Warburg impedance absence

At high frequencies, a semicircle is expected as a result of a parallel combination of R and Cg. At low frequencies a Warburg impedance may be found as part of the interfacial impedance. In some cases it may dominate the interfacial impedance as in Fig. 10.13(a), in which case only the diffusion coefficient of the salt will be determinable. It should be noted that, in the absence of a supporting electrolyte, the electroactive species, in this case Li, cannot diffuse independently of the anions. 

III.l [see also Eq. (17) and Fig. 2], and that in the presence of a faradaic reaction [Section III. 2, Fig. 4(a)] are found experimentally on liquid electrodes (e.g., mercury, amalgams, and indium-gallium). On solid electrodes, deviations from the ideal behavior are often observed. On ideally polarizable solid electrodes, the electrically equivalent model usually cannot be represented (with the exception of monocrystalline electrodes in the absence of adsorption) as a smies connection of the solution resistance and double-layer capacitance. However, on solid electrodes a frequency dispersion is observed that is, the observed impedances cannot be represented by the connection of simple R-C-L elements. The impedance of such systems may be approximated by an infinite series of parallel R-C circuits, that is, a transmission line [see Section VI, Fig. 41(b), ladder circuit]. The impedances may often be represented by an equation without simple electrical representation, through distributed elements. The Warburg impedance is an example of a distributed element. 

Experiments carried out on monocrystalline Au(lll) and Au(lOO) electrodes in the absence of specific adsorption did not show any fre-quency dispersion. Dispersion was observed, however, in the presence of specific adsorption of halide ions. It was attributed to slow adsorption and diffusion of these ions and phase transitions (reconstructions). In their analysis these authors expressed the electrode impedance as = R, + (jco iJ- where is a complex electrode capacitance. In the case of a simple CPE circuit, this parameter is = T(Jcaif. However, an analysis of the ac impedance spectra in the presence of specific adsorption revealed that the complex plane capacitance plots (C t vs. Cjnt) show the formation of deformed semicircles. Consequently, Pajkossy et al. proposed the electrical equivalent model shown in Fig. 29, in which instead of the CPE there is a double-layer capacitance in parallel with a series connection of the adsorption resistance and capacitance, / ad and Cad, and the semi-infinite Warburg impedance coimected with the diffusion of the adsorbing species. A comparison of the measured and calculated capacitances (using the model in Fig. 29) for Au(lll) in 0.1 M HCIO4 in ths presence of 0.15 mM NaBr is shown in Fig. 30. 

In the context of EMM, the diffusion layer thickness at the anode may be more compared to that in conventional ECM due to absence of high flow rate of the electrolyte. Hence the effect of Warburg impedance is more prominent during anodic dissolution in the microscopic domain. 

Figure 5.11. (a) Electrical equivalent circuit model used to represent an electrochemical interface undergoing corrosion in the absence of diffusion control. Rp is the polarization resistance, Cpi is the double layer capacitance, Rp is the polarization resistance, and R, is the solution resistance [15]. (b) Electrical equivalent circuit model when diffusion control applies W is the Warburg impedance [13]. 

The kinetic impedance Zj represents the faradaie impedance in the absence of a concentration overpotential. In the simplest case, the kinetie impedance corresponds to the transfer resistance Rt, but in more complicated situations it may include several circuit elements. The diffusion impedance Z describes the contribution of the concentration overpotential to the faradaic impedance and therefore depends on the transport phenomena in solution. In the absence of convection, it is referred to as the Warburg impedance and, in the opposite case, as the Nernst impedance Z. ... 

As we noted earher, at w = 1, Eq. (8.24) transforms into the relationship for electrical capacitance. The average value of n for Q j is 0.9, and this is indicative of the capacitive nature of Q j, which can be considered the electrical analog to the double layer. Then, it is possible to assume that the parameter Eq approximately represents the double-layer capacitance, which amounts to 70—90 pF cm . Somewhat higher values of Eq were obtained for the Cu Cu(II) system in the absence of adsorption of organic substances [71, 76]. In the IPS series, the total Cu(ll) concentration varied from 6.5 to 15 mM. According to the well-known equation for Warburg impedance [77], it is possible to estimate the value of Eq, which amounts to about 0.1 cm s - for a 10 mM Cu(II) solution and the transfer of one elec-... 

In the case of cell E2 in the absence of defects with variable charges the proportionality factor is (Reon + R-ion)- The Warburg impedance can itself be built... 

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