Transfer impedance

FIG. 7 Simplified equivalent circuit for charge-transfer processes at externally biased ITIES. The parallel arrangement of double layer capacitance (Cdi), impedance of base electrolyte transfer (Zj,) and electron-transfer impedance (Zf) is coupled in series with the uncompensated resistance (R ) between the reference electrodes. (Reprinted from Ref. 74 with permission from Elsevier Science.)... 

In our opinion, the interesting photoresponses described by Dvorak et al. were incorrectly interpreted by the spurious definition of the photoinduced charge transfer impedance [157]. Formally, the impedance under illumination is determined by the AC admittance under constant illumination associated with a sinusoidal potential perturbation, i.e., under short-circuit conditions. From a simple phenomenological model, the dynamics of photoinduced charge transfer affect the charge distribution across the interface, thus according to the frequency of potential perturbation, the time constants associated with the various rate constants can be obtained [156,159-163]. It can be concluded from the magnitude of the photoeffects observed in the systems studied by Dvorak et al., that the impedance of the system is mostly determined by the time constant. 

Flash Rusting (Bulk Paint and "Wet" Film Studies). The moderate conductivity (50-100 ohm-cm) of the water borne paint formulations allowed both dc potentiodynamic and ac impedance studies of mild steel in the bulk paints to be measured. (Table I). AC impedance measurements at the potentiostatically controlled corrosion potentials indicated depressed semi-circles with a Warburg diffusion low frequency tail in the Nyquist plots (Figure 2). These measurements at 10, 30 and 60 minute exposure times, showed the presence of a reaction involving both charge transfer and mass transfer controlling processes. The charge transfer impedance 0 was readily obtained from extrapolation of the semi-circle to the real axis at low frequencies. The transfer impedance increased with exposure time in all cases. 

At 60 minutes only, dc potentiodynamic curves were determined from which the corrosion current was obtained by extrapolation of the anodic Tafel slope to the corrosion potential. The anodic Tafel slope b was generally between 70 to 80 mV whereas the cathodic curve continuously increased to a limiting diffusion current. The curves supported impedance data in indicating the presence of charge transfer and mass transfer control processes. The measurements at 60 minutes indicated a linear relationship between and 0 of slope 21mV. This confirmed that charge transfer impedance could be used to provide a measure of the corrosion rate at intermediate exposure times and these values are summarised in Table 1. 

The above formulas may become inapplicable for systems with adsorption processes or/and coupled chemical steps in solution whose characteristic times are comparable with the inverse frequency within the impedance measurement interval. In this case the charge-transfer resistance, Rct, must be replaced by a complex charge-transfer impedance, Zct. Another restriction of this treatment is its assumption of the uniform polarization of the m s interface which requires to ensure a highly symmetrical configuration of the system. Refs. [i] Sluyters-Rehbach M, Sluyters JH (1970) Sine wave methods in the study of electrode processes. In Bard A/ (ed) Electroanalytical chemistry, vol. 4. Marcel Dekker, New York, p 1 [ii] Bard A], Faulkner LR (2001) Electrochemical methods, 2nd edn. Wiley, New York [iii] Retter U, Lohse H (2005) Electrochemical impedance spectroscopy. In Scholz F (ed) Electroanalytical methods. Springer, Berlin, pp 149-166 [iv] Bar-soukov E, Macdonald JR (ed) (2005) Impedance spectroscopy. Wiley, Hoboken... 

In Equation 6.18, Rt is a function of current density and temperature, Rm is less dependent on the current density but is strongly dependent on the temperature, and Rmt is the mass transfer impedance, which is strongly dependent on current density and temperature. Note that this equation is only accurate at an AC impedance frequency at or near zero. 

Parsons, J. S., Yates, WAllace, and Scholoss, The measurement of dynamic properties of materials using Transfer Impedance Technique. Report 2981, Naval Ship R D center, Washington, D. C., April, 1969. 

Figure 10.5 Electrical circuit providing the equivalent to the impedance response for a single electrochemical reaction coupled with a mass transfer impedance.

This equation may be also obtained directly by assuming that the charge-transfer reaction is reversible and calculating the mass-transfer impedance from... 

For the processes for which the transfer coefficient, a, is equal to 0.5, the minimum of R is observed at the half-wave potential. Similarly, the mass-transfer impedance equals... 

The Warburg impedance has a minimum at 1/2. The mass-transfer impedance is a vector containing real and imaginary components that are identical, that is, the phase angle (p = atan(Z" v/Z w) = atan(-l) = 5°. The faradaic impedance is shown in Fig. 11(b) (dashed line). On the complex plane plot, it is a straight line with a slope of 1 and intercept The total electrode impedance consists of the solution resistance, R, in series with the parallel connection of the double-layer capacitance, Qi,... 

When the surface and bulk concentrations are the same, that is, when the mass-transfer impedance may be neglected, the equivalent circuit corresponds to that in Fig. 4. hi this case a semicircle is observed on the complex plane plots. In the other limiting case, when the charge-transfer resistance is neglected (reversible case), a straight line with a slope of 1 is obtained on the complex plane. 

The dependence of the mass-transfer and charge-transfer impedances on the electrode potential is displayed in Fig. 12. The charge-transfer and mass-transfer impedances have a minimum at Es [Eq. (68)] and Ey2, respectively, according to Eqs. (67) and (69). 

The mass-transfer impedance may be obtained from Eq. (64). Assuming a reversible dc process, one obtains, similar to the case of linear diffusion ... 

The influence of the nonlinearity of diffusion on the observed complex plane plots is shown in Fig. 13. Spherical mass transfer causes the formation of a depressed semicircle at low frequencies instead of the linear behavior observed for linear semi-infinite diffusion. For very small electrodes (ultramicroelectrodes) or low frequencies, the mass-transfer impedances become negligible and the dc current becomes stationary. On the Bode phase-angle graph, a maximum is observed at low frequencies. 

The limit of faradaic impedance at infinite frequency is also called the transfer impedance, R, while the limit at zero frequency is called the polarization resistance, Rp ... 

On the other hand, when is negligible compared to the mass-transfer impedance, which is the case for a nemstian system, the following expression applies ... 

It was mentioned in sub-section 13.5.2 that the cut-off frequency for effective screening is in the range of 0.5 kHz to 2.0 kHz for external interference. At frequencies higher than about 1 MHz it is useful to consider the coupling between the screen and the core as an impedance that relates the screen current to the core open-circuit voltage. In such a case it is not specified how the current appears in the screen. It could be by mutual induction from nearby cables, but more often by radio waves received from local radio transmitters, radio telephones, or a radar antenna. The impedance is called the shield transfer impedance Zj and it can be measured by a relatively simple test procedure. The expression for the impedance Zj is -... 

For a reversible system under pure diffusion control, the mass transfer impedance (Warburg), Z, is given by ... 

Electrodes are the most important part of an impedance-measuring system (Geddes 1972). They determine the sensitivity field (Section 10.5), which determines the contribution of each small voxel to the overall result. Three- and four-electrode systems are more complicated because, as we shall see, they introduce volumes of negative sensitivity because they measure transfer impedance. 

The four-electrode tetrapolar system of Figure 10.10 is very different from the two-electrode mono-and bipolar systems (Grimnes and Martinsen 2007). It measures transfer impedance because the potential is recorded at a separate PU port and not at the CC port. If the two ports are far apart, no signal will be transferred from the CC to the PU port and the transfer impedance will be virtually 0 2. 

According to the theorem, PU and CC electrodes can be swapped without change in measured transfer impedance. This may sound contraintuitive, but it is so. Reciprocity is destroyed if the system is nonlinear, for example, if the CC electrodes have larger contact area than the PU electrodes. After swapping, the small CC electrodes may then be driven into nonlinearity because of the increased current density. Reciprocity may also be destroyed if the properties of the biomaterial have changed. 

The most validated method is prediction of TBW from four-electrode whole-body transfer impedance measurements at 50 kHz. It is not really a whole-body measurement because the results are dominated by the wrist and ankle segments with very little influence from the chest because of the large cross-sectional area. By using more than four electrodes, it is possible to measure more than one body segment. With two electrodes at each hand and foot, the body impedance can, for instance, be modeled in five segments arms, legs, and chest. 

Electric current is typically injected in one CC electrode pair and the voltages of all the other PU electrode pairs are recorded. Current injection can then be successively shifted until all electrode pairs have been used as a CC pair. The quantity measured is a group of transfer impedances. 

Ret is the charge transfer resistance while cra / (l — i) is the Warburg, or mass transfer, impedance. Eqs.5 and 6 can now be used to study the electrode reaction in detail. For example, a cot (f> versus dc potential plot will aid in finding the charge transfer coefficient, while a cot (j> versus plot serves to find the heterogeneous rate constant. Details on these examples can be found in the literature. ... 

Bioimmittance is measured in vivo or in vitro. The tissue may be kept alive and perfused under ex vivo conditions. Bioimmittance can be measured with two-, three- or four-electrode systems. With four electrodes, one electrode pair is current carrying and the other pair picks up the corresponding potential difference somewhere else in the tissue. If the measured voltage is divided by the applied current, the transfer impedance is calculated. If no voltage is measured, the transfer impedance is zero. This is equivalent to the bioelectricity case in which a signal from the source, such as the heart, is transferred to the skin surface electrodes. Zero transfer impedance does not mean the tissue conducts well, only that no signal transfer occurs. With the bioimpedance two-electrode technique, the transfer factor is eliminated because current application and signal pickup occur at the same site, which means that measured impedance reflects tissue electrical properties more directly. 

Foster and Schwan (1986), Stuchly and Stuchly (1990), Duck (1990), and Holder (2005). Gabriel et al. (1996a) made a literature survey. Their own measurements (Gabriel et al., 1996b) were made with a two-electrode technique and a coaxial probe in the frequency range of 10 Hz to 20 GHz. In that way, the transfer impedance component was eliminated. 

Zt is a scalar in space, but may be a time vector Zt related to a frequency dependence of p. Both the lead vector H and file scalar transfer impedance Zt are transfer factors between the CC and PU dipoles. The relationship between them is Zt = H-Lcc [il]. 

Schmitt (1957) called the lead vector H transfer impedance. This may he misleading hoth because impedance is a spatial scalar, whereas H is a spatial vector and with dimension [Q/meter]. 

Swapping the PU and CC pairs does not change the transfer impedance as long as the system is electrically linear (reciprocity). This is valid for both tripolar and tetrapolar electrode systems. 

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