitude than Io,An expression resembling to Ohm’s Law permits to determine the impedance of the system as follows:where, K is sin (ω t)/sin (ωt+ Φ).So impedance can be measured in two forms: magnitude (Zo) and phase shift (Φ). Also in addition, the plot between Et (X‐axis) vs It (Y‐axis) was made and oval named as “Lissajous Figure” was obtained as resultant (Figure 2.5). The figure obtained was than analyzed as impedance measurement before the application of modern electrochemical instrumentations.Figure 2.4 The sinusoidal current response in a linear system on application of potential.Figure 2.5 The making of Lissajous figure.From Euler’s theorem, the expression of impedance can be written in complex form as:So the potential can be best described as:While the current response can be recorded as,Putting these values in impedance formula, the complex equation is formed as,The complex equation is composed of a real and imaginary components, who are plotted on X‐axis and Y‐axis in graph forming “Nyquist Plot” (Figure 2.6). The impedance can be best presented as an arrow or vector with dimensions of |Z|, whereas the angle made in between this vector and X‐axis, commonly known as “Phase Angle.”The most common equivalent circuit, which has been in use to sculpt corrosion of exposed metal in liquiform electrolyte, is called Randles circuit as presented in Figure 2.7.Where RΩ is the solution resistance, due to the presence of the electrolyte between the reference and working electrodes, polarization resistance Rp and Cdl or CPEdl is the double‐layer capacitance or double‐layer constant phase element (CPE). Another plot to mark presentation of impedance is the Bode Plot (Figure 2.8), where the impedance is plotted with log frequency on the X‐axis and both the absolute values of the impedance (|Z| = Zo) and the phase‐shift on the Y‐axis. This plot can give frequency information.Figure 2.6 Typical Nyquist plots for a Randles equivalent circuit with Cdl CPEdl with N = 0.8 (red dots).Figure 2.7 A typical Randles plot.For the recent analysis, the impedance is mainly measured with amplifiers or frequency‐response analyzers, which are consider being faster and are also more convenient than impedance bridges. The basic principle involves interpretation of the equivalent resistance and capacitance standards in provision of interfacial aspect. This technique is precise and intermittently in usage for evaluating amalgamate charge transfer criterion to get knowledge of double‐layer arrangement. The mathematical value of Rp obtained from electrochemical impedance spectroscopy can be considered more perfect compared to other monitoring techniques. The graph obtained such as Nyquist and Bode gives better understanding of corrosion procedure happening.Linear Polarization TechniqueThis electrochemical technique, which commonly also known as linear polarization resistance, is the only corrosion monitoring technique in its type method that permits measurement of corrosion rates directly across real time. So, it is fast and a nonintrusive method that needs an association in between metal reinforcement to get assess of on‐going corrosion in structures [28, 29]. One disadvantage of it is that it is only confined to electrolytically conducting liquids. While its response time and data quality are far more superior compared to other corrosion monitoring techniques. It can be harvested to get current–potential (i–E) domain, which can be monitored by applying polarization resistance at a very small voltage differences generally less than 30 mV, above and below its corrosion potential [30]. The obtained current response is linear over narrow range of corrosion potential. So the slope of this current–potential curve is defined as polarization resistance (Rp) whose value is constant. As per Stern and Geary in 1957, current value can be obtained by given equation, where Rp is inversely proportional to the instantaneous corrosion rate, at some conditions [31].Figure 2.8 Typical Bode plot. β a and βb are obtained Tafel constants from Tafel plots, polarization measurements for the studied system. In the last phase, the corrosion rate of the structure can be calculated via Icorr.The numerical value of ΔE/ΔI is known as the polarization resistance. This variable can be conveniently measured by putting another electrode/auxiliary in the liquid, and in turn connecting it to the working/corroding/test electrode via external power supply. The whole set‐up is given in circuit provided (Figure 2.9).Here, Rp is polarization resistance, Rs is solution resistance, while Ce is electrode capacitance. An important advantage of using LPR is that it does not take more than half an hour to provide a conclusion with preliminary apparatus adjustments, balancing of readings, calculating process, and computation of the polarization resistance Rp.Figure 2.9 Circuit for linear polarization resistance.4 NondestructiveGamma RadiographyGamma radiography technique is one of the nondestructive methods for thickness loss or testing concrete to obtain information relating concrete quality, and deterioration or defects present in reinforced concrete structures. It is best to report cracks, voids, or any kind of variation present within it [32, 33]. There are two different techniques under this umbrella, tangential radiography technique and double‐wall radiography technique as shown in Figure 2.10.In the tangential method, radiation crosses through the sidewall thickness of the pipe made from metal and the area of the radiograph, which is placed below the tangential position, can be monitored. This specific technique has some important benefits for getting the thickness of the insulation pipes. It also gives the corrosion both internally and externally. In addition, it is having some disadvantage also like it need higher energy and intensity of the provided radiation, which is due to long beam pass via matter. While on the other hand, some effects such as radiography arrangement, power source to film distance, exposure and source beam path thickness, as well as build‐up factor and linear atomic absorption coefficient in non‐insulated pipes have been quantified in double‐wall radiography technique [34–42].In the tangential technique radiation allowed to passes through the sidewall thickness of the studied pipe and the area of the radiograph, which is located below the tangential position. So the parts of radiograph, which lies behind the tangential location of the pipe, are interpreted only [43].UltrasonicThis technique helps to measure the thickness of the metal used along with size of defects. The principle involves the determination of thickness by monitoring the amount of time, which ultrasonic wave travels from the transducer via material to the back end of the material, which then reflects back to the transducer. From this, the width of the tested material can be calculated depending upon the speed of the sound passed through tested material. This technique is very efficient for inspecting the condition of vessels, tankers, pipeline in underground. The major advantage of using this technique is that readings can be taken from outside the wall of any operating structures, as they do not need connection on the dual side of the sample structure. This makes easy way to get width of the pipelines where the internal surface cannot be measure.
