Diffusion impedance Rotational

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... 

Table 18.1 Experimental diffusion impedance data obtained at a rotation speed of 600 rpm.

The experimental diffusion impedance data presented in Table 18.1 were obtained at a rotation speed of 600 rpm. Find the numerical value of the Schmidt number by using equation (18.3). 

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. 

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... 

The solvated electron concentration was estimated chronopotentiometrically on a rotating disc electrode and by measuring the diffusion impedance both... 

In the diffusion region the reorientational motion of the molecules is impeded by a frictional force exerted by a medium considered structureless (continuum). For a spherical molecule, the rotational diffusion coefficient, D, is given by the Stokes-Einstein-Debye equation42... 

Closely linked to its extraordinary solvent capacities is water s role in transporting dissolved materials throughout the organism. With the exception of air-filled channels like the tracheal systems of insects, most of the transport processes of organisms involve movement of dissolved solutes. Diffusion of solutes within water is rapid, as is the translational and rotational movement of water itself. The extensive networks of hydrogen bonds that form among water molecules and between water and solutes do not impede this dynamic move-... 

The last of these is the impedance which has been considered throughout this chapter. We now consider forced convection. For low frequencies the diffusion layer thickness due to the a.c. perturbation is similar to that of the d.c. diffusion layer in these cases convection effects will be apparent in the impedance expressions. For the rotating disc electrode these frequencies are lower than 40 Hz33. For higher frequencies where the two diffusion layers are of quite different thicknesses, the advantage of hydrodynamic electrodes is that transport is well defined with time, as occurs with linear sweep voltammetry. 

On a RDE, in the absence of a surface layer, the EHD impedance is a function of a single dimensionless frequency, pSc1/3. This means that if the viscosity of the medium directly above the surface of the electrode and the diffusion coefficient of the species of interest are independent of position away from the electrode, then the EHD impedance measured at different rotation frequencies reduces to a common curve when plotted as a function of p. In other words, there is a characteristic dimensionless diffusional relaxation time for the system, pD, strictly (pSc1/3)D, which is independent of the disc rotation frequency. However, if v or D vary with position (for example, as a consequence of the formation of a viscous boundary layer or the presence of a surface film), then, except under particular circumstances described below, reduction of the measured parameters to a common curve is not possible. Under these conditions pD is dependent upon the disc rotation frequency. The variation of the EHD impedance with as a function of p is therefore the diagnostic for... 

Finite diffusion — Finite (sometimes also called -> limited) diffusion situation arises when the -> diffusion layer, which otherwise might be expanded infinitely at long-term electrolysis, is restricted to a given distance, e.g., in the case of extensive stirring (- rotating disc electrode). It is the case at a thin film, in a thin layer cell, and a thin cell sandwiched with an anode and a cathode. Finite diffusion causes a decrease of the current to zero at long times in the - Cottrell plot (-> Cottrell equation, and - chronoamperometry) or for voltammetric waves (see also - electrochemical impedance spectroscopy). Finite diffusion generally occurs at -> hydrodynamic electrodes. 

In membrane separation of the olefin/paraffin mixture, the predominant selective separation of the olefin is evident. First, the olefin molecule is smaller in size compared to the respective paraffin. Specifically, C—C distance in paraffins is 0.1534 nm, whereas the C=C distance in olefins is 0.1337 nm. Atoms of carbon in paraffins feature sp hybridization and free rotation around C—C bonds. Atoms of olefins feature sp hybridization. The rigid C=C bond impedes internal rotation in the olefin molecule and makes it flat. It is therefore clear why olefin molecules are smaller in size compared to paraffin and why the diffusion coefficients of olefins in polymers would be higher than those of paraffins. Second, the presence of unsaturated bonds in olefin molecules makes them capable of specific interactions with the membrane matrix. Efforts to take advantage of these capabilities resulted in the development of an important field of research facilitated transport. 

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. 

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. ... 

C. Deslouis, I. Epelboin, C. Gabrielli, and B. Tribollet, "Impedance Elec-trom canique obtenue au Courant Limite de Diffusion a Partir d lme Modulation Sinusoidale de la Vitesse de Rotation d une Electrode a Disque," Journal of Electroanalytical Chemistry, 82 (1977) 251-269. 

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. 

For details and an exact derivation of the reader is referred to ref. [13]. The derivation also shows that Z is in series with as shown in Fig. 4.13a. Typically, the Warburg impedance leads to a linear increase of Z with rising Z" and the slope is 45° as also shown in Fig, 4.13a. In this case, Z has been calculated assuming an infinite thickness of the diffusion layer. Any convection of the liquid limits the thickness of the diffusion layer. The latter is limited to a well defined value when a rotating disc electrode is used (see Section 4.2.3). In this case, the impedance spectrum is bent off at low frequencies as shown in Fig. 4.13b. The Z branch i.s only linear at its high frequency end where it shows a slope of 45°. 

The rotational motion of the water molecules in the cage is impeded, and this affects viscosity and diffusion rates. 

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