Faradaic charge transfer process

Figure 16. Equivalent circuit (a) and a simulated Nyquist plot (b) for the charge transfer pathway illustrated in Figure 15. The capacitance C represents that of the space-charge layer and the parallel branch components represent the Faradaic charge transfer process. Refer to the original work for further details. (Reproduced with permission from Ref. [84).)...

From the derivations in Appendix B, it is evident that the present faradaic rectification formulations for multiple-electron charge transfer not only enable the determination of kinetic parameters for each step of three-electron charge transfer processes but may also be extended to charge transfer processes involving a higher number of electrons. However, the calculations become highly involved and complicated. 

Both the double-layer charging and the faradaic charge transfer are non-linear processes, i.e. the charging current density, jc, and the faradaic... 

The faradaic current corresponding to any charge transfer process depends on the surface gradient (dco/dx)x=0, which can be expressed as the ratio of the difference between the bulk and surface concentrations of the oxidized species and the linear diffusion layer, <5 0,... 

The ohmic drop causes the potential imposed between the working electrode and the reference one ( ) to differ from the applied potential ( ), according to E=E IRU. Moreover, it can be assumed, at least approximately, that the current can be expressed as the sum of a pure faradaic current because of the charge transfer process plus a charging current... 

Fig. 5.11 Current-potential response of CV and SCV (for A = 5mV) for a Nemstian charge transfer process taking place at a planar electrode for different values of the scan rate (shown in the figure). Dashed-dotted lines Pure faradaic component (SCV and CV) calculated by using the numerical procedure proposed in [21, 22]. Dashed lines Charging current calculated from Eqs. (5.77) (SCV) and (5.76) (CV). Solid lines total current calculated as indicated in Eq. (5.75). /JU = 0.1K 2, C,u 20pFcm 2, Area = 0.05 cm2, cj, = ImM, = 0, Do = Dr = 10 5cm2s 1...

This technique is of special interest in the case of charge transfer processes at surface-bound molecules since it allows a simple and more effective correction of the non-faradaic components of the response than Cyclic Voltammetry. Moreover, this technique presents an intense peak-shaped signal for fast charge transfer, whereas other multipulse techniques give rise to nonmeasurable currents under these conditions and it is necessary to use short potential pulses to transform the response to quasi-reversible, which is much more difficult to analyze [4, 6, 10]. 

The adsorption isotherms discussed in Section 19 describe the potential dependence of the fractional coverage 0. For an intermediate formed in a charge-transfer process, as shown, for example, in Eq. 191, the fractional coverage is associated with a faradaic charge q. If we denote the charge required to form a complete monolayer of a monovalent species by q, we have the simple relationship... 

VanderNoot69has studied poorly separated faradaic and diffusional processes. He has found that a complex, nonlinear, least-squares regression is capable of extracting kinetic information from impedance measurements when the ratio of the charge-transfer process time constant tf=... 

Experimentally measured ac current or total admittances are functions of the electrode potential. Figure 17 presents the dependence of the total admittances of a process limited by the diffusion of electroactive species to and from the electrode and the kinetics of the charge-transfer process, on the electrode potential. Information on the kinetics of the electrode process is included in the faradaic impedance. It may be simply... 

In the present system with the copper-2% zinc electrodes, all three processes of protein adsorption, charge transfer, and Faradaic oxidations and reductions are possible. The peaks observed in the anodic and cathodic processes are related, respectively, to oxidations and reductions of the electrode. Copper oxides, chlorides, basic chlorides, phosphates, etc., as well as zinc products, are probable compounds for these electrochemical reactions. Increased Faradaic processes and charge transfer processes with protein solutions are factors for increasing the j-U profiles at U s less than +0.3 V. Since the sweep rate is a constant here, the capacitance of the double layer must increase for the protein solutions, if the increase in j is not all due to Faradaic processes One analog of the electrical double layer capacitance incorporates three capacitors in series (44). Hence... 

Measurement of the electric conductivity of an electrochemical cell can be the basis for an electrochemical sensor. This differs from an electrical (physical) measurement, for the electrochemical sensor measures the conductivity change of the system in the presence of a given solute concentration. This solute is often the sensing species of interest. Electrochemical sensors may also involve measuring capacita-tive impedance resulting from the polarization of the electrodes and/or the faradaic or charge transfer processes. 

The electrolyte conductance measurement technique, in principle, is relatively straightforward. However, the conductivity measurement of an electrolyte is often complicated by the polarization of the electrodes at the operating potential. Faradaic or charge transfer processes occur at the electrode surface, complicating the conductance measurement of the system. Thus, if possible, the conductivity electrochemical sensor should operate at a potential where no faradaic processes occur. Also, another important consideration is the formation of the double layer adjacent to each electrode surface when a potential is imposed on the electrochemical sensor. The effect of the double layer complicates the interpretation of... 

The procedure employed assumes that the heterogeneous charge transfer process is quasi-reversible on the a.c. time scale and reversible (nernstian) on the d.c. time scale (quasi-reversible systems on the d.c. time scale normally are not selected for assay work). Under these conditions, the faradaic rate law may be written as... 

As shown in Figure 1.7, the pseudocapacitance can also arise from the intercalation of electrolyte ions (e.g., LF) into the tunnels, van der Waals gaps, or lattice of redox-active electrode materials (e.g., M0O3) accompanied by a faradaic charge transfer [11,77-79]. It is worth noting that only when such intercalation process is fast enough, the electrode exhibits pseudocapacitive behavior. Otherwise, it will behave like a battery-type electrode. 

Similarly, using C03O4 as pseudocapacitive materials in the KOH electrolyte, the surface faradaic reaction is involved with OH- ions adsorption/desorption or inser-tion/extraction accompanied by the charge transfer process. This can be expressed as follows [127,128] ... 

Improved charge transfer capacity is commonly estimated by using a reversible charge injection process through either double layer capacitive reactions and reversible faradaic charge transfer reactions at the electrode/electrolyte interface as... 

When the electroactive species or an intermediate adsorbs on the electrode surface, the adsorption process usually becomes an integral part of the charge transfer process and therefore cannot be studied without the interference of a faradaic current. In this situation, surface coverages cannot be measured directly and the role of an adsorbate must be inferred from a kinetic investigation. Tafel slopes and reaction orders will deviate substantially from those for a simple electron transfer process when an adsorbed intermediate is involved. Moreover the kinetic parameters, exchange current or standard rate constant, are likely to become functions of the electrode material and even the final products may change. These factors will be discussed further in the section on electrocatalysis (Section 1.4). 

The equations for the diffusion and charge transfer processes into the crystalline ionic-electronic conductors were obtained by Wagner [11] and Yokota [12]. They became the basis for study of transport properties of solid electrolytes, in particular, for determination of the electronic conductivity value [13]. However, these theories are no longer tme if the Faradaic process of electrochemical decomposition of the PFC occurs at the interfaces. The elementary theory for stationary process at such conditions [8] and some experimental examples [9] are considered below. 

Semi-infinite linear diffusion is considered in the Randles model, and the capacitive current is separated from the faradaic current, which is justified only when different ions take part in the double-layer charging and the charge transfer processes (i.e., a supporting electrolyte is present at high concentrations). Finite diffusion conditions should be considered for well-stirred solutions when the diffusion takes place only within the diSusion layer, and also in the case of siuface films that have a finite thickness. However, the two cases are different, since in the previous... 

Thus, the equivalent circuit consists of a solution resistance, / s. in series with the double layer capacitance, Qi, and /fp, the Faradaic resistance associated with the charge-transfer process. However, if an adsorbed intermediate is involved in the charge-transfer process, such as ... 

The electrode reaction of Cr / CyDTA has been studied in detail by Tanaka et al. [lb]. They report a value of kob = 0.029 cm s K We have tried to estimate this kob in the pH-range 4 to 8 where E is independent of pH. Using cyclic voltammetry (CV) and faradaic impedance measurements we confirm that kob is smaller than 0.1 cm s and a (charge transfer coefficient) < 0.4. Up to now we are unable to get exact values for these constants because a chemical pre-equilibrium of unidentified origin interferes with the charge transfer process. Further work is underway to clarify this point. 

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