Impedance spectroscopy frequency range

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... 

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... 

Impedance spectroscopy is a versatile electrochemical tool, helpful to characterize the intrinsic dielectric properties of various materials. The basis of this technique is the measurement of the impedance (opposition to alternating current) of a system, in response to an exciting signal over a range of frequencies (Bard and Faulkner, 2001). 

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. 

Warburg impedance is a well-known term in the field of impedance spectroscopy because of the early date at which it was published, the formulation came before the rest of the properties of the interface were known. In fact, for nearly all real situations examined in electrochemistry, the Warburg impedance is relatively small. Thus, for a concentration of 1 mol liter and a frequency of 1 kilocycle s l, and using the normal parameters for room temperature, the resistance is in the milliohm cm-2 range. 

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). 

Impedance spectroscopy is one of the most informative methods in electrochemistry research [1,2], The essence of the method consists in investigating the response of a target taking place in stationary conditions to weak influences of a variable voltage or to an electric current in a wide range of frequencies. It is possible... 

The measurements in an impedance spectroscopy test of a simple electrolyte are normally obtained in the hertz to some megahertz frequency range with an impedance analyzer for this purpose impedance spectroscopy as a methodology is similar with DS (see Section 8.6.2). 

In experimental impedance spectroscopic studies, however, several factors may complicate the interpretation of the spectra and a few of these complications will briefly be touched upon i) If high conductivities are considered (a > 10-3 S cm-1), then the corresponding relaxation frequencies are well above the measurement range of a conventional impedance set-up (frequencies up to ca. 10 MHz). Hence, processes with high conductivites cannot be separated by conventional impedance spectroscopy. ii) The assumption of a quasi-one-dimensional current flow, which is the basis of the above presented brick layer model, is often violated [203, 211-214]. Some complications due to multi-dimensional potential distributions will be discussed in Sec. 3.2.1. iii) Highly conductive regions perpendicular to the electrodes (e.g. highly... 

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 6.49. In situ AC impedance spectroscopy at a frequency range of 3500 to 0.1 Hz at 0.91 A/cm2, 100% RH, and 30 psig pressure at 80°C, 100°C, and 120°C [44]. (Reproduced by permission of ECS—The Electrochemical Society, and of the authors, from Tang Y, Zhang J, Song C, Liu H, Zhang J, Wang H, MacKinnon S, Peckham T, Li J, McDermid S, Kozak P, Temperature dependent performance and in situ AC impedance of high temperature PEM fuel cells using the Nafionl 12 membrane.)...

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.)...

The conductivity of sintered pellets was obtained from two-probe impedance spectroscopy. Platinum electrodes were applied on both surfaces of pellets by coating platinum paste and then firing at 850°C for 0.5h. Measurements were made with an computer-interfaced impedance analyzer (GenRad 1689 Precision RLC Diglbridge) over a frequency range of 12-10 Hz in the temperature range of 500°C-800°C. Each sample was measured in air and H2 atmospheres, respectively. 

Impedance spectroscopy (IS) is a measurement of the conductive and dielectric properties of electroactive systems over a wide range of frequencies. Its popularity and applicability has increased dramatically over the past 25 years with the advent of fast-response potentiostats and frequency response analyzers. Impedance spectroscopy has been applied extensively in electrochemistry, especially in battery and sensor research, and it has been used to study active transport in biological membranes. Skin impedance has also been investigated with IS, but many of these studies attempted to correlate impedance with hydration and provided no insight into the mechanism of charge transport. More recent studies have used IS to elucidate the pathways of ion transport through skin, with special emphasis on understanding the mechanism... 

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. 

Figure 3.5. Overall impedance response of a proton exchange membrane (PEM) fuel cell for different cell temperatures, depicted as corresponding values of the real and imaginary parts of the complex impedance (sometimes denoted a Nyquist plot). Each sequence of points represents frequencies ranging from 10 to 10 Hz, with the highest values corresponding to the leftmost points. From M. Ciureanu, S. Mik-hailenko, S. Kaliaguine (2003). PEM fuel cells as membrane reactors kinetic cinalysis by impedance spectroscopy. Catalysis Today 82, 195-206. Used with permission from Elsevier).

Regression problems in impedance spectroscopy may become ill-conditioned due to improper selection of measurement frequencies, excessive stochastic errors (noise) in the measured values, excessive bias errors in the measured values, and incomplete frequency ranges. The influences of stochastic errors and foequency range on regression are demonstrated by examples in this section. The issue of bias errors in impedance measurement is discussed in Chapter 22. The origin of stochastic errors in impedance measurements is presented in Chapter 21. 

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... 

In impedance spectroscopy [IS also referred to as dielectric spectroscopy (DS)], a sinusoidal electric field is applied across a sample, and the resulting polarization (or electric displacement) is determined as a function of frequency. The frequency sweep typically ranges from about 1 MHz down to about 1 mHz, but measurement may be performed at higher frequencies by using special equipment. 

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