Diffusion impedance rotating disk

Plot, on an impedance plane format, the impedance obtained for a Nernst stagnant diffusion layer and the impedance obtained for a rotating disk electrode under assumption of an infinite Schmidt number. Show that, while the behaviors of the two models at high and low frequencies are in agreement, the two models do not agree at intermediate frequencies. Explain. 

Solution At high-frequencies, all models for convective diffusion to a rotating disk approach the Vfarburg impedance, given as equation (11.52). Thus, the convective diffusion impedance can be expressed as Zo co) = Zd(0)/y/Jcor. Following Example 1.7, which... 

A Nemst stagnant-diffusion-layer model was used to accovmt for the diffusion impedance. This model is often used to account for mass transfer in convective systems, even though it is well known that this model caimot ac-coimt accurately for the convective diffusion associated with a rotating disk electrode. 

The quantitative and qualitative analysis presented in Section 20.2.1 demonstrates that the finite-diffusion-layer model provides an inadequate representation for the impedance response associated with a rotating disk electrode. The presentation in Section 20.2.2 demonstrates that a generic measurement model, while not providing a physical interpretation of the disk system, can provide an adequate representation of the data. Thus, an improved mathematical model can be developed. 

Figure 20.11 Normalized residual errors for the fit of the convective-diffusion models presented in Figure 20.12 to impedance data obtained for reduction of ferricyanide on a Pt rotating disk electrode a) real and b) imaginary.

The three-term convective-diffusion model provides the most accurate solution to the one-dimensional convective-diffusion equation for a rotating disk electrode. The one-dimensional convective-diffusion equation applies strictly, however, to the mass-transfer-limited plateau where the concentration of the mass-transfer-limiting species at the surface can be assumed to be both uniform and equal to zero. As described elsewhere, the concentration of reacting species is not uniform along the disk surface for currents below the mass-transfer-limited current, and the resulting nonuniform convective transport to the disk influences the impedance response. ... 

Zjt tabulated dimensionless values for diffusion impedance where fc = 1,2,3, see equation (11.97) for a rotating disk electrode and equation (11.109) for a submerged impinging jet... 

C. Deslouis, B. Tribollet, M. Duprat, and F. Moran, "Transient Mass Transfer at a Coated Rotating Disk Electrode Diffusion and Electrohydrodynamical Impedances," Journal of The Electrochemical Society, 134 (1987) 2496-2501. 

Impedance may also be studied in the case of forced diffusion. The most important example of such a technique is a rotating disk electrode (RDE). In a RDE conditions a steady state is obtained and the observed current is time independent, leading to the Levich equation [17]. The general diffusion-convection equation written in cylindrical coordinates y, r, and q> is [17]... 

Figure 7-14. Impedance diagrams of a diffusion-controlled reaction on a rotating disk electrode (RDE) System Pt/0.02 M [Fe(CN)6]. [Fe(CN)j] + 0.5 M Na2S04 (N2) rotation frequency/roi/s" a) 0, b) 10,...

An example of a transfer function based on a physical model is the Nemst impedance of a transport controlled electrode reaction. The impedance spectra in Fig. 7-14, which were obtained on a rotating platinum disk electrode at the equilibrium potential of the iron hexacyanoferrate redox system, exhibit the typical shape of a transport-controlled process. The transfer function cannot be described by a limited number of electrical circuit elements but must be derived from the differential equations of Fick s 2nd law and the appropriate boundary conditions. For finite linear diffusion, the so-called Nemst impedance Z can be derived theoretically... 

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