Rotating uniform accessibility

The constancy of the diffusion layer over the entire surface and thus the uniform current-density distribution are important features of rotating-disk electrodes. Electrodes of this kind are called electrodes with uniformly accessible surface. It is seen from the quantitative solution of the hydrodynamic problem (Levich, 1944) that for RDE to a first approximation... 

Up until the mid-1940s, most physical electrochemistry was based around the dropping mercury electrode. However, in 1942, Levich showed that rotating a disc-shaped electrode in a liquid renders it uniformly accessible to diffusion, yet the hydrodynamics of the liquid flow are soluble and the kinetic equations relatively simple. In addition, in contrast to the case of a stationary planar electrode, the current at an RDE rapidly attains a steady-state value. 

When p = 1 (disc electrode), 5N is independent of r. This shows us immediately that the rotating disc electrode is a uniformly accessible surface, whereas the rotating ring electrode is not. Substitution of eqn. (24) into eqn. (22) and evaluation gives the well-known... 

The wall-jet disc electrode is clearly not uniformly accessible (current density oc r s/4 ). Another important point is that iL depends on the three-quarter power of the flow rate it is more sensitive in this sense than rotating or tube/channel electrodes. 

Besides the RDE and DME, other uniformly accessible electrodes under laminar flow have been described. They include the rotating hemispherical and rotating cone electrodes, which were developed to obviate the problem of trapped gas bubbles at the centre of an RDE their use is not widespread. 

One of the principal reasons for the extensive use of the rotating disc electrode is its uniform accessibility. However, if the solution conductivity is not sufficiently high, it does not have a uniform current distribution. Experimental investigations have provided criteria for the concentration of inert electrolyte necessary to add to ensure uniformity [89]. Current... 

Rotating electrodes have been used considerably owing to the simplifications introduced by the disc s uniform accessibility. 

A unique small active site close to a uniformly accessible rotating disk electrode is considered in this derivation. For the sake of simplification, the geometry of the active site is rectangular with its length perpendicular to the streamline of the flow (Fig. 5-1). By neglecting diffusion in the z direction, the mathematical problem is locally reduced to two dimensions, and the complete mass balance equation is formulated as follows ... 

In general, the effects of mass-transport limitations are not as easy to characterize. The direction of fluid flow, the flow regime, and the local fluid velocity all influence the current distribution. Fluid flow to the rotating disk is unusual in that fluid velocity normal to the disk is dependent only on the normal distance from the disk surface, and not on radial distance. Because the disk surface is uniformly accessible to incoming reactants, mass-transport limitations tend to reduce the current density in regions of high... 

Normally, such as at stationary planar electrodes and at uniformly accessible hydrodynamic electrodes, for example the rotating disc, the flux over the electrode surface is constant in this case we have the simple relation... 

A rotating disc sucks solution from below and spreads it out sideways. The rotating disc electrode is uniformly accessible, although the rotating ring is not (Fig. 8.2a). 

In Sections 6.3-6.5 expressions for the analysis of the voltammograms corresponding to the simple electron transfer process O + ne-— R, obtained for uniformly accessible electrodes such as the rotating disc electrode, were presented. In this section these expressions will be applied to hydrodynamic electrodes in general. 

For the rotating disc electrode, a uniformly accessible electrode, the concentration only varies in the direction perpendicular to the electrode hence the time-dependent convection-diffusion equation is given by equation (10.18) ... 

The rotating disk electrode (RDE) is an important system in electrochemistry. Axial followed by radial flow across the disk brings fresh solution to all points across the disk (Fig. 6). The surface is therefore uniformly accessible to reacting species. The RDE operates under laminar flow for Re < 1.7 X 105. Flow is turbulent above 3.5 X 105 and is transitional in between (4). Thus the system is less practical for the study of corrosion under turbulent conditions but enjoys widespread use in research electrochemistry. For the rotating disk electrode, the laminar mass transport correlation obtained in the literature is given by Levich (10) ... 

Both Sq and S have the same value over the entire electrode surface, which has given rise to the description of the electrode as a uniformly accessible surface. The concepts of a hydrodynamic and a diffusion boundary layer have no theoretical significance as such but serve mainly to provide a suitable model for the hydrodynamic conditions related to the rotating electrode. 

A refined process model was used that correctly accoimts for convective diffusion to a rotating disk electrode imder the assumption that the surface is uniformly accessible. This model also employs a constant-phase element to address complexities seen at high frequency. ... 

As indicated in the right panel in this figure, rotation about the main axis of the cylinder forces the solution toward the flat end that contains the inlaid disk and ring electrodes. As the surface is closely approached, the solution spreads outward, forming a uniformly accessible diffusion layer along the surface of the disk. The RRDE has proven exceedingly useful in studies of 02 reduction, as solution phase... 

Fig. 3. (a) A rapid transition in the number of electrons transferred (ntS) is observed at the uniformly accessible rotating disc electrode when the diffusion layer becomes sufficiently thin for the intermediate (shown stippled) to survive long enough to cross it (b) A more gradual transition is seen at the channel electrode, where some intermediate escapes (upstream electrode edge) and some is always trapped (downstream electrode edge), due to the shape of the diffusion layer. 

In hydrodynamic systems Planar diffusion to a uniformly accessible electrode, e.g. for rotating disk electrodes (hypothetical Nernst model with S = diffusion layer thickness)... 

The use of well-known model systems has been undertaken to confirm the validity and define the limits of the treatment of sonovoltammetry in line with the model of a uniformly accessible electrode and also to assess the influence of ultrasound on homogeneous chemical reactions coupled to the electron transfer. The uniformly accessible electrode model allows the introduction of a reaction layer, which has also been successfully employed for rotating disc voltammetry, in studies using channel electrodes [64] and in a slightly more complex form for studies in turbulent voltammetry [65]. 

We note from Eqn. 11 that the thickess of the diffusion layer is inversely proportional to Therefore as rotation speed is increased, the diffusion layer thickness decreases, and the rate of mass transfer to the electrode (the mass transport flux) increases. Hence we see that the diffusion layer thickness can be accurately controlled by means of the rotation speed. We also note from Eqn. 11 that the diffusion layer thickness is independent of the radial coordinate r (see Fig. 2.2). This means that the diffusion layer is uniformly thick over the entire surface of the electrode. In technical terms the electrode is said to be uniformly accessible, and as a consequence the current density is uniform over the entire surface of the disk. 

The RDE consists of a disc (e.g. of Pt, Ni, Cu, Au, Fe, Si, CdS, GaAs, glassy carbon and graphite) set into an insulating (PTFE) surround. The electrode is rotated about its vertical axis (Figure 11.13), typically between 400 and 10,000 rpm. The theory for the hydrodynamics at the RDE (40-42) assumes that the electrode is uniformly accessible and affords a precise and reproducible control of the convection and diffusion of reactant to the electrode. Hence, the RDE can be used to study the kinetics of interfacial processes. 

One should be careful in applying the foregoing considerations to electrodes of widely different dimensions. For example, if one were to employ the RDE in an industrial cell using, say, an electrode area of1000 cm, the critical Reynolds number would be reached at the rim of the electrode at a rotation rate of only 30 rpm, and turbulence could set in at even lower rotation rates. Such electrodes may still be of practical value in an industrial process, as long as one is aware that flow may become turbulent beyond a certain radius, and the surface will no longer be uniformly accessible. 

A solution to this problem is to use a rotating cone electrode (RConeE). It turns out that RCone electrodes are similar to RDE in that they act as uniformly accessible surfaces, producing a uniform rate of mass transport to all parts of the electrode surface. For a cone having an opening angle of 0, the current density is given by... 

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