Electrochemical impedance spectroscopy double-layer 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. 

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... 

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. 

Understanding the oxidation mechanism is important. Impedance spectroscopy was recently used to study methanol electrooxidation, and kinetic parameters can be deduced from impedance spectra. Figure 6.58 shows an equivalent circuit that was developed for methanol oxidation on a Pt electrode, but which is common for all electrochemical reactions. In this circuit, a constant phase element was used rather than a double-layer capacitance, since a CPE is more realistic than a simple capacitor in representing the capacitive behaviour. 

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. 

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... 

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. 

The value of double-layer capacitance Qi can be determined by electrochemical impedance spectroscopy (EIS], which is a key factor to characterize electrochemical systems as components of doublelayer capacitors. The electrochemical response of a conductive or... 

Electrical double layer EDI). Favorable electron-transfer capabilities make ionic hquids good conductive media and vahd substitutes for conventional electrolytes. Electrolytic properties of ionic hquids were studied to determine the capacitance-layer thickness relationship of the EDL by electrochemical impedance spectroscopy (EIS). EIS data combined with supporting SFG analysis indicate that the EDL formed by ionic hquids at the electrode-ioitic liquid interface follows the Helmholtz model and corresjtonds to a Helmholtz layer of one ion thickness [35,36]. 

Analysis based on electrochemical impedance spectroscopy (EIS also called AC impedance spectroscopy) allows estimation of frequency behavior, quantification of resistance, and the ability to model equivalent circuits (ECs) of ES systems. The fundamental EC for a double-layer circuit, as discussed in Chapter 2, contains series resistance and double-layer capacitance. In addition, there is often a faradic parallel resistance from impurities in the carbon. In the pseudocapacitive case, the faradic resistance is a related reciprocal of the overpotential-dependent charge transfer [2,21]. 

Electrochemical Impedance Spectroscopy (EIS) is a powerful nondestructive method to characterize biomaterials. Electrode materials, solution resistance, elec-trode/electrolyte interface impedance, charge transfer resistance, and surface rough-ness/double layer capacitance can be measured and their frequency response properties can be determined in a fast frequency scan. 

Table 3. Charge Transfer Resistance and Double-Layer Capacitance Values Derived for Alloy "A and B Oxides from Electrochemical Impedance Spectroscopy Measurements in pH 10 Solutions at 25°C...

An ideal electrode-electrolyte interface with an electron-transfer process can be described using Randle equivalent circuit shown in Fig. 2.7. The Faradaic electron-transfer reaction is represented by a charge transfer resistance and the mass transfer of the electroactive species is described by Warburg element (W). The electrolyte resistance R is in series with the parallel combination of the double-layer capacitance Cdi and an impedance of a Faradaic reaction. However, in practical application, the impedance results for a solid electrode/electrolyte interface often reveal a frequency dispersion that cannot be described by simple Randle circuit and simple electronic components. The interaction of each component in an electrochemical system contributes to the complexity of final impedance spectroscopy results. The FIS results often consist of resistive, capacitive, and inductive components, and all of them can be influenced by analytes and their local environment, corresponding to solvent, electrolyte, electrode condition, and other possible electrochemically active species. It is important to characterize the electrode/electrolyte interface properties by FIS for their real-world applications in sensors and energy storage applications. 

Measurements of double-layer capacitance (proportional to pore surface area inversely proportional to pore radius) as a function of time during potentiostatic aging of dealloyed layers on Au-Ag, showing the effects of potential and chloride ions. (From Kelly, R.G. et al. Electrochemical Impedance Spectroscopy (J.R. Scully, D.C. Silverman, and M.W. Kendig, eds.), ASTM, ASTM STP 1188, Philadelphia, PA, 1991, p. 94.)... 

In a later chapter we shall discuss the technique of electrochemical impedance spectroscopy, (EIS), which can provide the most accurate measurements of the double-layer capacitance over a wide range of experimental conditions. Here we shall discuss two methods, requiring relatively simple instrumentation. 

In summary AC impedance spectroscopy provides concrete evidence for the formation of an effective electrochemical double layer over the entire gas-exposed electrode surface. The capacitance of this metal/gas double layer is of the order of 100-300 pF/cm2, comparable to that corresponding to the metal/solid electrolyte double layer. Furthermore it permits estimation of the three-phase-boundary length via Eq. 5.62 once the gas exposed electrode surface area NG is known. 

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