Transfer function complex capacitance

For this potential, the plot of the electrochemical capacitance Aq/AE(o)) (Fig. 21b) in the complex plane shows two loops. This demonstrates that two charged species are involved in the charge compensation process. For E = —0.55 V vs. SCE, the plot of Am Aq co) also shows two loops like in the simulation part (see Fig. 12). This demonstrates that the solvent is involved in the redox reaction in addition to anions and cations. Now, the plots of the partial electrogravimetric transfer function will help to identify the loop related to each species. 

The above analysis shows that in the simple case of one adsorbed intermediate (according to Langmuirian adsorption), various complex plane plots may be obtained, depending on the relative values of the system parameters. These plots are described by various equivalent circuits, which are only the electrical representations of the interfacial phenomena. In fact, there are no real capacitances, inductances, or resistances in the circuit (faradaic process). These parameters originate from the behavior of the kinetic equations and are functions of the rate constants, transfer coefficients, potential, diffusion coefficients, concentrations, etc. In addition, all these parameters are highly nonlinear, that is, they depend on the electrode potential. It seems that the electrical representation of the faradaic impedance, however useful it may sound, is not necessary in the description of the system. The systen may be described in a simpler way directly by the equations describing impedances or admittances (see also Section IV). In... 

In the restricted case of linear constitutive properties, by multiplying the previous transformed function (shown in Equation 11.51) by the capacitance, one is able to express the transformed effort, and then deduce the well-known expressions of the complex transfer fnnctions that are the admittance and the impedance ... 

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