Electrochemical impedance spectroscopy frequency range

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 nonfaradaic) at a given applied potential.268,269 EIS has been used to study polycrystalline Au, Cd, Ag, Bi, Sb, and other electrodes.152249 270-273... 

Electrochemical impedance spectroscopy techniques record impedance data as a function of the frequency of an applied signal at a fixed potential. A large frequency range (65 kHz-1 mHz) must be investigated to obtain a complete impedance spectrum. Dowling et al. and Franklin et al. demonstrated that the small signals required for EIS do not adversely affect the numbers, viability, and activity of microorganisms within a biofilm. EIS data may be used to determine the inverse of the corrosion... 

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. 

The simplest application of electrochemical impedance spectroscopy (EIS) is the determination of the conductivity of the electrolyte solution, where polarisation of the electrode surfaces is eliminated by choosing an appropriate frequency range for measurement of the conductivity31. 

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). 

One of the most important applications of neural network methodology is in the extrapolation of electrochemical impedance data obtained in corrosion studies.34 Electrochemical impedance spectroscopy (EIS) can be used to obtain instantaneous corrosion rates. The validation of extension of EIS data frequency range, which is conventionally difficult, can be done using a neural network system. In addition to extension of impedance data frequency range, the neural network identifies problems such as the inherent variability of corrosion data and provides solutions to the problems. Furthermore, noisy or poor-quality data are dealt with by neural works through the output of the parameters variance and confidence.33... 

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... 

Figure 6.68. Impedance spectra of a DMFC cathode. Experimental conditions 75°C, air stoichiometric ratio 10, 69 mA cnT2, 0.879 V, and frequency range 10 kHz-0.1 Hz [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.)...

If the series resistance is high and the parallel resistance is low, one faces an adverse experimental situation. In this case, measurements should be conducted over a range of frequencies, with the highest possible accuracy, and the optimum conditions for the experiment should be carefully chosen. Under such conditions, electrochemical impedance spectroscopy apparatus may be indispensable. 

In principle, the Kramers-Kronig relations can be used to determine whether the impedance spectrum of a given system has been influenced by bias errors caused, for example, by instrumental artifacts or time-dependent phenomena. Although this information is critical to the analysis of impedance data, the Kramers-Kronig relations have not found widespread use in the analysis and interpretation of electrochemical impedance spectroscopy data due to difficulties with their application. The integral relations require data for frequencies ranging from zero to infinity, but the experimental frequency range is necessarily constrained by instrumental limitations or by noise attributable to the instability of the electrode. 

A historical perspective on impedance spectroscopy is presented in Table 1. A brief listing of advances in this field cannot be comprehensive, and many important contributions are not mentioned. The reader may wish to explore other historical perspectives, such as that provided by Macdonald. Chapters written by Sluyters-Rehbach and Sluyters and by Lasia provide excellent overviews of the field. Nevertheless, Table 1 provides a useful guide to the trends in areas related to electrochemical impedance spectroscopy. These areas include the types of systems investigated, the instrumentation used to make the measurements, including changes in the accessible frequency range, the methods used to represent the resulting data, and the methods used to interpret the data in terms of quantitative properties of the system. 

In design of electrochemical sensors (and biosensors) especially helpful is electrochemical impedance spectroscopy (EIS), providing a complete description of an electrochemical system based on impedance measurements over a broad frequency range at various potentials, and determination of all the electrical characteristics of the interface.60-61 Generally it is based on application of electrical stimulus (known voltage or current) across a resistor through electrodes and observation of response... 

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... 

Noticeable progress has been made in recent years in the application of electrochemical impedance spectroscopy to biosensors. Compared to potentiometric detection, it requires a more complex electrode arrangement (three electrodes) and a more demanding detection circuit (potentiostat). In addition, the signal decreases with the electrode area and the measurements are taken over a range of frequencies. It is likely that both techniques are used in the future for different applications. For instance, potentiometric detection is particularly suitable for real-time detection, while EIS offers information for both charged and uncharged species. 

Electrochemical Impedance Spectroscopy (ElS) is a method used to characterize electron-transfer reactions by perturbing the system in a sinusoidal manner over a wide range of frequencies. This method, which is very sensitive to the properties of the electrode interface, provides information regarding electron-transfer kinetics, diffusion of charged species, charging/discharging, and system conductance. 

When a range of frequencies is applied to the DUT, both El and ECI techniques are called spectroscopies, i.e., electrical impedance spectroscopy and electrochemical impedance spectroscopy. Electrochemical impedance spectroscopy (EIS) profiles, measured as a function of the interrogating frequency, can be presented by two popular plots complex plane impedance diagrams, sometimes called Nyquist or Cole-Cole plots, and Bode (I Z I and 6) plots (Fig. 2). As the impedance, Z, is composed of a real and an imaginary part, the Nyquist plot shows the relationship of the imaginary component of impedance, Z" (on the Y-axis), to the real component of the impedance, Z (on the X-axis), at each frequency. A diagonal line with a slope of 45° on a Nyquist plot represents the Warburg... 

Electrochemical impedance spectroscopy is extensively employed for the investigation of SAMs because the broad range of frequencies covered by this technique (usually from 10 to 10 Hz) may allow processes with different relaxation times taking place within the electrified interphase to be detected and sorted out. Unfortunately, the various relaxation times often differ by less than 2 orders of magnitude, thus requiring a certain amount of arbitrariness and of physical intuition for their separation. In fact, it is well known that the same impedance spectrum can often be equally well fitted to different equivalent circuits, which are consequently ascribed to different relaxation processes. Impedance spectra are frequently reported on a Y /co versus Y"/co plot, where Y and Y" are the in-phase and quadrature components of the electrochemical admittance and co is the angular frequency. This plot is particularly suitable for representing a series RC network. Thus, a series connection of R and C yields... 

Electrochemical impedance spectroscopy is a mature technique, and its fundamental mathematical problems are well understood. Impedances can be written for any electrochemical mechanism using standard procedures. Modem electrochemical equipment makes it possible to acquire data in a wide range of frequencies and with various impedance values. The validity of experimental data can be verified by standard procedures involving Kramers-Kronig transforms. Several programs either allow for the use of predefined simple and distributed elements in the construction of electrical equivalent circuits or directly fit data to equations (which should be defined by the user). 

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