Electrochemical impedance spectroscopy equivalent circuits

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. 

Impedance Spectroscopy for More Complex Interfacial Situations. The electrochemical interfacial equivalent circuits shown in Figs. 7.48 and 7.49 are the simplest circuits that can be matched to actual electrochemical impedance measurements. The circuit in Fig. 7.49 would be expected to apply to an electrode reaction that involves only electron transfer (e.g., redox systems of the type Fc3+ + e Fe2+), no adsorbed intermediate. 

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. 

Finally, it can be seen from Fig. 9.9a that the real impedance does not remain constant at low frequencies for the textile electrode, and this effect is more pronounced at higher electrolyte concentrations. Probably, Zr is influenced by other effects only occurring in the low-frequency range. This effect is frequently observed and described in the literature and is caused by non-uniformity of surfaces at the micro-scale, which in fact is the case for the textile electrodes. It is also not possible to explain this effect by a pure resistor or a pure capacitor in the electrical equivalent circuit. For this purpose, constant-phase elements are implemented as described in the theoretical discussion of electrochemical impedance spectroscopy (presented in Chapter 2, section 2.4). 

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. 

Immittance — In alternating current (AC) measurements, the term immittance denotes the electric -> impedance and/or the electric admittance of any network of passive and active elements such as the resistors, capacitors, inductors, constant phase elements, transistors, etc. In electrochemical impedance spectroscopy, which utilizes equivalent electrical circuits to simulate the frequency dependence of a given elec-trodic process or electrical double-layer charging, the immittance analysis is applied. 

The immittance analysis can be performed using different kinds of plots, including complex plane plots of X vs. R for impedance and B vs. G for admittance. These plots can also be denoted as Z" vs. Z and Y" vs. Y, or Im(Z) vs. Rc(Z), and Im( Y) vs. Re( Y). Another type of general analysis of immittance is based on network analysis utilizing logarithmic Bode plots of impedance or admittance modulus vs. frequency (e.g., log Y vs. logo)) and phase shift vs. frequency ( vs. log co). Other dependencies taking into account specific equivalent circuit behavior, for instance, due to diffusion of reactants in solution, film formation, or electrode porosity are considered in - electrochemical impedance spectroscopy. Refs. [i] Macdonald JR (1987) Impedance spectroscopy. Wiley, New York [ii] Jurczakowski R, Hitz C, Lasia A (2004) J Electroanal Chem 572 355... 

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-... 

When we begin to investigate an electrochemical system, we normally know little about the processes or mechanisms within the system. Electrochemical impedance spectroscopy (EIS) can be a powerful approach to help us establish a hypothesis using equivalent circuit models. A data-fitted equivalent circuit model will suggest valuable chemical processes or mechanisms for the electrochemical system being studied. From Chapter 1, we know that a fuel cell is actually an electrochemical system involving electrode/electrolyte interfaces, electrode reactions, as well as mass transfer processes. Therefore, EIS can also be a powerful tool to diagnose fuel cell properties and performance. 

Figure 6.23. Finite transmission-line equivalent circuit describing the impedance behaviour of a PEMFC electrode [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.)...

Figure 6.69. Equivalent circuit for the impedance of a pore wall in a DMFC cathode [57], (Reproduced by permission of ECS—The Electrochemical Society, from Piela P, Fields R, Zelenay P. Electrochemical impedance spectroscopy for direct methanol fuel cell diagnostics.)...

Although simple impedance measurement can tell the existence of an anodic film, electrochemical impedance spectroscopy (EIS) can obtain more information about the electrochemical processes. In general, the anode/electrolyte interface consists of an anodic film (under mass transport limited conditions) and a diffuse mobile layer (anion concentrated), as illustrated in Fig. 10.13a. The anodic film can be a salt film or a cation (e.g., Cu ) concentrated layer. The two layers double layer) behave like a capacitor under AC electric field. The diffuse mobile layer can move toward or away from anode depending on the characteristics of the anode potential. The electrical behavior of the anode/electrolyte interface structure can be characterized by an equivalent circuit as shown in Fig. 10.13. Impedance of the circuit may be expressed as... 

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. 

Membrane structures that contain the visual receptor protein rhodopsin were formed by detergent dialysis on platinum, silicon oxide, titanium oxide, and indium—tin oxide electrodes. Electrochemical impedance spectroscopy was used to evaluate the biomembrane structures and their electrical properties. A model equivalent circuit is proposed to describe the membrane-electrode interface. The data suggest that the surface structure is a relatively complete single-membrane bilayer with a coverage of 0.97 and with long-term stability/... 

To determine numerical values for the different elements of the equivalent circuit they have to be separated, for example, by electrochemical impedance spectroscopy (EIS). Similar to the above-described lock-in measurement a small ac signal of a few mV is superimposed to the electrode potential. The resulting current and its phase shift are then measured as a function of the frequency. Typical impedance spectra of thin oxide films on aluminum are shown in Fig. 17. At high frequencies (10 — lO Hz) the capacitors act as shorts and only the electrolyte resistor determines the impedance, which is typically 10 Ohm for concentrated electrolytes and independent of the electrode. At the lowest frequencies, for example, 10 Hz or below, current flow through the capacitors is impossible and the impedance of the system is given by the sum of the 3 resistors in the current path. The... 

Electrochemical impedance spectroscopy An alternating current technique that measures the impedance of an electrochemical system. The resulting spectra can be used to estimate the various components of an equivalent circuit that represent an electrochemical cell. 

Electric Double Layer and Fractal Structure of Surface Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or non-faradaic) at a given applied potential. The main difficulty in the analysis of impedance spectra of solid electrodes is the frequency dispersion of the impedance values, referred to the constant phase or fractal behavior and modeled in the equivalent circuit by the so-called constant phase element (CPE) [5,15,16, 22, 35, 36]. The frequency dependence is usually attributed to the geometrical nonuniformity and the roughness of PC surfaces having fractal nature with so-called selfsimilarity or self-affinity of the structure resulting in an unusual fractal dimension... 

Equivalent Circuit Modeling using the Gamry EIS 300 Electrochemical Impedance Spectroscopy Software Gamry Application Note, USA, (2001)... 

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. 

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