Rotating disk electrode mass transfer

Mass-transfer rates from limiting-current measurements in well-supported solutions should invariably be correlated with ionic and not with molecular diffusivities. The former can be calculated from limiting-current measurements, for example, at a rotating-disk electrode. 

Experimental results obtained at a rotating-disk electrode by Selman and Tobias (S10) indicate that this order-of-magnitude difference in the time of approach to the limiting current, between linear current increases, on the one hand, and the concentration-step method, on the other, is a general feature of forced-convection mass transfer. In these experiments the limiting current of ferricyanide reduction was generated by current ramps, as well as by potential scans. The apparent limiting current was taken to be the current value at the inflection point in the current-potential curve. 

Recently significant advances have been made in the analytical solution of mass transfer to a sinusoidally modulated rotating disk electrode. The resulting expressions, confirmed by refined experimental techniques, allow deter-... 

Despite the importance of the ORR and long history of study, very little is known about the reaction mechanism.126,130,131 Mechanistic information has been derived almost exclusively from rotating disk electrode (RDE)131,132 and rotating ring disk electrode (RRDE)133-136,62,128 studies. The rotating electrode minimizes mass transfer effects and allows a kinetic current density to be extracted. In the RRDE setup, the ring surrounding the disk electrode detects species weakly adsorbed to the electrode that are ejected due to electrode rotation. The ORR reaction (eqn 4) is... 

The mass transfer boundary layer thickness, d, on a rotating disk electrode can be estimated by d = 1.6/J V a) where D is the substrate diffusion coefficient, v is the solution viscosity, and CO is the disk rotation speed. 

A rotating disk electrode (RDE) [7] is used to study electrode reactions, because the mass transfer to and from the electrode can be treated theoretically by hydrodynamics. At the RDE, the solution flows toward the electrode surface as shown in Fig. 5.22, bringing the substances dissolved in it. The current-potential curve at the RDE is S-shaped and has a potential-independent limiting current region, as in Fig. 5.6. The limiting current (A) is expressed by Eq. (5.33), if it is controlled by mass transfer ... 

C. Deslouis and B. Tribollet present the theoretical basis and state of the art of a novel technique for kinetic analysis, in which the mass transfer rate to a rotating disk electrode is modulated. The capabilities and limitations of this technique are demonstrated along with illustrations of typical applications. 

Koutecky-Levich plot — The diffusion-limited current fiim> diff at a -> rotating disk electrode is given by the -> Levich equation based totally on mass-transfer-limited conditions. The disk current in the absence of diffusion control, i.e., in case of electron transfer control, would be... 

The current densities in KIO3 are lower than in K3pe(CN)6 solutions. The pH of minimum potential is also shifted to somewhat higher pH in KIO3 solution. The difference in their behavior may be attributed to ionic radii of IO3 and Fe(CN)6 ions. IO3 ions have much larger size and are thus may provide a hindrance to the anodic dissolution reactions. The value of 5ln(Iss)/8pH is about 1.45. This is lower than the value of 2.303 obtained by Macdonald et al. This study was carried out in static environment, unlike the rotating disk electrode set-up used by MacDonald et al. The differences in the value of this slope may probably be attributed to the differences in mass transfer properties in solution. 

Figure 36. Current-voltage curves for a rotating disk electrode (1) without and (2) with substrate added. The regions indicated are a, control by electron transfer b, mixed control by electron and mass transfer c. control by mass transfer.

The rotating disk electrode, described in Section 11.6, has the advantage that the fluid flow is well defined emd that the system is compact and simple to use. The rotation of the disk imposes a centrifugal flow that in turn causes a radially uniform flow toward the disk. If the reaction on the disk is mass-transfer controlled, the associated current density is imiform, which greatly simplifies the mathematical description. As discussed in sections 5.6.1 and 8.1.3, the current distribution below the mass-transfer-limited current is not uniform. The distribution of current and potential associated with the disk geometry has been demonstrated to cause a frequency dispersion in impedance results. The rotating disk is therefore ideally suited for experiments in which the disk rotation speed is modulated while im-der the mass-transfer limited condition. Such experiments yield another t)q)e of impedance known as the electrohydrodynamic impedance, discussed in Chapter 15. 

On a film-covered rotating disk electrode, for example, the concentration of a mass-transfer-limited species is given by ... 

The mass-transfer problem for a rotating disk electrode at a constant rotation speed is presented in Section 11.6.2. Under modulation of the rotation speed of the electrode, equation (11.80) becomes... 

Graphical methods can be used to extract information concerning mass transfer if the data are collected under well-controlled hydrodynamic conditions. The systems described in Chapter 11 that are imiformly accessible with respect to convective diffusion would be appropriate. The analysis would apply to data collected on a rotating disk electrode as a function of disk rotation speed, or an impinging jet as a function of jet velocity. 

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 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, 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. 

D. T. Schwartz, T. J. Rehg, P. Stroeve, and B. G. Higgins, "Fluctuating Flow with Mass-Transfer Induced by a Rotating-Disk Electrode with a Superimposed Time-Periodic Modulation," Physics of Fluids A-Fluid Dynamics, 2 (1990) 167-177. 

M. Durbha and M. E. Orazem, "Current Distribution on a Rotating Disk Electrode Below the Mass-Transfer Limited Current Correction for Finite Schmidt Number and Determination of Surface Charge Distribution," Journal of The Electrochemical Society, 145 (1998) 1940-1949. 

With a few exceptions, the fluid flow must be simulated before the mass-transfer simulations can be rigorously performed. Nevertheless, here are several important situations, such as that at a rotating disk electrode, where the fluid flow is known analytically or from an exact, numerical solution. Thus there exists a body of work that was done before CFD was a readily available tool (for example, see Refs. 34-37). In many of these studies, a boundary-layer analysis, based on a Lighthill transformation (Ref. 1, Chapter 17), is employed. 

The electrochemical aspects of mass transfer are examined here at the electrode-, or separator- solution interface. In certain cases, such as with rotating disk electrodes, precise hydrodynamic analyses are possible and thus the diffusion equations for these systems can be solved exactly. 

FIGURE 26.21 Primary, secondary, and mass transfer limited current distributions on a rotating disk electrode of radius r . 

For a rotating disk electrode, the treatment of steady-state, mass-transfer-controlled electrode reactions applies, where the mass-transfer coefficient is mo = 0.61Dq Here, Dq is the dif-... 

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