Electrochemical Impedance Spectroscopy

Electrochemical impedance spectroscopy (EIS) (sometimes also called AC impedance) is an electrochemical technique that surfaced in the late 1960's but did not become extensively studied until the late 1970's and early 1980's when computer controlled laboratory equipment became the norm. The reason is that the technique is most easily controlled with a laboratory computer. While many of the idiosyncrasies of the technique are now reasonably understood, the ability to use the technique to model all corrosion systems remains elusive.

The Technique

The technique itself is conceptually rather simple. A low amplitude alternating potential (or current) wave is imposed on top of a DC potential (often the corrosion potential with zero imposed current). The frequency is varied from as high as 105 Hertz to as low as about 10-3 Hertz in one experiment in a set number (often between 5 and 10) steps per decade of frequency. Varying frequency from low to high frequency is also possible. The corrosion process usually forces the measured current to be out of phase (denoted by the phase angle) with the input voltage. Dividing the input voltage by the output current furnishes the impedance. The variation in impedance (magnitude and phase angle) is used for the interpretation. This technique is in essence built on the DC polarization resistance technique in which a direct current voltage (or current) ramp is imposed. The relationships might be depicted as shown in this figure:

A simplified scheme of the instrumentation is shown in this picture:
The out-of-phase relationship between the input voltage and output current is analyzed by the frequency response analyzer. The technique has found practical application in such areas as:

  • estimating corrosion rates especially low corrosion rates
  • examining corrosion inhibitor functionality
  • examining coatings on metal surfaces

This technique has been used in a number of areas beyond corrosion including battery research. Several vendors supply equipment that enables these measurements to be made. These vendors provide information on the electronic characteristics of their equipment. Further background information on the technique can be found at http://www.argentumsolutions.com/tutorials/impedance_tutorialpg2.html and the references mentioned there.

Analogous Circuits and Electrochemical Impedance Spectroscopy

Most corrosion practitioners have attempted to analyze impedance spectra using combinations of analogous circuit elements. The reasoning used to justify this approach might be summarized as follows:

  • Corrosion of alloys and related conductive materials is an electrochemical degradation process governed by kinetics and thermodynamics.
  • This chemistry is often difficult to interpret in real-life complex and often poorly characterized systems normally encountered.
  • Analogous circuit elements enable the corrosion practitioner to bridge gaps in knowledge.
  • Such bridging enables use of electrochemical impedance spectroscopy to estimate corrosion rates and corrosion mechanisms in poorly characterized systems.

The specific circuit elements often used are the capacitor, resistor, and inductor. One point that cannot be emphasized enough is that corrosion is an electrochemical process involving molecules and ions. The analogous circuit components provide a way of modeling and discussing the corrosion process. They are not components of the corrosion process itself. An example of a simple circuit that can model a very passive alloy (e.g. titanium in water) is a parallel combination of a resistor and capacitor in series with a resistor. This circuit can be pictured as:

This circuit can model a real system as shown in the following figure of titanium in an acidic aqueous solution.
In this case, Rs models and provides a value for the solution resistance, Rp provides a value for the polarization resistance (which should be inversely proportional to the corrosion rate), and Cdl provides a value for the capacitance that exists across the interface between the alloy and the environment. The equations used to model this circuit can be found at http://www.argentumsolutions.com/tutorials/impedance_tutorialpg3.html.

The above system is fairly simple. Numerous examples exist in which more than one capacitive type element is required for modeling. Two practical corrosion systems that often require more complex models are alloys such as steel or copper being protected by corrosion inhibitors or alloys such as steel or aluminum being protected by an organic or inorganic coating. A discussion of the complexities introduced in these types of systems can be found at http://www.argentumsolutions.com/tutorials/impedance_tutorialpg6.html and the references cited in that tutorial.

Some systems require incorporation of a circuit element that has the characteristics of an inductor. Such an element is only providing a model of some rather complex surface reactions. An example of an impedance spectrum exhibiting the need for such a circuit element in the model is shown in this figure.

Two characteristic of the spectrum that alert the practitioner of the need for an element modeling inductance is that the modulus does not continue to increase as frequency is decreased and the sign on the phase angle reverses at low frequency. Pseudoinductance is sometimes used to refer to this behavior. Further information on a type of chemistry that can lead to this type of spectrum and how such a spectrum can be analyzed can be found at http://www.argentumsolutions.com/tutorials/impedance_tutorialpg9.html.

Complications can arise that make modeling of electrochemical impedance spectra more difficult.

  • Multiple RC (parallel combinations of a resistor and capacitor) time constants may have no 1:1 correspondence to corrosion processes
  • Distributed processes on the surface (e.g. transmission line)
  • Diffusion processes between the surface and bulk fluid
  • Additional surface reactions affected at low frequency
  • Cell geometry and electrode placement
  • Heterogeneously distributed surface reactions
  • Surface Roughness
  • Violation of requirements for the frequency response to be an impedance

Some of the above contributors are the result of poor experimental design. Others are part of the physics of the system and cannot be avoided. One of the methods of accounting for some of these influences is by using the constant phase element in place of the capacitance. Further information on the constant phase element can be found at http://www.argentumsolutions.com/tutorials/impedance_tutorialpg4.html and the references cited in that tutorial.

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