Electrochemical impedance spectroscopy capacitance

The capacitance. The electrical double layer may be regarded as a resistance and capacitance in parallel see Section 20.1), and measurements of the electrical impedance by the imposition of an alternating potential of known frequency can provide information on the nature of a surface. Electrochemical impedance spectroscopy is now well established as a powerful technique for investigating electrochemical and corrosion systems. 

The monotonic increase of immobilized material vith the number of deposition cycles in the LbL technique is vhat allo vs control over film thickness on the nanometric scale. Eilm growth in LbL has been very well characterized by several complementary experimental techniques such as UV-visible spectroscopy [66, 67], quartz crystal microbalance (QCM) [68-70], X-ray [63] and neutron reflectometry [3], Fourier transform infrared spectroscopy (ETIR) [71], ellipsometry [68-70], cyclic voltammetry (CV) [67, 72], electrochemical impedance spectroscopy (EIS) [73], -potential [74] and so on. The complement of these techniques can be appreciated, for example, in the integrated charge in cyclic voltammetry experiments or the redox capacitance in EIS for redox PEMs The charge or redox capacitance is not necessarily that expected for the complete oxidation/reduction of all the redox-active groups that can be estimated by other techniques because of the experimental timescale and charge-transport limitations. 

Most often, the electrochemical impedance spectroscopy (EIS) measurements are undertaken with a potentiostat, which maintains the electrode at a precisely constant bias potential. A sinusoidal perturbation of 10 mV in a frequency range from 10 to 10 Hz is superimposed on the electrode, and the response is acquired by an impedance analyzer. In the case of semiconductor/electrolyte interfaces, the equivalent circuit fitting the experimental data is modeled as one and sometimes two loops involving a capacitance imaginary term in parallel with a purely ohmic resistance R. 

Rational optimization of performance should be the main goal in development of any chemical sensor. In order to do that, we must have some quantitative tools of determination of key performance parameters. As we have seen already, for electrochemical sensors those parameters are the charge-transfer resistance and the double-layer capacitance. Particularly the former plays a critical role. Here we outline two approaches the Tafel plots, which are simple, inexpensive, but with limited applicability, and the Electrochemical Impedance Spectroscopy (EIS), based on the equivalent electrical circuit model, which is more universal, more accurate, and has a greater didactic value. 

The second meaning of the word circuit is related to electrochemical impedance spectroscopy. A key point in this spectroscopy is the fact that any -> electrochemical cell can be represented by an equivalent electrical circuit that consists of electronic (resistances, capacitances, and inductances) and mathematical components. The equivalent circuit is a model that more or less correctly reflects the reality of the cell examined. At minimum, the equivalent circuit should contain a capacitor of - capacity Ca representing the -> double layer, the - impedance of the faradaic process Zf, and the uncompensated - resistance Ru (see -> IRU potential drop). The electronic components in the equivalent circuit can be arranged in series (series circuit) and parallel (parallel circuit). An equivalent circuit representing an electrochemical - half-cell or an -> electrode and an uncomplicated electrode process (-> Randles circuit) is shown below. Ic and If in the figure are the -> capacitive current and the -+ faradaic current, respectively. 

Dispersion — Frequency dispersion results from different frequencies propagating at different speeds through a material. For example, in the electrochemical impedance spectroscopy (EIS) of a crevice (or porous) electrode, the solution resistance, the charge transfer resistance, and the capacitance of the electric double layer often vary with position in the crevice (or pore). The impedance displays frequency dispersion in the high frequency range due to variations in the current distribution within the crevice (pore). Additionally, EIS measurements in thin layer cells (such as electro chromic... 

Finite-space diffusion takes place during the charging of insertion electrodes at moderate frequencies, transforming into mainly capacitive behavior within the limit of very low frequencies, in contrast to the semi-infinite diffusion for solution redox-species (except for thin-layer solution electrochemistry) electrochemical impedance spectroscopy becomes a very useful diagnostic tool for the characterization of insertion mechanisms ... 

Transmission line — This term is related to a more general concept of electric -> equivalent circuits used frequently for interpretation of experimental data for complex impedance spectra (-> electrochemical impedance spectroscopy). While the complex -> impedance, Z, at a fixed frequency can always by obtained as a series or parallel combinations of two basic elements, a resistance and a capacitance, it is a much more compli-... 

To increase fundamental knowledge about ionic resistance, it is important to develop a methodology to experimentally isolate the contributions of the various cell components. Electrochemical impedance spectroscopy has been widely used by Pickup s research group to study the capacitance and ion conductivity of fuel cell catalyst layers [24-27] they performed impedance experiments under a nitrogen atmosphere, which simplified the impedance response of the electrode. Saab et al. [28] also presented a method to extract ohmic resistance, CL electrolyte resistance, and double-layer capacitance from impedance spectra using both the H2/02 and H2/N2 feed gases. In this section, we will focus on the work by Pickup et al. on using EIS to obtain ionic conductivity information from operational catalyst layers. 

Figure 6.25. Capacitance plots obtained at a DC bias potential of 0.2 V vs. Ag/AgCl for electrodes with a 1-3 xL of catalyst ink applied and b 4-6 rL of catalyst ink applied [24], (Reprinted from Electrochimica Acta, 50(12), Easton EB, Pickup PG. An electrochemical impedance spectroscopy study of fuel cell electrodes. Electrochim Acta, 2469-74, 2005, with permission from Elsevier and the authors.)...

The best method to measure the double-layer capacitance is to use a phase-sensitive voltmeter. This instrument is sometimes incorporated into a frequency response analyzer, designed to make electrochemical impedance spectroscopy measurements, but it can also be used independently. In Part Two we devote a full section to the operation of such instruments and the analysis of results obtained by them. Here we shall limit the discussion to the measurement of capacitance. 

Remember 5.4 The capacitance commonly encountered in electrochemical impedance spectroscopy may arise from charge redistribution at interfaces or from dielectric phenomena. 

Instrumental electroanalysis offers some alternatives for the detection of biological recognition events in immunosensors such as capacitive immunosensors and sensors based on electrochemical impedance spectroscopy. Both techniques are universal platforms for the detection of immunoreactions and hence bacteria, viruses, tumor markers, and more, as described above, have been detected with these methods. 

Electrochemical impedance spectroscopy (EIS) or ac impedance methods have seen a tremendous increase in popularity in recent years. Initially applied to the determination of the double-layer capacitance " and in ac polarography, " they are now used to characterize electrode processes and complex interfaces. This method studies the system response to the application of a periodic small-amplitude ac signal. The measurements are carried out at different ac frequencies and thus the name impedance spectroscopy was later adopted. Analysis of the system response contains information about the interface, its structure, and the reactions taking place there. Electrochemical impedance spectroscopy is now described in the... 

IMPS uses modulation of the light intensity to produce an ac photocurrent that is analysed to obtain kinetic information. An alternative approach is to modulate the electrode potential while keeping the illumination intensity constant. This method has been referred to as photoelectrochemical impedance spectroscopy (PEIS), and it has been widely used to study photoelectrochemical reactions at semiconductors [30-35]. In most cases, the impedance response has been fitted using equivalent circuits since this is the usual approach used in electrochemical impedance spectroscopy. The relationship between PEIS and IMPS has been discussed by a number of authors [35, 60, 64]. Vanmaekelbergh et al. [64] have calculated both the IMPS transfer function and the photoelectrochemical impedance from first principles and shown that these methods give the same information about the mechanism and kinetics of recombination. Recombination at CdS and ZnO electrodes has been studied by both methods [62, 77]. Ponomarev and Peter [35] have shown how the equivalent circuit components used to fit impedance data are related to the physical properties of the electrode (e.g. the space charge capacitance) and to the rate constants for photoelectrochemical processes. 

This operation determines the values of R and C that, in series, behave as the cell does at the measurement frequency. The impedance is measured as a function of the frequency of the ac source. The technique where the cell or electrode impedance is plotted V5. frequency is called electrochemical impedance spectroscopy (EIS). In modem practice, the impedance is usually measured with lock-in amplifiers or frequency-response analyzers, which are faster and more convenient than impedance bridges. Such approaches are introduced in Section 10.8. The job of theory is to interpret the equivalent resistance and capacitance values in terms of interfacial phenomena. The mean potential of the working electrode (the dc potential ) is simply the equilibrium potential determined by the ratio of oxidized and reduced forms of the couple. Measurements can be made at other potentials by preparing additional solutions with different concentration ratios. The faradaic impedance method, including EIS, is capable of high precision and is frequently used for the evaluation of heterogeneous charge-transfer parameters and for studies of double-layer structure. 

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