Faradaic rectification

It may be noted first that the name of this method is misleading because, as we have seen, the electrical double layer also contributes to the rectification signal. 

It follows from Table 5 that both SF and Sc can be considered as step functions, applied at the moment (t = 0) the sine wave train is started. By elimination of AE2 from eqns. (76) and (79), with substitution of eqn. (74), an integral equation in Ajii2 = AjfF- 2 = — Ajrc, 2 is obtained 

This equation can be solved most practically via Laplace transformation (see Sect. 2.5) and then C 1 / A/i 2dt can be resubstituted into eqn. (79) to give AE2 = AEM. The result is [69] 

In the faradaic rectification method, the perturbation is galvanostatic, i.e. the alternating current density, is controlled by the function Aj = yA sin u H t. This compels a rather trivial substitution for E occurring in the expressions for SF and Sc 

---

Recent Developments in Faradaic Rectification Studies Agarwal, H. P. 20... 

CS = coulostatic method, CV = cyclic voltamogram, FD = Faradaic distortion method, FR = Faradaic rectification, GD = galvanostatic double pulse method, IP = impedance method, PS = potential step method. See also list of... 

This value represents the upper limit of a first order reaction rate constant, k, which may be determined by the RHSE. This limit is approximately one order of magnitude smaller that of a rotating electrode. One way to extend the upper limit is to combine the RHSE with an AC electrochemical technique, such as the AC impedance and faradaic rectification metods. Since the AC current distribution is uniform on a RHSE, accurate kinetic data may be obtained for the fast electrochemical reactions with a RHSE. 

Relaxation methods for the study of fast electrode processes are recent developments but their origin, except in the case of faradaic rectification, can be traced to older work. The other relaxation methods are subject to errors related directly or indirectly to the internal resistance of the cell and the double-layer capacity of the test electrode. These errors tend to increase as the reaction becomes more and more reversible. None of these methods is suitable for the accurate determination of rate constants larger than 1.0 cm/s. Such errors are eliminated with faradaic rectification, because this method takes advantage of complete linearity of cell resistance and the slight nonlinearity of double-layer capacity. The potentialities of the faradaic rectification method for measurement of rate constants of the order of 10 cm/s are well recognized, and it is hoped that by suitably developing the technique for measurement at frequencies above 20 MHz, it should be possible to measure rate constants even of the order of 100 cm/s. 

The present chapter will cover detailed studies of kinetic parameters of several reversible, quasi-reversible, and irreversible reactions accompanied by either single-electron charge transfer or multiple-electrons charge transfer. To evaluate the kinetic parameters for each step of electron charge transfer in any multistep reaction, the suitably developed and modified theory of faradaic rectification will be discussed. The results reported relate to the reactions at redox couple/metal, metal ion/metal, and metal ion/mercury interfaces in the audio and higher frequency ranges. The zero-point method has also been applied to some multiple-electron charge transfer reactions and, wheresoever possible, these results have been incorporated. Other related methods and applications will also be treated. 

It was therefore thought appropriate to suitably modify and develop the faradaic rectification theory for the study of multiple-electron charge transfer reactions. 

If A co, is the rectification potential due to the first step of the reaction and AJECO 1 is the rectification potential contribution due to the second step, then the total rectified potential should be the sum of the rectified potentials for each individual step, i.e., AE + A oo . The combined faradaic rectification change for both the steps of electron charge transfer can be represented as38... 

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. 

Faradaic Rectification Studies at Metal Ion/Metal(s) Interfaces (f) Experimental Techniques... 

Figure 1. Circuit diagram for Faradaic rectification studies at metal ion/metal(s) interface.

Recently, the kinetic parameters for each step of this reaction in different supporting electrolytes have been obtained39,42 by applying the faradaic rectification theory as extended to multiple-electron charge transfer reactions. The kinetic parameters are listed in Table 1. 

By applying the recently developed theory of faradaic rectification as applied to multiple-electron charge transfer reactions under the condition that k° and C°R = 1. Kinetic parameters are obtained for each step of the electron charge transfer. The value of /c° reported is of the order of 10 6 to 10-9 cm/s whereas that of fc is of the order of 10 3 cm/s in different supporting electrolytes.51... 

Gaiser and Heusler53 have shown that the electrode reaction Zn2+ + 2e Zn proceeds in two steps Zn2+ 4- e Zn+ and Zn+ + e Zn(s). Van Der Pol et a/.,54 using ac coupled with the faradaic rectification polarography method, also concluded that this reaction is a multistep reaction. Hurlen and Fischer55 have studied this reaction in an acid solution of potassium chloride and... 

This reaction is found to be stable in sodium acetate and acetic acid buffer (pH 4.65), and so it has only been studied in this medium. The faradaic rectification theory becomes highly complicated when extended to three-electron charge transfer reactions due to the formation of the two intermediate species Al(II) and A1(I). In order to determine the three rate constants and the two unknown concentration terms, C°Rl and C°Ru, corresponding to the two intermediate species formed, it becomes necessary to carry out the experiment at five different concentrations of aluminum ion, each below 2.00 mM. 

---