ABSTRACT
The measurement of electrochemical impedance is a potentiostatic procedure.[1,5] The system under study is polarized at a fixed DC potential (E0). Once a stationary state is reached (determined when the current reaches a constant value), a small amplitude (5-10mV RMS) AC voltage is superimposed and the Corresponding AC current is measured. The traditional method is by use of an impedance bridge,[1,2] but nowadays it is only rarely employed. Instead, there are two techniques currently employed:[1] a phase-sensitive detector (PSD), or frequency domain measurement, or, alternatively, the use of Fourier analysis or time domain measurements. Each one has its own strengths and weaknesses. We will now address the main aspects of electrochemical impedance measurements. More details can be found in the literature.[2,35,36]
Frequency Domain Measurements At the heart of these methods is the PSD, an electronic device that modulates the signal under measurement with a reference one.[1,2] In EIS (Fig. 6), the measured signal is a voltage proportional to the total current flowing through the circuit (obtained from the potentiostat), and the reference is the same AC voltage fed as perturbation to the electrode; in this case, a sinusoidal signal is employed. The measuring signal will be, in the more general case, composed by the superposition of a number of sinusoidal signals of different frequencies, including that of the reference signal. Because modulation produces the sums and differences between the frequencies of the reference signal and of all the components in the measuring one, in the special case of the measured component whose frequency is equal to that of the reference (component that is proportional to the AC current flowing in response to the perturbation), a resulting signal of zero frequency (DC) is obtained form the difference. By filtering out all the remaining AC components, the value of this DC signal can be measured and the amplitude of the original AC current in phase with the reference can be determined. If the procedure is repeated, but with the phase of the reference signal shifted by 90°, the amplitude of the current in quadrature with the reference is obtained. Because the perturbation signal is taken as having zero phase, the in-phase current component is directly the real part of the current in its complex representation, whereas the quadrature component is the imaginary part. The measurement is repeated by changing the frequency of the perturbation signal to obtain data at all frequency values of interest. As shown in Fig. 6, the PSDs and associated electronics are included in an instrument known as lock-in amplifier (LIA). The output of the LIA is usually fed to a computer, where it is processed to yield other results such as magnitude/phase representation, impedance calculation, etc. Often, a frequency response analyzer (FRA) is employed. An FRA embodies a signal generator, a LIA, and additional logic to measure at several frequencies and to process the results yielding the impedance (or admittance) frequency spectrum of the system studied. Anyway, the FRA is frequently interfaced to a computer for data storage and further processing.
