Very edge current density

This consideration of the very edge current density can be elaborated mathematically in the following way [5] assuming the total ohmic control, the voltage drop in the solution between the electrodes inside the homogeneous field is given by... 

The UMDE evinces strong edge effects or very uneven current densities along the radius of the disk. It shares this problem with all the other flat microelectrodes such as microbands or rings. The exception of course are the hemispherical or hemicylindrical microelectrodes, which have no effective edges and behave as half of a sphere or cylinder, and also deeply recessed disks or bands, which approach the shrouded types. 

In such cases basket anodes are frequently used. These have a relatively large surface and work at a low driving voltage due to their special construction. A cylinder of platinized titanium-expanded metal serves as the basket to which a titanium rod is welded. This serves as the current lead and carrier, and ends in a plastic foot that contains the cable lead and at the same time serves as the mounting plate. The expanded metal anode exhibits a very uniform anode current density distribution, even at large dimensions, in contrast to the plate anode. The reason is the many comers and edges of the metal that make the point effect only evident at the outer edges of the anode. 

In these clusters tantalum atoms are bound to other tantalum atoms and are also edge bridged via halide. As our deposit was completely amorphous without any XRD peak we concluded that it did not consist of crystalline tantalum but rather of such clusters. We varied the electrode potential for deposition and tried deposition with very low constant current densities, but in no case was crystalline tantalum obtained. Thus, the electrochemical window of our liquid was surely wide enough, but for some reason the electrodeposition stopped before Ta(0) was obtained. When we studied the literature dealing with metal clusters we found that the cluster chemistry with fluoride seems to be less comprehensive. Consequently... 

The local current density on an electrode is a function of the position on the electrode surface. The current distribution over an electrode surface is complicated. Current will tend to concentrate at edges and points, and unless the resistance of the solution is very low, it will flow to the workpieces near the opposite electrode more readily than to the more distant work-pieces. It is desired to operate processes with uniform current distribution. That is, the current density is the same at all points on the electrode surface. 

As an example, Fig. 2.9 is a sketch of the various current distributions for a parallel-plate cell with electrodes of length L and of infinite width, and with fully developed laminar flow. The primary current distribution shows the current to be uniform over most of the electrode but with a considerable edge effect at x = 0 and jc = L the current goes to a very high value at these ends. The secondary distribution is similar but is even closer to the ideal while the limiting tertiary distribution shows that in these conditions the current density drops sharply along the electrode. 

It can be assumed that a homogeneous electric field and, consequently, a uniform current density distribution are present over the entire electrode surface up to the very edge of the electrode, where the current density increases abruptly. This problem has been studied in detail in Refs. [2, 3, 5-7], and a relatively rough approximation will be used here. This approximation is based on the following assumptions ... 

Taking into account Eqs. (3.10) and (3.12) for L) >0 (assuming that the current density in the homogeneous field is equal to the overall one, i.e., that the current density distribution is uniform over the entire electrode, except for the very edge), Eq. (3.24) can be rewritten in the form ... 

The electrolyte resistivity increases with the decrease of the H2SO4 concentra-ti(Mi (Fig. 3.8c). In this way, the ohmic potential drop becomes more significant. The polarization curves lose their S shape and become more straight Unes. The limiting current density plateau is not so weU pronounced, and it becomes shorter as the / values increase. Finally, the plateau of the limiting diffusion current density disappears at very large electrode edge-side waU distances. This is illustrated for / = 50 mm. 

The overpotential-apparent current density and the cell voltage (edge overpotential)-apparent current density plots for the Ag deposition from both the nitrate and the ammonium electrolytes are presented in Fig. 3.16a, b, respectively. For Ag deposition from the nitrate electrolyte, /q > > is valid, and at / < < nucleation in the middle of the electrode does not occur because the overpotential is very low. Hence, deposition from the nitrate electrolyte is only expected at the... 

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