Complex-Capacitance-Plane Representation

The double-layer capacitance of the blocking electrode can be obtained from the zero-frequency asymptote. The as3rmptotic value for the reactive system is scaled by the term (1 -f- Re/R).  

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The complex-capacitance-plane plot is presented in Figure 16.11. The data are presented as a locus of points, where each data point corresponds to a different measurement frequency. As discussed for the impedance- and admittance-plane representations (Figures 16.1 and 16.6, respectively), the complex-capacitance-plane... 

Therefore admittance data can also be plotted in the complex plane (V versus F with (o implicit). Some researchers choose to display data in terms of the complex capacitance C( o>) here C( a>) = Y j(o)lj(o. The latter type of representation can be useful when examining the electrochemical response of electronically conducting polymer films. The low-frequency redox pseudocapacitance can be read directly from a plot of C" versus C at low frequency. 

This impedance is plotted in the complex plane representation in Fig. 6. Qualitatively, the impedance appears to be a pure capacitance at low frequencies, where the phase angle tends toward ir/2. At higher frequencies. 

A2.4 Representation in the complex plane A2.5 Resistance and capacitance in series A2.6 Resistance and capacitance in parallel A2.7 Impedances in series and in parallel A2.8 Admittance... 

Fig. A2.1. Representation in the complex plane of an impedance containing resistive and capacitive components.

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... 

It is convenient to display the results of EIS in the complex-plane impedance representation. The X-axis on this plot is ReZ, which is the Ohmic resistance, and the y-axis is -ImZ, which, in the present case, is the capacitive impedance -j/o) C. 

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