Impedance-experimental parameters

What precedes is true for any other electrochemical technique, using in each case the appropriate experimental parameter for varying the diffusion rate (the frequency in impedance methods, the measurement time in potential-step techniques, and so on). 

Remember 8.3 Impedance measurements entail a compromise balance behveen minimizing bias errors, minimizing stochastic errors, and maximizing the information content of the resulting spectrum. The optimal instrument settings and experimental parameters are not universal and must be selected for each system under study. 

The magnitude of the stocheistic errors in impedance measurements depends on the selection of experimental parameters as detailed in Chapter 8. The simulation results described by Carson et a 00,25i,255 particular provide insight into differences between commonly used impedance instrumentation, including methods based on Fourier analysis and on phase-sensitive detection. ... 

In many cases, complex systems present a distribution of relaxation times and the resulting plot is a depressed semicircle, which is associated with a nonideal capacitor or a constant phase element (CPE), and its impedance is expressed by Q(a) = To(7(o)" , where Tq represents the admittance and n is an experimental parameter (0 < < 1)... 

It has been found [213] that the kinetic parameters of the Volmer-Heyrovsky type of mechanism cannot be unambiguously determined. In fact, two sets of kinetic parameters can describe the experimental parameters of current and impedance, and formally these two solutions are indistinguishable and arise from the permutation of the parameters of the Volmer and Heyrovsky reactions ... 

It should also be added that use of the equivalent circuits may introduce ambiguities. It is clear that in the Voigt circuit (a), permutation of the values of elements f 2 - C2 and f 3 C3 does not change the impedance values and the attribution of values to one or another set is arbitrary, i.e. when fitting one can converge on either set. This fact is important when the system is studied as a function of the electrode potential (or other experimental parameter) to not exchange of these parameters (e.g. set of parameters 2 and 3). However, such an ambiguity does not appear in the ladder circuit (b). 

Finally, mice a correct physicochemical model is found and its parameters determined, then one may set about determining the kinetic parameters of the system. It should be emphasized that impedance parameters (e.g., resistances, capacitances, or other mechanism-related parameters) are derivatives of rates of electrochemical and chemical reactimis and are complex functions of the rate constants and other parameters, for example, adsorption and concentration. Such analyses are carried out using nonlinear approximations of the impedance parameters as functions of the electrode potential and other experimental parameters, and these analyses are being performed on an increasingly frequent basis. Of course, one cannot neglect error analysis to check the reliability of the procedure. 

Theory of Time Resolved Electrochemical Impedance Spectroscopy (TREIS). A prerequisite for the development and the improvement of fnel cells is the knowledge of the mechanistic processes that take place dnring operation. The nnderstanding of the kinetic behavior of the fuel cells requires the variation of different experimental parameters. Often, the variation of distinct parameters canses situations where steady state conditions are no longer fulhlled. In practice, EIS analysis often suffers from the fact that the steady state condition is violated dne to... 

At present, the microwave electrochemical technique is still in its infancy and only exploits a portion of the experimental research possibilities that are provided by microwave technology. Much experience still has to be gained with the improvement of experimental cells for microwave studies and in the adjustment of the parameters that determine the sensitivity and reliability of microwave measurements. Many research possibilities are still unexplored, especially in the field of transient PMC measurements at semiconductor electrodes and in the application of phase-sensitive microwave conductivity measurements, which may be successfully combined with electrochemical impedance measurements for a more detailed exploration of surface states and representative electrical circuits of semiconductor liquid junctions. 

Under this electrochemical configuration, it is commonly accepted that the system can be expressed by the Randles-type equivalent circuit (Fig. 6, inset) [23]. For reactions on the bare Au electrode, mathematical simsulations based on the equivalent circuit satisfactorily reproduced the experimental data. The parameters used for the simulation are as follows solution resistance, = 40 kS2 cm double-layer capacitance, C = 28 /xF cm equivalent resistance of Warburg element, W — R = 1.1 x 10 cm equivalent capacitance of Warburg element, IF—7 =l.lxl0 F cm (

charge-transfer resistance, R = 80 kf2 cm. Note that these equivalent parameters are normalized to the electrode geometrical area. On the other hand, results of the mathematical simulation were unsatisfactory due to the nonideal impedance behavior of the DNA adlayer. This should... 

Workers have shown theoretically that this effect can be caused both at the microstructural level (due to tunneling of the current near the TPB) as well as on a macroscopic level when the electrode is not perfectly electronically conductive and the current collector makes only intermittent contact. ° Fleig and Maier further showed that current constriction can have a distortional effect on the frequency response (impedance), which is sensitive to the relative importance of the surface vs bulk path. In particular, they showed that unlike the bulk electrolyte resistance, the constriction resistance can appear at frequencies overlapping the interfacial impedance. Thus, the effect can be hard to separate experimentally from interfacial electrochemical-kinetic resistances, particularly when one considers that many of the same microstructural parameters influencing the electrochemical kinetics (TPB area, contact area) also influence the current constriction. 

The experimental results mainly obtained by EIS supported the mechanism of the build up of an oxide passive layer. They lead to the determination of quantitative parameters related to the change of surface reactivity. The measurements constituted a series of impedance diagrams obtained at successive time intervals. Examples given in Eig. 11 represent [12] the time variation of the Nyquist diagram resulting from the build up of an insulating layer, after reaction ofSClonan initially bare hydrophobic... 

Many engineering problems involve several parameters, that impede the elaboration of the pi space. Fortunately, in some cases, a closer look at a problem (or previous experience) facilitates reduction of the number of physical quantities in the relevance list. This is the case when some relevant variables affect the process by way of a so-called intermediate quantity. Assuming that this intermediate variable can be measured experimentally, it should be included in the problem relevance list, if this facilitates the removal of more than one variable from the list. 

Cases in which Impedance Spectroscopy Becomes Limited. One might say that if one understands an interface well, the results of Z-to measurements can be readily understood. Of course, the interest is in the other direction, in using Z-to plots when one does not understand the interlace. Then the task is to find an interfacial structure and mechanism (and its resulting equivalent circuit) that provides a Z that is consistent in its dependence on to with the experimental results of the impedance measurement. This requires finding reasonable parameters to fit the value of the C s and R s as a function of to for the individual elements in the various equivalent circuits. If the shape of the calculated Z-to plot can only be made to match experiment by using C s and R s that are physically unreasonable, the proposed structure and the equivalent circuit to match it are not acceptable and another must be tried. 

Fig. 1.1. Electrochemical impedance (x) obtained from Eq. (1-4) with the experimental measurements of ZEHD o and ZEHD P. Electrochemical impedance (o) directly measured at the half wave potential. Curve in full line represents the theoretical variation. The coordinates are normalized by the electrochemical impedance value at zero frequency Zac(0). The parameter is the dimensionless frequency pScwl. After [29].

Two such circuits having different relaxation time constants and connected in series lead to two semicircles as shown in Fig. 2.55(b). As in the case of any other spectroscopic analysis the separate responses may overlap and the experimental curve must then be resolved into its separate constituent semicircles. Impedance spectroscopy makes use of other electrical parameters, including the admittance (Y = Z 1), to assist in quantifying the circuit parameters. 

The impedance spectroscopy is most promising for electrochemical in situ characterization. Many papers have been devoted to the AB5 type MH electrode impedance analysis [15-17]. Prepared pellets with different additives were used for electrochemical measurements and comparing. Experimental data are typically represented by one to three semicircles with a tail at low frequencies. These could be described to the complex structure of the MH electrode, both a chemical structure and porosity [18, 19] and it is also related to the contact between a binder and alloy particles [20]. The author thinks that it is independent from the used electrolyte, the mass of the electrode powder and the preparing procedure of electrode. However, in our case the data accuracy at high frequencies is lower in comparison with the medium frequency region. In the case, the dependence on investigated parameters is small. In Figures 3-5, the electrochemical impedance data are shown as a function of applied potential (1 = -0.35V, 2 = -0.50V and 3 = -0.75V). 

The interpretation of measured data for Z(oi) is carried out by their comparison with predictions of a theoretical model based either on the (analytical or numerical) integration of coupled charge-transport equations in bulk phases, relations for the interfacial charging and the charge transfer across interfaces, balance equations, etc. Another way of interpretation is to use an -> equivalent circuit, whose choice is mostly heuristic. Then, its parameters are determined from the best fitting of theoretically calculated impedance plots to experimental ones and the results of this analysis are accepted if the deviation is sufficiently small. This analysis is performed for each set of impedance data, Z(co), measured for different values of external parameters of the system bias potentials, bulk concentrations, temperature... The equivalent circuit is considered as appropriate for this system if the parameters of the elements of the circuit show the expected dependencies on the external parameters. 

Experimental arcs in the spectrum are not always ideal semicircles, and this complicates parameter estimation. Nevertheless, there are still basic rules for estimating the initial values [8, 9], The key is to identify the region of the spectrum in which one element dominates and then estimate the value of the element in this region. For example, the resistor s impedance dominates the spectrum at a low frequency, while the impedance of a capacitor approaches zero at a high frequency and infinity at a low frequency also, individual resistors can be recognized based on the horizontal regions in a Bode plot. 

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