ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY

5.10 ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY

Electrochemical methods based on alternating currents can be used to obtain insights into corrosion mechanisms and to establish the effectiveness of corrosion control methods, such as inhibition and coatings. In an alternating - current circuit, impedance determines the amplitude of current for a given voltage. Impedance is the proportionality factor between voltage and current. In electrochemical impedance spectroscopy (EIS), the response of an electrode to alternating poten- tial signals of varying frequency is interpreted on the basis of circuit models of the electrode/electrolyte interface. Figure 5.11 shows two circuit models that can

Figure 5.11. ( a ) Electrical equivalent circuit model used to represent an electrochemical interface undergoing corrosion in the absence of diffusion control. R p is the polarization resistance, C dl is the double layer capacitance, R p is the polarization resistance, and R s is the

solution resistance [15] . ( b ) Electrical equivalent circuit model when diffusion control applies; W is the Warburg impedance [13] .

76 KINETICS: POL ARIZATION AND CORROSION R ATES

be used for analyzing EIS spectra. The simplest model for characterizing the metal – solution interface, Fig. 5.11 ( a ), includes the three essential parameters, R s (the solution resistance), C dl (the capacitance of the double layer), and R p (the polarization resistance). When direct - current measurements are carried out (i.e., frequency is zero), the impedance of the capacitor approaches infi nity. In parallel electrical circuits, the circuit with the smallest impedance dominates, with the result that, under these conditions, the sum of R s and R p is measured. If R s if sig- nifi cant, the corrosion rate is underestimated.

When diffusion control is important, another element, Z D , sometimes called the Warburg impedance, is added in series with R p , as shown in Fig. 5.11 ( b ). In electrochemical impedance spectroscopy, the impedance of the corroding metal is analyzed as a function of frequency. A sinusoidal potential change is applied to the corroding electrode at a number of frequencies, ω . At each fre- quency, the resulting sinusoidal current waveform is out of phase with the applied potential signal by an amount, the phase angle, θ , that depends on the circuit parameters. The current amplitude is inversely proportional to the impedance of the interface. The electrochemical impedance, Z ( ω ), is the frequency - dependent proportionality factor in the relationship between the voltage signal and the current response,

where E is the voltage signal, E = E 0 sin( ω t ); i is the current density, i = i 0 sin ( ω t + θ ); Z is the impedance (ohm - cm 2 ); and t is the time (seconds) [12] . Impedance is a complex number that is described by the frequency - dependent modulus, | Z |, and the phase angle, θ , or, alternatively, by the real component, Z ′ , and the imaginary component, Z ″ . The mathematical convention

for separating the real and imaginary components is to multiply the magnitude of the imaginary component by j [ = −1 ] and report the real and imaginary

values as a complex number. The equations for electrochemical impedance are [13]

E = E real + E imaginary =′+ E jE ′′ (5.18)

I = I real + I imaginary = ′ + ′′ I jI (5.19)

2 Z = ( Z ′+ ) 2 ( Z ′′ ) 2 (5.22) In electrochemical impedance analysis, three different types of plots are com-

monly used: Nyquist plots (complex plane, showing − Z ″ versus Z ′ ) and two dif-

THEORY OF C ATHODIC PROTEC TION

Figure 5.12. Electrochemical impedance data for cast 99.9% magnesium in pH 9.2 sodium borate presented in the Nyquist format [14] . ( Reproduced by permission of ECS, The Electro- chemical Society. )

ferent types of Bode plots, showing the impedance magnitude versus log frequency and showing phase angle versus log frequency. One example of each type of plot is shown in Figs. 5.12 and 5.13 . Figure 5.12 illustrates electrochemical impedance data for cast 99.9% magnesium in pH 9.2 sodium borate in the Nyquist format. This fi gure shows a single capacitive semicircle, indicating that the only process occurring is charge transfer.

Figure 5.13 shows Bode magnitude and phase angle plots for a system with the equivalent circuit shown in Fig. 5.11 ( a ) [15] . From Fig. 5.13 , it can be seen that, at very low frequencies,

Z = R s + R p (5.23) At very high frequencies, Z = R s (5.24)