Negative Faradaic resistance

As we saw earlier, systems with a negative faradaic resistance, such as in Fig. 13.15, may be stable, depending on the value of the solution resistance. However, such impedance is not Kramers-Kronig-transform compliant. This is related to the general characteristics of transfer functions. However, there are two types of impedance experiments potentiostatic or galvanostatic. When an ac voltage is applied and ac current measured, the corresponding transfer function (Laplace transform of the output to the Laplace transform of the input) is admittance. 

Figure 12.5 Complex-plane impedance plots for p-Si in 1.0 mol dm NH4F (pH 4.5). Note that the faradaic resistance (derived from the low-frequency intercept on the real axis) can be positive or negative. The negative value at 1.75 V indicates that the current decreases with increasing potential in this region of the current-potential curve (see Fig. 12.4). Adapted from Bailes et al (1998).

First, it has been supposed that the faradaic current instantaneously adjusts to a change in the double-layer potential. This means that all other quantities that affect the current, such as concentration of the reactive species and the coverage of adsorbates, are assumed to vary on a time scale that is much shorter than the time scale on which typical variations of the potential occur. In other words, all other quantities are assumed to adjust immediately to their equilibrium values and can be adiabatically eliminated. Second, chemical instabilities have been excluded. In the presence of chemical instabilities, the current is no longer a unique function of ( l and the state of the system is only defined when taking into account another variable. The absence of chemical instability also implies that a negative differential resistance can only be realized if the current-potential characteristics of the interface exhibit the shape of an N (or multiple Ns) as shown in Fig. 2(a). In contrast, an S-shaped characteristic, being just one example of another characteristic possessing an NDR, would require the existence of a chemical instability. 

On the other hand, depending on the resistance p and the ratios of the time scales e, steady states with a negative faradaic impedance can become unstable. If Det (7) < 0, the stationary state is always a saddle point. From Eq. (7b) it is evident that provided /d i < 0, the determinant is... 

Label-free detection of ligand-aptamer interaction was also demonstrated by means of impedance spectroscopy technique [52,53]. Simultaneously, Radi et al. [52] and Rodriguez et al. [53] reported application of Faradaic impedance spectroscopy (FIS) in detection of interaction of proteins with DNA aptamers. The detection method is based on the measurement of resistance in presence of redox mediator Fe(CN)6-In absence of target protein, the negatively charged aptamer repulse the redox mediator molecules from the sensor surface. In a paper by... 

The analysis of LSV and CV curves (today, usually computer assisted) requires electrochemical experiments free from artifacts to provide an accurate faradaic response [112]. The influence of the uncompensated solution resistance, R, (see Eq. (13)) can be greatly reduced by the use of a powerful potentiostat with fast output. However, in the common case of undercompensation of the solution resistance (e.g., in solutions with low concentration of the supporting electrolyte) the effect is the increase of the cathodic and the corresponding anodic peak separation in a manner that could be mistaken for an apparent slow rate electron transfer or the quasi-reversible regime (potentials are shifted to more negative/positive directions). 

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