Inductive behavior

Cutts, J.H. and R.L. Noble (1964). Estrone-induced mammary tumors in the rat B. Effect of alteration in hormonal environment on tumor induction, behavior, and growth. Cancer Res., 24 1124—1130. 

The predominant capacitive behavior of a given circuit at a given frequency w will cause a positive phase shift, where current leads voltage by the phase difference /. The predominant inductive behavior of a circuit at frequency co will cause a negative phase shift, where current lags voltage by the phase difference . 

For the last approximation it was assumed that Cp corresponds to the nominal capacitance CN and that there are only small polarization losses, that is, 1 + tan28E 1. (Each capacitor is specified by the manufacturer with a nominal capacitance CN and nominal or rated voltage Vr.). The quantity jo is the resonance frequency . At ffi a transition from a capacitive to an inductive behavior takes place. Further characteristic quantities for capacitors are ... 

Certain artifacts are also observed in studies in low-conductivity media [682]. In studies in pure 80 % and 100 % acetic acid a very important influence of the distance between the tip of a Luggin capillary and a working electrode made of stainless steel was observed (Fig. 16.1). These solutions were characterized by very large resistivities, 8-10 kii cm for 80 % and 8-12 Mi2 for 100 % acetic acid. At short distances, high-frequency capacitive-inductive behavior is apparent Similar behavior was also observed when a ft pseudo-reference electrode was used. Such behavior was explained by the capacitive-resistive coupling between working and reference, working-auxiliary, and reference-auxiliary electrodes [682]. 

Impedance Spectra with Inductive Behavior at Low Frequencies Relaxation Impedance. Based on the concept of impedance elements, Gdhr [1986] described the Faradaic impedances as connections of impedance elanents each of which is associated with a single process. One of such an impedance element is the relaxation impedance, desalbing the surface relaxation of the interface and explaining the development of the pseudoinductive behavior in the low frequency range (frequency < 3 Hz) in the impedance spectra of the fuel cell. This behavior was first found by Muller et al. [1999] during poisoning the anode of a PEFC with... 

For illustration, in Figure 4.5.47 a simulated impedance spectra, presented as a Nyquist plot (a) and a Bode plot (b) with an inductive behavior in the low frequency range is shown, which looks similar to the impedance spectra measured at PEFC with H2+ 100 ppm CO as fuel gas. 

Inductive behavior in the low frequency range of impedance spectra was also observed in systems in which a reaction consisting of two successive electron transfer steps proceeding by an adsorbed intermediate species ... 

Combined with small alloy variations, primary treatments and field annealing treatments, a wide variety of annealed states can be realized to vary the induction behavior. The field dependence of the permeability of some high-permeability Ni—Fe alloys (designations according to Vacuumschmelze GmbH) are shown in Fig. 4.3-14 [3.16]. 

In general, the impedance of solid electrodes exhibits a more complicated behavior than predicted by the Randles model. Several factors are responsible for this. Firstly, the simple Randles model does not take into account the time constants of adsorption phenomena and the individual reaction steps of the overall charge transfer reaction (Section 5.1). In fact the kinetic impedance may include several time constants, and sometimes one even observes inductive behavior. Secondly, surface roughness or non-uniformly distributed reaction sites lead to a dispersion of the capacitive time constants. As a consequence, in a Nyquist plot the semicircle corresponding to a charge-transfer resistance in parallel to the double-layer capacitance becomes flattened. To account for this effect it has become current practice in corrosion science and engineering to replace the double layer capacitance in the equivalent circuit by a... 

The frequency in which the series resonant circuit changes from capacitive to inductive behavior is called the self-resonance frequency (Equation 9.27). At this frequency, fhe imaginary part of the impedance is zero. Because the... 

The pseudo-inductive impedance pattern has also been observed by other researchers when H2/CO was used as the fuel. The size of the impedance circle is related to the overpotential of the anode according to Wang et al [56]. A higher overpotential results in a smaller circle. Ciureanu and Wang [7] and Wang et al. [56] found that at potentials lower than the CO oxidation potential, the inductive behavior did not exist. Since the CO oxidation potential is lower on PtRu and PtSn than on Pt, the appearance of the inductive loop should appear at lower anode overpotentials on these alloys. This was indeed observed by Leng et al [22]. 

The pseudo-inductive behavior is known to happen in systems with adsorbed species the coverage of which changes with the potential [12]. Ciureanu and Wang postulated that the pseudo-inductive impedance in the presence of CO was due to... 

In a DMFC, methanol can transport through the membrane to the cathode side, where it is oxidized. This results in a much lower mixed cathode potential. Piela et al. found that the cathode impedance spectrum in a DMFC also showed pseudo-inductive behavior. They modeled such a behavior by treating the cathode as a highly non-equipotential electrode consisting of the ORR and the methanol oxidation [35]. 

Electrochemical impedance spectroscopy (EIS) technique has been used for the experimental assessment of CO tolerance on different Pt-alloy catalysts and at different temperatures [187]. Hsing et al. [187] proposed that the critical potential at which pseudo-inductive behavior occurs could be used as a criterion for the evaluation of CO tolerance. A mathematical impedance model based on two state-variables (Pt-H and Pt-CO) was also developed to elucidate the reaction kinetics and mechanism of the H2/CO oxidation on a Pt/C catalyst [188]. In fact, this study has given better insight into explicitly understanding the impedance patterns and the quantitative assessment of the effect of applied potentials upon the oxidation reaction kinetics in a broad range of applied potentials. Nevertheless, with the consideration of only two adsorbed species, Pt-H and Pt-CO, the impedance model based on two state-variables was not able to explain the experimental observation... 

We can see, finally, that this procedure has resulted in the appearance of an inductance L which expresses the inductive behavior which is systematically found at high frequencies with experimental measures of impedance. Its origin is most often linked to the way in which the voltage at the terminals of the component is measured. 

Bai, L. and Conway, B.E. (1993) Three-dimensional impedance spectroscopy diagrams for processes involving electrosorbed intermediates, introducing the third electrode-potential variable—examination of conditions leading to pseudo-inductive behavior. Electrochim. Acta, 38 (14), 1803-1415. 

As illustrated in this chapter, Eq. (6), in parallel with the double-layer capacitance Qj, generates identifiable shapes on the impedance curves in die Bode or Nyquist plane making possible to determine the number of chemical entities and Cj participating in the reaction mechanism and thus providing information on the reaction pattern. In terms of dissolution-passivation processes, capacitive responses and negative resistances are related to inhibition or passivation whereas inductive behaviors arise from catalytic efiects or activating intermediates [4-8], Acquisition and processing of the transient response of electrochemical systems are easily performed by modem laboratory equipment [5,6,49] and do not deserve special attention in this chapter. 

One intensive properly of the film probably its ionic conductance, is at the origin of the inductive behavior. 

Hi) Possible Explanations of the Origin of the Inductive Behavior of the Transients Suggested by Various Authors... 

There are also some questionable explanations for the inconsistency between a low Tafel slope and the inductive behavior that characterizes the consecutive charge transfer. One of them is to accept that the symmetry factor has a totally asymmetric value, such as the limiting values 0 or 1, and that it is strongly potential dependent the other is to deny the mechanistic significance of steady-state characteristics, that is, of the Tafel slope and reaction orders, because they are influenced by the sweep rate and waiting time arbitrarily chosen by the experimentalists. ... 

Nevertheless, one must be aware of the fact that once concordance between any reaction scheme and the experimental data has been established, it is not a foregone conclusion that all other concepts about the iron mechanism are invalidated. First of all, any reaction scheme represents a simplified model. Inter alia, one must take into consideration that the inductive behavior exhibited by the transient response of the electrode during the step-pulse polarization as well as the first inductive loop displayed in AC measurements could be the result of superposition of hydrogen anodic desorption and some other unknown effect produced by the iron reaction itself. Finally, artifacts are always possible as long as our models are based on the existence of hypothetical intermediates. 

It is easy to demonstrate that in the first three cases, the electrode system displays an inductive behavior, that is, i, < i. Based on the above-mentioned limiting conditions. 

This kind of mechanism accounts for the positive reaction order in SO " found experimentally and exhibits the incompatibility between the low steady-state Tafel slope (30-40 mV dec" ) and the inductive behavior of the electrode. 

Around 1980, some branching mechanisms were proposed with the intention of describing the processes occurring in the active, transition, and prepassive ranges of the overall active state, and explaining the different values of the experimental kinetic data obtained by their authors. In addition to this, the supporters of the consecutive electron-transfer concept offered an explanation for the disagreement between the experimental low steady-state Tafel slope and the inductive behavior of the electrode, on the one hand, and the theoretical predictions, on the other, as demonstrated by Plonski " since 1969. 

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