Edge diffusion effects

Advances in mathematical approaches to the semiintegration of electrochemical data allowed Saveant etal. [22,27], as well as Oldham and Mahon, who introduced the so-called extended semiintegrals [25], to minimize the above-mentioned constraints, although at the cost of increased complexity in computation methods. The problem of the computation of edge diffusion effects with reasonable computational times was elegantly solved by the introduction of partial sphere approximations [26, 29], which simplify the two-dimensional diffusion problem into an easily solved one-dimensional one. Estimation of the planar component needed for semiintegral analysis can be performed by convolutive reshaping, as described by Mahon [29]. 

Other transport limitations, such as diffusion-controlled reactions, can lead to localized depletion of etchant, which results in a number of observable etch effects. The size and density of features can influence the etch rate at different locations on a single wafer, thus producing "pattern sensitivity." Depletion across a wafer produces a "bulls eye" effect, while depletion across a reactor is indicated by the fact that the leading wafer edge etches faster than the trailing edge. Similar effects are noted when product removal is transport-limited. Most of these effects can be reduced... 

Above and to the right of line A, the contribution of edge diffusion will be less than 3 %. This is convenient when quantitative interpretation of the data is attempted, because the calculation of the effects of edge diffusion are somewhat more complicated than planar diffusion. Below and to the left of line B, the iR error will be less than 3 mV. Finally, it is desirable to work in the region to the left of line C where distortion of the shape of the voltammogram by the RC time constant of the cell is not significant. Figure 16.6 predicts that... 

All terms of the transport equations are retained and included in the solution. This is significant because both thermal diffusion effects and the ion drag affect the calculated performance. Boundary conditions for these equations have electron retaining sheaths at the edges of the plasma. Electrode area ratios and electron reflectivities are included in the boundary conditions also. Electron back emission from the collector is in the collector side boundary conditions, but ion emission from the emitter has been neglected. 

If reaction is initiated rapidly and extensively across all faces of a cube [1,2] of edge a, then, after a short time, close spacing of nuclei results in the rapid (low ar) generation of a coherent reaction zone that, in the absence of diffusion effects (considered below), advances inwards at a constant rate ( g). The progress of this reaction is described by [1-5] ... 

Most of the initial practical and theoretical work in cyclic voltammetry was based on the use of macroscopic-sized inlaid disc electrodes. For this type of electrode, planar diffusion dominates mass transport to the electrode surface (see Fig. II. 1.13a). However, reducing the radius of the disc electrode to produce a micro disc electrode leads to a situation in which the diffusion layer thickness is of the same dimension as the electrode diameter, and hence the diffusion layer becomes non-planar. This non-linear or radial effect is often referred to as the edge effect or edge diffusion . 

Nonlinear diffusion. The voltammetric behavior related to linear (e.g. at short times) and spherical (e.g. at large times or small electrodes) diffusion has been discussed in Sect. 2.1.2. Of course, there are intermediate situations, in which mixed behavior is observed, which may be regarded as a distortion of either of the extreme types of transport. In particular, use of conventionally sized electrodes at slow scan rates causes the increase of peak currents (normahzed to with decreasing v since additional nonlinear transport of material across the edge of the electrode occurs ( edge diffusion or edge effect [47]). Consequently, too slow scan rates should be avoided. 

Edge effect — Enhanced diffusion to the edges of an inlaid electrode. See electrode geometry, and diffusion, subentry -> edge diffusion. 

While the axial position of multistage impellers to their diffusers is not critical, they should line up reasonably well. Impellers are not extremely sensitive to leading-edge dings and minor damage, but anything, such as erosion on the exit tips, that tends to decrease the effective diameter of the impeller is more serious. Front shroud clearance on open impellers should be maintained close to the design values to minimize capacity loss. 

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