Electrochemical impedance spectroscopy capacitive circuit

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. 

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-... 

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. 

RuofF et al. have performed some of the most in-depth studies on the capacitance of PMM A-transferred CVD graphene. One of their studies used a mono-layer sample where either one, or both sides, of the graphene were exposed to solution (for details on electrode fabrication, see Figure 4.6) before electrochemical impedance spectroscopy (EIS) measurements were performed (amplitude 10 mV frequency 100 kHz to 1 Hz) in 4 M sulfuric acid [89]. In order to determine the capacitance, the results were fitted to an R RC) equivalent circuit. 

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]. 

As discussed above, the corrosion current density (Icorr), the critical current density (Icri), and the passive current density (Ipass) were obtained from potentiodynamic polarization. The capacitance (Qf) and the resistance (Rf) of oxide layer were obtained from electrochemical impedance spectroscopy (EIS) equivalent circuits. And the weight-loss rate (Wbss) was obtained from weight-loss immersion test. All these data were taken from experiments at ambient temperature (25°C) in 0.5 M H2SO4. 

Electrochemical impedance spectroscopy is useful in the evaluation of coatings, the elucidation of transport phenomena in electrochemical systems, and the determination of corrosion mechanisms and rates. Bode and Nyquist plots are the most common data output formats, and an example of each for a simple parallel-connected resistance-capacitance circuit are shown in Figs. 31.3, and 31.4, respectively. The Bode plot format shows the... 

Figure 11. (a) A commonly used circuit model representing resistive and capacitive elements in a corrosion cell, and (b) graphical derivation of values for / s and from a Bode plot of the modulus and phase angle values as a function of applied sweep frequency in an electrochemical impedance spectroscopy experiment. 

Features of the impedance spectra of Fig. 3.15a may be modeled by a simple modified Randles-Ershler equivalent circuit shown in Fig. 3.15c. In this model, is the solution resistance, and is the charge-transfer resistance at the electrode/eIectrol e interface. A constant phase element (CPE) was used instead of a doublelayer capacitance to take into account the surface roughness of the particle. Qn is the insertion capacitance, and Zw is the Warbui impedance that corresponds to the solid-state diffusion of the Li-ion into the bulk anode. The Warburg element was used only for impedance data obtained at the tenth charge. The electrical components of the surface film which is likely formed on the electrode were disregarded, because no time constant related to this process could be seen in the electrochemical impedance spectroscopy (EIS) spectra. It was also checked that their inclusion in the model of Fig. 3.15c does not improve the fit. 

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. 

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. 

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