The alternating current (AC) corrosion measurement, known as AC impedance or electrochemical impedance spectroscopy (EIS) technique is performed over a range of low magnitude polarising voltages in the same way as LPR. It involves the application
of a small-amplitude sinusoidal potential perturbation on the sample at a number of discrete frequencies (ω). The resulting current waveform at each applied frequency will display a sinusoidal response that is out of phase with the applied potential thereby yielding values of resistance and capacitance which can give information on the corrosion behaviour and rates, and also an idea of the corrosion rate-controlling mechanisms at the material-electrolyte interface (especially in the presence of an adsorbed film or material coating) [43]. AC voltages have variable magnitudes with both anodic and cathodic polarity in each polarisation cycle. The applied voltage amplitude can range from 5 to 20 mV centred on the free corrosion potential with resulting frequencies for the impedance measurements from 100 kilohertz to a few millihertz [43].
The measurement is possible because an electrical double layer (EDL) (a charge separation between the metal surface and the solution) can have electrical properties similar to those for a simple electrical circuit composed of resistors and a capacitor as illustrated in Figure 2.7. Impedance is the AC analogue of DC resistance. It is a term used to describe the resistance to the flow of electrons in AC circuits with capacitors and inductors. An EDL capacitive reactance (Cedl) is similar to the capacitor capacitance, which is determined by the type of metal with its associated electrolyte composition. The charge-transfer resistance (Rct) is similar to corrosion resistance, which resists the transfer of excess electrons to electrochemically active species whilst Rs is the solution resistance.
Figure 2.7: Simple electrical circuit having electrical properties similar to an EDL [43].
A capacitor or inductor takes time to reach full charge i.e. relaxation, and this charging period presents a shift between current and voltage amplitude curves as shown in Figure 2.8. This shift (or phase angle) and its magnitude are different for each polarising voltage frequency and tend to be plotted as positive quantities for EIS data irrespective of the fact that their values are negative [43].
Figure 2.8: AC voltage and current response [43].
AC (and DC) current and voltage are vectors and consequently so is impedance. An impedance vector can be resolved into components as shown in Figure 2.9, where the impedance is a solid arrow and the components are dashed arrows.
Figure 2.9: An impedance vector resolved into X-Y components [43].
Phase angle
Hence, the total impedance Z(ω) of the electrochemical interface can be written as:
(2.33)
where , the angular frequency, is the voltage (V), is the current (A) is real impedance magnitudes, is imaginary impedance magnitudes and √ . For a simple circuit in Figure 2.7 [43],
(2.34)
(2.35) | | √ (2.36)
and phase angle,
( ) (2.37)
From the above, it is evident that each polarising voltage frequency gives a different magnitude for phase angle, total impedance and the component vectors. Unlike DC polarisations, which cause ions to move in one direction for each DC magnitude and polarity, AC voltages cause ions to move back and forth between counter and working electrodes in response to the changes in polarity during an AC cycle. Hence, electron transfer also moves to and from the working electrode and electrochemically active species during polarisation.
When polarising the sample by applying an AC voltage, the EDL is forced to try and change its chemical composition as fast as the polarising voltage frequency changes.
The EDL takes time to change to a composition that corresponds to a given polarising voltage magnitude [43]. A range of frequencies exist where the time it takes for a full polarisation cycle to be completed is similar to the time taken for the EDL composition to change. It is reasonable to assume that the EDL time constant will be part of this
frequency range and essentially determine its location. The response of the EDL to these frequency changes may be different to frequency ranges outside of this region.
It is important to note that the EDL is not the only source of time constants and a given electrode can possess much more than one. Inhibitor films or corrosion products such as iron carbonate (FeCO3) can have capacitive reactance and resistance properties [43]. Water and ions are capable of moving through porous films in response to AC polarisation and the movement of these species is hindered by the morphology of the film which produces a pore resistance.
The equivalent circuit for a corroding, coated metal which would produce two time constants is illustrated in Figure 2.10. The circuit for metallic corrosion is nested inside the coating circuit. Nested circuits are used as opposed to series circuits to indicate that pores in the coating, or regions that are not protected by the coating can cause metallic corrosion as these are areas where the electrolyte has direct access to the metal surface.
Figure 2.10: Equivalent circuit with two time constants used to model a corroding, coated metal. Cedl is the EDL capacitance. Rct is the charge-transfer resistance, Cf is the capacitance of the film, Rf is the resistance of the film and Rs is the solution resistance [43].