A theoretical D.C. polarographic and faradaic impedance study of systems with first-order chemical reactions following and preceding the charge transfer step: the CEC and the CECEC mechanism
✍ Scribed by P.W.C. Migchielsen; M. Sluyters-Rehbach; J.H. Sluyters
- Publisher
- Elsevier Science
- Year
- 1973
- Weight
- 830 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0022-0728
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✦ Synopsis
polarogram makes it possible to handle the waves separately. Then the problem is simplified considerably, different boundary conditions for both waves being used.
In this paper we will discuss the d.c. polarographic behaviour and the frequency and potential dependence of the faradaic impedance parameters for both the Nernstian and non-Nernstian case.
The resulting equations can be easily transformed into simpler ones for limiting cases of the mentioned reaction mechanism.
THE ORETICAL
If the d.c. polarogram of a solution, containing the reducible species O and Y, which are in chemical equilibrium with each other, shows two well-defined waves, the first wave can be ascribed to the reduction of the more reducible species, e.g.O. So, in the potential region of the first wave, Y is not reducible and reaction scheme (R4) simplifies to scheme (R3).
Reaching the potential region where also Y is reducible, the second wave in the d.c. polarogram arises; the shape of this wave will be controlled by the mass transfer of both species O and Y. However, it was assumed that the second wave appears in the limiting current region of the first wave. Then the surface concentration of O will be zero in the potential region of the second wave. Use of this boundary condition makes it possible to give a relatively simple solution of the mass transfer problem pertaining to the second wave.
Several authors 7-lo have given general solutions for mechanisms involving first-order chemical reaction coupled to a single charge transfer step. Recently, equations for a.c. polarographic waves have been derived on the basis of the expanding plane model 11-~3. From these treatments, which must be considered asthe most rigorous for a DME, a study could be made of the amplitude and phase angle of the faradaic admittance as functions of frequency and potential in the case of a CEC mechanism (scheme R3) and probably of a CECEC mechanism (scheme R4). However, in order to check whether measured impedances are in accordance with a certain model, it is more profitable to have expressions for the potential and frequency dependence of the real component Yo' I and the imaginary component Y~' I' of the electrode admittance. These could be derived from the theories mentioned, but only in a very implicit form, which should be handled numerically. Therefore, we prefer a less rigorous, but much simpler approach, assuming that the surface concentrations of a species i can be split up into a d.c. component ci and an a.c. component Aq. As before, we will make use of a treatment given by Jacq to express ~ as a function of potential, which is based on the concepts of the diffusion layer theory ~4'~5. This treatment will serve both to describe the d.c. current-voltage characteristic and the potential dependence of ~l and Y~' v 1. The d.c. polarogram (R3) 1.1 The first wave As stated before, the first wave can be described with the aid of reaction scheme kl ksh, i k4 Y~+~-O+ne( -'R~A (R3) k2 E~ k 3