Edge diffusion

In this case, however, if the step separation i is small, the consecutive steps are coupled via the terrace diffusion held, and the width cannot increase as fast as but increases slowly, like the edge-diffusion-limited growth, as [68]... 

Figure 1. Three limiting mechanisms for atomic processes which mediate step fluctuations, a) Step-edge diffusion b) Evaporation-recondensation c) Terrace diffusion with diffusion kernel P(). By appropriate choice of P(J), this case can reduce to cases a) and b) (see text).

Ignoring direct interactions, neighbouring steps do not influence each other if the dynamics is dominated by evaporation-recondensation or by step-edge diffusion. In either of these cases, the single step results derived in Section 2 (i.e. Eq. (22) and (26)) then hold. However, if the dynamics is mediated by terrace diffusion, neighbouring steps influence each other through the diffusion field on the terraces, and a coupled set of Langevin equations must be solved, as shown below (see also [13-17]). 

Some attention must be paid to the electrode dimensions (see Fig. 9.9). The working electrode s lower edge should be close to the bottom of the cell plates to minimize iR-drop problems. The width of the working electrode in contact with the thin layer of solution should be small to minimize edge diffusion. As noted earlier, a vertical orientation is not desirable however, it is convenient and compatible with the horizontal optical path of virtually all commercial spectrophotometers. Recommended sources of cell components (including minigrids) are listed in Table 9.1. Thin-layer cells for chromatographic detection and electron spin resonance spectroscopy are discussed in Chapters 27 and 29, and their application in optical studies is described in Chapter 3. 

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... 

Figure 23.6 Depiction of (left) linear diffusion and (right) combined linear and radial (or edge ) diffusion to electrodes.

Thus, in a step-edge site transfer mechanism there are two possible paths direct transfer to a kink site and the step-edge diffusion path. 

Edge diffusion — The diffusion edge is the fictional boundary between the diffusion layer and the bulk. It is a convenient concept when an extending diffusion later reaches an object to react, e.g., at a pair electrode and a -> scanning electrochemical microscope [i]. Ref. [i] Bard AJ, Faulkner LR (2001) Electrochemical methods, 2nd edn. Wiley, New York, p 669... 

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. 

One of the most important attributes of STM is the ability to quantitative evaluate the rate parameters associated with various surface processes. The dynamics of individual surface atoms, that is, terrace and step edge diffusion, have been monitored with STM, although for many... 

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]. 

Figure 1. Range of ultramicroelectrodes radii (rQ in fim) to be used to obtain an undistorted voltanunogram at a given scan rate (v in V.s ) as adapted from ref. 16. (i) limit for least edge diffusion interference (5% error on peak current, from ref. 15). (ii) limit for least ohmic drop due to Faradaic current (10 mV). limit for least ohmic drop due to capacitive current (10 mV) or cell constant. For a 90% on-line ohmic drop compensation boundaries ii and iH are pushed upward to and uigQ%t respectively. All limits are established for a one electron transfer at 20 C, ba on errors given above and D = 10 cm. s p = 20fi.cm, C = 10 /iF.cm and C = 5 mM. Above limit (io-) coupling between diffusion layer and double layer is predicted to occur. The thick horizontal line represents the location of the voltammograms shown in Figure 2.

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

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