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David C. Silverman |
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Inductive behavior of an electrochemical impedance response as a function of frequency is manifested by the resistance in the limit of zero frequency being smaller than the modulus at an intermediate frequency. In Nyquist format, the spectrum would have the appearance shown in this figure A brief comment about inductors and inductance is necessary before discussing how these figures were generated. In electricity, a magnetic field in the vicinity of a coiled wire carrying a current induces a potential that causes the current to change. This phenomenon obviously has little relationship to the physics occurring on a corroding surface. The value of an inductor used as part of an analogous circuit to model an electrochemical impedance spectrum very likely has little relationship to the process being modeled. Hence, the term "pseudoinductance" is used in this tutorial to describe this dependence of impedance on frequency. As stated in the section on Analysis Using Simple Circuits corrosion of alloys and related conductive materials is often an electrochemical degradation process governed by chemical kinetics and thermodynamics. This statement means that for the inductance to be real and not an experimental artifact, it should be relatable to actual corrosion kinetics. The equation used to generate the above simulations was originally proposed for an adsorption process with electron transfer at equilibrium that precedes the rate determining step (I. Epelboin, M. Keddam, and H. Takenouti, J. Appl. Electrochem. 2, 71 (1972)). The kinetic equations might be written as A + M ↔ A-M A-M → Product where A is the adsorbing reactant, M is the metal and A-M is the adsorbed species. The impedance equation related to such a reaction sequence was written as  (21)
The simulations assumed that Rs was 10 ohm-cm2, R1 was 104 ohm-cm2, R2 was 4.3x103 ohm-cm2, τ1 was 1 second, and τ2 was 100 seconds. The important point is that an inductor was not used in the model. Also, note the effect of the value of β on the appearance of the spectrum. Once again, a constant phase element should be assumed in place of a capacitance. The following case study (D. C. Silverman, Corrosion, 45(10), 824 (1989)1  (439k))
provides an example of how one might verify that the pseudoinductive behavior is not
an artifact and the type of information that may be obtained about corrosion. The
following impedance spectrum was observed when analyzing corrosion of steel in a waste
stream under controlled velocity conditions
One procedure for ensuring the absence of experimental artifacts is as follows:
In this case, linearity was examined by generating the spectra at three excitation amplitudes, 2mV, 5mV, and 10mV. The results are shown in these figures, Nyquist format Though the spectra were not generated with both decreasing and increasing frequency, they were generated at a stable corrosion potential. The corrosion potential before and after generation of the spectra was virtually the same. Thus, stability might be assumed, to be verified by comparison of corrosion rate estimates. The following table shows a comparison of corrosion rates.
The agreement of polarization resistance values between those estimated from the impedance spectrum and those estimated from polarization resistance measurements strongly suggest that the pseudoinductance is real. The agreement of the corrosion rates by impedance and mass loss strongly suggest that the low frequency resistance is, indeed, the polarization resistance. Following is another impedance spectrum showing pseudoinductance | ||||||||||||||||||||||||||||||||||||
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Previous Page: Diffusion Impedance 1 © NACE International publication and year shown in citation above. All rights reserved. Displayed with permission from NACE International, Houston, TX (http://www.nace.org). Published in Corrosion, in the month and year shown in the citation above. | ||||||||||||||||||||||||||||||||||||
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David C. Silverman, Ph.D. - Primary Consultant |
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