1.1 Why Impedance?
Among the various electrochemical techniques, electrochemical impedance spectroscopy (EIS) holds a special place. The classical electrochemical techniques present measurements of currents, electrical charges or electrode potentials as functions of time (which can also be related to the electrode potential). In contrast, EIS presents the signal as a function of frequency at a constant potential. This often poses some problems in understanding what is happening because electrochemists try to think in terms of time, not frequency. On the other hand, in optical spectroscopy, nobody thinks that light consists of the sinusoidal oscillations of electric and magnetic vectors of various frequencies, phases, and amplitudes. In spectroscopy, we used to think in terms of the frequency domain (wave number, frequency, or some related functions as wavelength) and that what we observed was the Fourier transform of the optical signal.
The issues associated with understanding EIS also relate to the fact that it demands some knowledge of mathematics, Laplace and Fourier transforms, and complex numbers. The concept of complex calculus is especially difficult for students, although it can be avoided using a quite time-consuming approach with trigonometric functions. However, complex numbers simplify our calculations but create a barrier in understanding complex impedance. Nevertheless, these problems are quite trivial and may be easily overcome with a little effort.
The advantages of using EIS are numerous. First of all, it provides a lot of useful information that can be further analyzed. In practical applications of cyclic voltammetry, simple information about peak currents and potentials is measured. These parameters contain very little information about the whole process especially when hardware and software is able sampling the current-potential curve producing thousands of experimental points every fraction of mV. On the other hand, one can use voltammetry with convolution, which delivers information at each potential, although very few people know and use this technique in current research. EIS contains analyzable information at each frequency. This is clearly seen from the examples that follow.
Steady-state polarization measurements, that is measurement of the current at constant potential or potential at the constant current provide current-potential curves from which a slope, that is, a polarization resistance, R p = d E/ d j , can be determined. An example of such a curve for a fuel cell is displayed in Fig..
Fig. 1.1
Voltage ( E )-current ( j ) curve for fuel cell. The slope is the polarization resistance ( R p)
However, taking the impedance at each potential produces series of data values at different frequencies. Examples of complex plane impedance plots that is imaginary versus real part at various frequencies for different fuel cells are presented in Fig.. The polarization resistance is the only point corresponding to zero frequency, as indicated in the plots. One may observe that the impedance plots, besides R p, produce much more information that is not available in steady-state measurements. Impedance plots display complex curves that are rich in information. Such information is contained in every point, not only in one value of R p. However, one must know how to find this information on the system being studied. This is a more complex problem and can be solved by the proper physicochemical modeling.
Fig. 1.2
Examples of complex plane impedance plots for fuel cells; arrows : polarization resistance also found in steady-state measurements; impedances are in
To characterize more complex electrochemical systems other studies of the system: including microscopic, surface morphology, structure, composition, and dc electrochemical characterization, should be carried out and understood thoroughly prior to EIS analysis. Studies may begin with EIS only for the electrical circuits and simple, well understood, systems. Beginning studies of complex systems with EIS is not recommended.
EIS supplies a large amount of information, but it cannot provide all the answers. EIS is usually used for fine-tuning mechanisms and determining the kinetics of processes, resistances, and capacitances, and it allows for the determination of real surface areas in situ. It is a very sensitive technique but must be used with care; it is often abused in the literature.
EIS has numerous applications. It is used in the following types of studies:
Interfacial processes: redox reaction at electrodes, adsorption and electrosorption, kinetics of homogeneous reactions in solution combined with redox processes, forced mass transfer
Geometric effects: linear, spherical, cylindrical mass transfer, limited-volume electrodes, determination of solution resistance, porous electrodes
Applications in power sources (batteries, fuel cells, supercapacitors, membranes), corrosion, coatings and paints, electrocatalytic reactions (e.g., water electrolysis, Cl2 evolution), conductive polymers, self-assembled monolayers, biological membranes, sensors, semiconductors, and others.
1.2 Short History of Impedance
EIS uses tools developed in electrical engineering for electrical circuit analysis [) by transforming them into a system of algebraic equations. Heaviside defined impedance, admittance, reactance, and operational impedance and explained the relation between Laplace and Fourier transforms by introducing a complex operator s=+j . The main advantage of EIS is the fact that it is based on the linear time-invariant system theory, most commonly known as LTI system theory, and the validity of data may be verified using integral transforms (KramersKronig transforms) that are independent of the physical processes involved.
Chemical applications of impedance spectroscopy began with the work of Nernst [] developed the impedance of mass transfer (the so-called Warburg impedance), which allowed further applications of EIS to redox reactions.
The development of EIS is displayed schematically in Table . However, the electrical equivalent circuits are often used in practice.
