Diffusional impedance

It should be noted that the presence of diffusion controlled corrosion processes does not invalidate the EIS method but does require extra precaution. In the case of a finite diffusional impedance added in series with the usual charge transfer parallel resistance shown in Fig. 3b, the frequency-dependent diffusional impedance can be described as (21)... 

For coatings that are inherently porous, or have suffered extensive pitting, the generalized model in Fig. 22a describes the EIS response. Degraded conversion coatings often exhibit one or two time constants in addition to a diffusional impedance. 

A similar equation hut containing the function coth was used hy Inzelt and L ng to descrihe the diffusional impedance of conducting polymers under reflective conditions [see Section III.6(ii) and Eq. (99)]. An electrical model containing this element accounted well for the impedance spectra, with a minimum number of free parameters. 

Practical limitations are imposed at low frequencies, however, where the rectification-smoothing function necessary to transduce the ac voltage magnirnde to a dc level becomes inaccurate. Ac voltmeters typically become seriously in error at frequencies below 20Hz. To obtain an accurate KK transform, it is necessary to extend the measurement frequency range significantly beyond the limits of frequency needed to elucidate the equivalent circuit under test. Thus, the method described here is not appropriate for aqueous electrochenfical systems for which the diffusional impedance is prominent. This method can be useful for systems in which the lowest frequency of interest is greater than 50 Hz or so, as is usually the case for solid ionic conductors, oxide films, and semiconductor surfaces. 

D. Gas phase diffusional impedance. This arc is observed mainly in high performance cathodes, and increases with cathodic polarization (negative applied potential). The observed impedance is in accordance with the presence of a stagnant gas layer close to the electrode surface. 

Figure 4.3.17. The Randles equivalent circuit, with resistance of a charge-transfer process and the diffusional impedance Z. R f and CPE i are the high frequency resistance and the double layer distributed capacitance, respectively.

The theoretical treatments referenced above all suffer from a major deficiency. The nonlinear term of interest in corrosion (the electron transfer process) is contained within a circuit comprising other linear (electrolyte resistance) and nonlinear (double-layer capacitance and diffusional impedance) terms. Since the voltage dropped across nonlinear circuit elements cannot be considered to linearly superimpose, we cannot use the equivalent circuit method to isolate the impedance terms of interest. Properly, one must solve for the system as a whole, including diffusional and double-layer terms, and identify the harmonic components associated with the faradic process of interest. 

Abrantes, L., Fleischmann, M. and Peter, L. (1988) On the diffusional impedance of microdisc electrodes. Journal ofElectroanalytical Chemistry and Interfacial Electrochemistry, 256, 229-233. 

Following this idea we can write the diffusional impedance at any frequency as... 

What about the situation at very high frequencies In this case the diffusional impedance can be neglected, and the Faradaic impedance Zp is given by Zp = / ct Hence Eqn. 346 reduces to... 

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