Equivalent circuit Randles-type

The impedance data have been usually interpreted in terms of the Randles-type equivalent circuit, which consists of the parallel combination of the capacitance Zq of the ITIES and the faradaic impedances of the charge transfer reactions, with the solution resistance in series [15], cf. Fig. 6. While this is a convenient model in many cases, its limitations have to be always considered. First, it is necessary to justify the validity of the basic model assumption that the charging and faradaic currents are additive. Second, the conditions have to be analyzed, under which the measured impedance of the electrochemical cell can represent the impedance of the ITIES. 

In particular, the coupling between the ion transfer and ion adsorption process has serious consequences for the evaluation of the differential capacity or the kinetic parameters from the impedance data [55]. This is the case, e.g., of the interface between two immiscible electrolyte solutions each containing a transferable ion, which adsorbs specifically on both sides of the interface. In general, the separation of the real and the imaginary terms in the complex impedance of such an ITIES is not straightforward, and the interpretation of the impedance in terms of the Randles-type equivalent circuit is not appropriate [54]. More transparent expressions are obtained when the effect of either the potential difference or the ion concentration on the specific ion adsorption is negli-... 

Under this electrochemical configuration, it is commonly accepted that the system can be expressed by the Randles-type equivalent circuit (Fig. 6, inset) [23]. For reactions on the bare Au electrode, mathematical simsulations based on the equivalent circuit satisfactorily reproduced the experimental data. The parameters used for the simulation are as follows solution resistance, = 40 kS2 cm double-layer capacitance, C = 28 /xF cm equivalent resistance of Warburg element, W — R = 1.1 x 10 cm equivalent capacitance of Warburg element, IF—7 =l.lxl0 F cm (

charge-transfer resistance, R = 80 kf2 cm. Note that these equivalent parameters are normalized to the electrode geometrical area. On the other hand, results of the mathematical simulation were unsatisfactory due to the nonideal impedance behavior of the DNA adlayer. This should... 

Fig. 16.5 Randles-type equivalent circuit for the interface between the electrode and the electrolyte...

Determination of Parameters from Randles Circuit. Electrochemical three-electrode impedance spectra taken on electrochromic materials can very often be fitted to the Randles equivalent circuit (Randles [1947]) displayed in Figure 4.3.17. In this circuit R /denotes the high frequency resistance of the electrolyte, Ra is the charge-transfer resistance associated with the ion injection from the electrolyte into the electrochromic film and Zt, is a Warburg diffusion impedance of either semi-infinite, or finite-length type (Ho et al. [1980]). The CPEdi is a constant phase element describing the distributed capacitance of the electrochemical double layer between the electrolyte and the film having an impedance that can be expressed as... 

Impedance Spectroscopy. Impedance spectroscopy has been carried out on devices with WO3 as the cathodic electrochromic layer, counter electrodes of iridium oxide, polyaniline or Prussian blue, and polymers as electrolytes (Katsube et al [1986], Friestad et al [1997]). The equivalent circuit for a whole device becomes very complicated. In the works quoted above simplified, Randles-type circuits were used for the two electrochromic layers, while the ion conductor was modeled by a pure resistance, or neglected. Extraction of device parameters from the data fitting was reported. However, it is clear that in many cases it will be difficult to distinguish the contributions from the different layers in a device, in particular if the migration impedances, ion diffusion impedances, etc. are of the same order of magnitude. When it comes to characterizing electrochromic devices, impedance spectroscopy is a very time-consuming process, since a spectrum down to low frequencies should be taken at a number of equilibrium potentials. Thus we believe that transient current measurements in many cases offer a faster alternative that sometimes allows a simple determination of diffusion coefficients. 

We extend the analysis and consider the entire ladder network in terms of distinct R and C circuit elements. The impedance x can be represented by a resistance Ri, which defined the resistance of counterions in the pore electrolyte. Furthermore the impedance element z, which is that of the solid polymer, is replaced by a Randles equivalent circuit (see Fig. 1.84), where there is a parallel arrangement of a resistor Rj. and a capacitor Q in series with a resistor Ra- Hence we see that the pore solution is modeled in terms of a simple resistor, whereas the solid polymer is a binary composite medium. TTie latter assumption can be justified as follows. From a macroscopic viewpoint (and this has been demonstrated experimentally), the electronic resistance of the polymer is due to two contributions the first, Ra, from regions of high structural order the second, R, from regions of low structural order. Hence Ra is smaller than R. From a microscopic point of view, the polymer may exhibit two fundamentally different types of conduction. As noted in... 

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