Impedance faradic

The electrode/solution interface, in the simpler case (no passive layer on the electrode surface) can be modeled using the following equivalent circuit (Figure 1.18), where Rel stands for the electrolyte resistance, CDL for the double layer capacitance, and ZF the faradic impedance. 

When the rate determining step of the electrode reaction is the charge transfer process (kinetic control), the faradic impedance ZF in Figure 1.18 can be described as RCJ, the charge transfer resistance [7,8], The impedance plot in the Nyquist plane describes a semicircle, as shown in Figure 1.19. 

Faradic impedance (//) is directly related to the rates of charge transfer reactions at and near the electrode/electrode interface. As shown in Figure 3.1, the Faradaic impedance acts in parallel with the double-layer capacitance Cd, and this combination is in series with the electrolyte resistance Rei The parameters Rei and Cd in the equivalent circuit are similar to the idea of electrical elements. However, X/ is different from those normal electrical elements because Faradaic impedance is not purely resistive. It contains a capacitive contribution, and changes with frequency. Faradaic impedance includes both the finite rate of electron transfer and the transport rate of the electroactive reagent to the electrode surface. It is helpful to subdivide Zj into Rs and Cs, and then seek their frequency dependencies in order to obtain useful information on the electrochemical reaction. 

The photoisomerization of a command interface resulting in different electrochemical kinetics of a soluble redox-probe also can be probed by faradic impedance spectroscopy. A small electron transfer resistance (R ) is found for the system when there is an attractive interaction between the charged redox-probe and the command interface, and a much larger one upon photoisomerization to the state when the repulsive interactions exist. This paradigm was demonstrated with a negatively charged redox-probe,... 

FIG. 7.15 Nyquist diagram for the faradic impedance measurements at the I la/l tth-monok er-modifled Au electrode in the presence of 10 mM [Fe(CN)J (a) 11 b-state, and (b) I la-state nwno-iayer. Applied bias constant potential, 0.6 V. amplitude of the alternating voltage, 10 mV Performed in 0.01 M phosphate buffer, pH 7.0. (Adapted from reference 77, Figure 4. Copyright 1998, American Chemical Society.)... 

Electronic and optical transduction of the formation of antigen-antibod/ affinity compleK-es on transducers (A) Amperometric transduction at an electrode (R /R is a redox label in the riec-trolyte solution). (B) Tnuisduction by faradic impedance >ectro cc. (C) hterogravimetric tpiartz crystal microbabnce (QCM) transduction in the presence of a piezoelectric quartz crystal. (D) Surface plasmon resonance transduction. 

Faradic impedance spectroscopy (FIS) was the electrochemical technique used in an aptasensor for the detection of lysozyme [48]. The duplex formed by the lysozyme aptamer and a partial... 

Y. Peng, D. Zhang, Y. Li, H. Qi, Q. Gao, and C. Zhang, Label-free and sensitive faradic impedance aptasensor for the determination of lysozyme based on target-induced aptamer displacement. Biosens. Bioelectron., 25, 94-99 (2009]. 

Figure 7 shows the detection principle of an impedimetric IME biosensor for bacterial detection [8]. It is based on measurements of electrochemical faradic impedance in the presence of [Fe(CN)6] " as a redox probe. When a bare interdigitated microelectrode is immersed into an electrolyte solution containing the redox couple and a small-amplitude AC potential (5 mV) is applied to the electrode, the faradic process of oxidation and reduction of the redox couple occurs, and then electrons are transferred between the two sets of array electrodes through the redox couple (Fig. 7a). When antibodies are immobilized onto the electrode surface (Fig. 7b) they form a layer that can inhibit the electron transfer between the electrodes, and thus an increase in the electron transfer resistance can be expected. If bacterial cells attach to the antibody-modified electrode surface (Fig. 7c), the intact cells can create a further barrier for...

The current, in general, is composed of a steady state or dc part determined by the mean dc potential E and the mean dc concentrations at the interface, Co and c , and an ac part, A/, determined by the ac perturbing potential A and the fluctuating concentrations Ac,. The faradic impedance is given by the ratio of the Laplace transforms of the ac parts of the voltage and current... 

Here Co and c are determined by the solution of the appropriate dc mass transport equations. The coefficients may then be substituted into Eq. (166) to give the overall faradic impedance. 

It should be anphasized that the development of the expressions for charge transfer kinetics given here is not completely general. It rests on the assumptions of absolute rate theory. More general treatments have been given in the literature where no a priori assumption of the form of the dependence of the rate constants on potential is made (Birke [1971], Holub et al. [1967]). A point which arises from these more general treatments is worth pursuing here. For the case of semiinfinite diffusion to a planar interface, the faradic impedance may be written in the form... 

A second aspect of the theory developed in this section is the assumption that the faradic current is decoupled from the nonfaradic current, hi other words, the impedance due to the double-layer capacitance is included afterward and placed in parallel to the faradic impedance, since... 

In order to derive the faradic impedance (Zp) we note that for sinusoidal variations in the potential and in the surface coverages of reaction intermediates we may write... 

The faradic impedance is readily obtained by first deriving expressions for dOi/dt. This is done by taking the total differentials of Eqs (32)-(35). For example in the case of Eq. (33) we write... 

The faradic impedance is composed of three impedances in series ... 

Figure 7 shows the detection principle of an impedimetric IME biosensor for bacterial detection [8], It is based on measurements of electrochemical faradic impedance in the presence of [Fe(CN)6] / as a redox probe. When a bare interdigitated microelectrode is immersed into an electrolyte solution containing the redox couple... 

Two types of impedances are measured in electrochemical impedance spectroscopy (EIS) faradic and nonfaradic. Faradic impedance is associated with the process which involves transfer of charge across an interface. In faradic impedance measurement, a redox probe is used which is alternately oxidized and reduced due to transfer of electrons to and from the metal electrode resulting from the biological events occurring near the electrode surface. Nonfaradic impedance (mostly capacitive measurements) on the other hand is associated with transient flow of current or displacement current without actual transfer of any electron. In this case, no redox probes are required. 

Figure 5.12 (a) Electron transfer event in faradic impedance-based immunoassay. The eiec-tron transfer resistance increases with increasing layers on the electrode-electrolyte interface, (b) Top-bottom electrode configuration. First set of electrodes (A1-A2) is functionalized whereas the second set (B1-B2) are the reference electrodes ie, without functionalization. 

This so-called faradic impedance Zp basically displays the frequency response of the elementary phenomena participating in the electrochemical transfer of charges across the interface. 

Each of these partial derivatives gives rise to a specific contribution to the faradic impedance. They can be split into two groups ... 

In order to get the true electrode capacitance F, related exclusively to the film growth, Eq. (14) can be further coprocessed with the faradic impedance of the disk ... 

In theory, the transient state is assumed to take place at times short enough to keep the concentration of (FeOH)j, frozen at its initial value. Therefore the initial transition is due only to the change of the reaction rate of step (26) or (27) under the effect of potential at constant (FeOH) concentration. The same discrimination between instantaneous and delayed contributions is at the origin of the frequency dependence of the faradic impedance. Table 1 shows the theoretical and experimental values of the steady-state and transient kinetic parameters for both mechanisms, according to Ref. 12. 

Steady-state current-voltage characteristics and faradic impedance associated with the mechanism (24) to (31) were derived and numerically simulated with the following assumptions ... 

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