Impedance models 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. 

Table 20.2 Estimated /v values for the regression of the model presented in Figure 20.1 to impedance data obtained for reduction of ferricyanide on a Pt 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. 

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. ... 

M. Durbha, M. E. Orazem, and B. Tribollet, "A Mathematical Model for the Radially Dependent Impedance of a Rotating Disk Electrode/ Journal of The Electrochemical Society, 146 (1999) 2199-2208. 

Very often modeling depends on the errors in the experimental data. Orazem et al. studied the approximation of synthetic data corresponding to the impedance response of a single electrochemical reaction on a rotating disk electrode under the conditions of nonuniform current and... 

Figure 4.4.12. Steady state polarization curves for iron in NaS04-H2S04 solutions according to Keddam et al. [1981] (a) Simulated curves, b) Experimental data. Rotating disk electrode (rotating speed = 1600rpm, diameter = 3 mm), T = 25 0.2°C. (From M. Keddam, O. R. Mattos, and H. J. Takenouti, Reaction Model for Iron Dissolution Studied by Electrode Impedance Determination of the Reaction Model, J. Electrochem. Soc., 128, 257-274, [1981]. Reprinted by permission of the publisher. The Electrochemical Society, Inc.)...

This part demonstrates how deterministic models of impedance response can be developed from physical and kinetic descriptions. When possible, correspondence is drawn between hypothesized models and electrical circuit analogues. The treatment includes electrode kinetics, mass transfer, solid-state systems, time-constant dispersion, models accounting for two- and three-dimensional interfaces, generalized transfer functions, and a more specific example of a transfer-function tech-nique.in which the rotation speed of a disk electrode is modulated. 

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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