EIS measurements

There are two options for controlling the perturbation to the measured system one is to control the current perturbation then record the voltage response from the system the other is to control the voltage perturbation then record the current response. For a current control measurement, when the leads are all connected the electrical load is set to a DC constant current. The FRA will generate an AC current perturbation and interrupt the fuel cell through a load bank or a potentiostat. The response to the interruption from the fuel cell will enter into the FRA for analysis to obtain the AC impedance spectra. 

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The F EI measures realistic maximum loss potential under adverse operating conditions. It is based on quantifiable data. It is designed for flammable, combustible, and reactive materials that are stored, handled, or processed. It does not address frequency (risk) except indirectly, nor does it address specific hazards to people except indirectly. 

Electrochemical impedance measurements of the physical adsorption of ssDNA and dsDNA yields useful information about the kinetics and mobihty of the adsorption process. Physical adsorption of DNA is a simple and inexpensive method of immobilization. The ability to detect differences between ssDNA and dsDNA by impedance could be applicable to DNA biosensor technology. EIS measurements were made of the electrical double layer of a hanging drop mercury electrode for both ssDNA and dsDNA [34]. The impedance profiles were modeled by the Debye equivalent circuit for the adsorption and desorption of both ssDNA and dsDNA. Desorption of denatured ssDNA demonstrated greater dielectric loss than desorption of dsDNA. The greater flexibility of the ssDNA compared to dsDNA was proposed to account for this difference. 

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 number m of these parameters must be smaller than the number of known levels n, i.e. m < n, otherwise the problem is unsolvable. If a set of parameters Rk exactly describes levels Si, and levels E, are measured accurately and identified correctly, then for finding the true values of these parameters, it would be enough to solve a system of m equations with m unknowns. In practice, due to non-observance of the above-mentioned conditions, the obtained roots of the system of m equations will not satisfy the remaining n — m equations. However, our purpose is to find values of parameters Rk, for which all equations are satisfied with the smallest error. Then the root-mean-square deviation of energy levels S, found from those Ei measured, would be minimal. 

The EIS measurements, performed with the use of QCM, have been employed for stereospecific recognition of histidine (Table 6) [179], For that purpose, a thin film of MIP was fabricated by sol-gel imprinting, in ethanol, of the L-histidine template. This chemosensor was appreciably sensitive to L-histidine at LOD of 25 nM with the linear concentration range extending from 50 nM to 1 mM. 

Figure 19 Schematic Bode plots from EIS measurements and equivalent circuits that could be used to fit them for various possible corrosion product deposit structures (A) nonporous deposit (passive film) (B) deposit with minor narrow faults such as grain boundaries or minor fractures (C) deposit with discrete narrow pores (D) deposit with discrete pores wide enough to support a diffusive response (to the a.c. perturbation) within the deposit (E) deposit with partial pore blockage by a hydrated deposit (1) oxide capacitance (2) oxide resistance (3) bulk solution resistance (4) interfacial capacitance (5) polarization resistance (6) pore resistance (7) Warburg impedance (8) capacitance of a hydrated deposit.

EIS has become an important method of characterizing inorganic coating of all types and the basis of the technique is briefly introduced here. For details on EIS measurements, hardware, data analysis, data presentation, and applications the reader is referred to the materials presented in Refs. 61-64. 

Equivalent circuit analysis is well suited for analysis of EIS measurements of conversion coatings and is the primary method for interpreting EIS spectra from conversion coated metal surfaces. A widely accepted generalized equivalent circuit model for the EIS response of pitted conversion coatings is shown in Fig. 22a (66,67). Several related models discussed below are also shown. In the gener-... 

An example of the use of EIS measurements to make long-term corrosion predictions for polymer coated metals is shown in Fig. 46 (110). In this plot, the ASTM D610 and D714 visual rankings of corrosion damage after 550 days of exposure in simulated seawater are plotted against a protection index, < (/), determined after only 10 days of exposure. The damage protection index is determined from the breakpoint frequency, /, as... 

Another method of spatially resolving variations in impedance involves constructing regular arrays of small cells on a sample surface and performing conventional EIS measurements in them on a serial basis (138). This method does not require any special measurement equipment beyond that needed for conventional EIS measurement. However, as the cell size and working electrode area is reduced, the measured current will be reduced to the point where noise and instrument current resolution become factors. These factors limit how small a cell can be and determine the spatial resolution of the technique. This technique has been used to examine the changes in the EIS response on coil coated galva-... 

In this expression, bd and bc refer to the appropriate anodic and cathodic Tafel constants. Comparison of weight loss data collected as a function of exposure time determined from R , Rf from EIS, and gravimetric measurements of mild steel exposure to 0.5 M H2S04 are often within a factor of two. This suggests that use of Rn in the Stern-Geary equation may be appropriate for the estimation of corrosion rate (147-150). However, Rn measurements may underestimate corrosion rates. / p is often measured at effective frequencies of 1(T2 Hz or less in linear polarization or EIS measurements, while Rn is measured at 1 Hz or greater. An example of this is provided in Fig. 57, which shows the corrosion rate of carbon steel in 3% NaCl solution as a function of exposure time determined by EIS, linear polarization, noise resistance, and direct current measurement with a ZRA. Among these data, the corrosion rates determined by noise resistance are consistently the lowest. 

Thus the importance of using a slow scan rate in the PR measurements (or equivalently, measuring down to a low frequency in the EIS measurements) can be seen. At very slow sweep rates, dV/dt is small, so the current through the capacitor is small. Therefore the impedance of the RC combination is only Rp. As the scan rate is increased, the fraction of current that flows through the capacitor increases, and the measured impedance falls, since the parallel combination of the resistor and capacitor will have a smaller impedance than the resistor alone. This effect will cause an underestimation of Rt and hence an overestimation of the corrosion rate. 

Based upon the EIS measurements, what would be the maximum scan rate that could be used without having appreciable capacitive current ... 

This set of experiments has focused on the use of two nondestructive electrochemical techniques to measure polarization resistance and thereby estimate the corrosion rate. In addition, the effects of scan rate and uncompensated ohmic resistance were studied. Three main points should have been made by this lab (1) Uncompensated ohmic resistance is always present and must be measured and taken into account before Rp values can be converted into corrosion rates, otherwise an overestimation of Rv will result. This overestimate of Rp leads to an underestimate of corrosion rate, with the severity of this effect dependent upon the ratio Rp/Ra. (2) Finite scan rates result in current shunted through the interfacial capacitance, thereby decreasing the observed impedance and overestimating the corrosion rate. (3) Both of these errors can be taken into account by measuring Ra via EIS or current interruption and by using a low enough scan rate as indicated by an EIS measurement in order to force the interfacial capacitance to take on very large impedance values in comparison to Rp. 

Finally, the basic equivalence of the two measuring techniques should be appreciated. Although there are many ways to approach such a comparison, the following simplified explanation will, we hope, give a more intuitive feeling for the relationship between EIS and PR measurements. As stated above, both techniques rely on the frequency dependence of the impedance of the double-layer capacitance in order to determine the polarization resistance. EIS uses low frequencies to force the capacitor to act like an open circuit. PR measurements use a slow scan rate to do the same thing. To make comparisons, the idea of equivalent scan rate is useful. Suppose that a particular electrochemical system requires EIS measurements to be made down to 1 mHz in order to force 99% of the current through Rp. What would the equivalent scan rate be for PR measurements A frequency of 1 mHz corresponds to a period of 1000 s. If the sine wave is... 

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... 

In order to understand electrochemical impedance spectroscopy (EIS), we first need to learn and understand the principles of electronics. In this chapter, we will introduce the basic electric circuit theories, including the behaviours of circuit elements in direct current (DC) and alternating current (AC) circuits, complex algebra, electrical impedance, as well as network analysis. These electric circuit theories lay a solid foundation for understanding and practising EIS measurements and data analysis. 

The impedance can be measured using various instalments and techniques, ranging from a simple oscilloscope display to a fast Fourier transform (FFT) analyzer. The most common instrument used is a frequency response analyzer (FRA), e.g., the Solartron FRA. A potentiostat or a load bank combined with a frequency response analyzer can perform the EIS measurements. The electrical connection between the FRA, the potentiostat (or the load bank), and the fuel cell is illustrated in Figure 3.19. 

Figure 3.19. Schematic EIS measurement configuration for a fuel cell...

Although EIS offers many advantages for diagnosing fuel cell properties, clear difficulties exist for applying impedance methods and fitting the data to the model to extract the relevant electrochemical parameters. The limitations of the EIS technique derive from the several requirements required to obtain a valid impedance spectrum, because the accuracy of EIS measurement depends not only on the technical precision of the instrumentation but also on the operating procedures. Theoretically, there are three basic requirements for AC impedance measurements linearity, stability, and causality. 

Electrochemical impedance spectroscopy can yield valuable information. However, experience and knowledge are necessary to conduct EIS measurements for fuel cells. Attention should be paid to the following ... 

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