Ohmic control

Oldham and Mansfeld" approached the problem of linearity in a different way and their derivation avoids the approximation used by Stern and Geary. They conclude that although linearity is frequently achieved this is due to three possible causes (a) ohmic control due to the IR drop rather than control according to linear polarisation, (b) the similarity of the values of b, and be and (c) a predisposition by the experimenter to assume that the AE — Ai curves near must be linear. In a later paper Oldham and Mansfeld" showed that linearity of the AE — Ai curve is not essential and... 

Mass-transport deposition control occurs when the exchange current density P is high and the limiting current density is low. Ohmic resistance can be a cause of nonuniformity if there is an appreciable difference in solution resistance from the bulk of the solution to peaks or to recesses. Distribution of the current density will be such that ip > i. and peaks will receive a larger amount of deposit than will recesses. Distribution of deposit in the triangular groove under conditions of mass transport and ohmic control nonuniform deposition, with ip > is shown in Figure 10.14. 

Under the conditions shown in Figure 10.14, the roughness of the surface increases. Thus, to get leveling of the surface it is necessary to change from diffusion and ohmic control to activation control. Activation control can result in uniform deposition (ip = iy) or in nonuniform deposition (with i. > ip). In nonuniform deposition with... 

Figure 10.14. Distribution of deposit in a triangular profile when 8. > 8p and ir

Hunkeler and Bohni used this approach to show that pit growth in A1 foils occurred under ohmic control (24). It was also shown that nitrate and chromate inhibitors, added to the electrolyte after pit initiation, inhibited pit growth kinetics though the effect due to chromate additions was small. Several other inhibitors added to solution increased pit growth kinetics, since their primary influence was in decreasing the solution resistance. 

When all the above conditions are met, as shown in Fig. 10.18, protruding and recess areas are in different electrochemical conditions. The protruding area directly contacts electrolyte and electrochemical dissolution occurs under ohmic control that is, its dissolution rate (/ d) is determined by the polarization... 

Ohmic Control The overall electrochemical reactor cell voltage may be dependent on the kinetic and mass-transfer aspects of the electrochemical reactions however, a third factor is the potential lost within the electrolyte as current is passing through this phase. The potential drops may become dominant and limit the electrochemical reactions requiring an external potential to be applied to drive the reactions or significantly lower the delivered electrical potential in power generation applications such as batteries and fuel cells. 

Using the recently derived equation (44), it was possible to elucidate the Ohmic-controlled electrodeposition of metals by the consideration of silver electrodeposition on the graphite electrode, where each microelectrode was independent relative to the other ones. 

In the case under consideration, complete Ohmic control of the deposition process can be expected for 70//L > 100 up to a current density about 0.95yh (Fig. 7) and for yo/yh = 10 up to 0.6yh (Fig. 9). It is obvious from Figs. 7-10 that, regardless of the shape of the polarization curve, which depends on the jo/jh ratio and /c, a limiting diffusion current density plateau is present in all cases. 

Obviously, increasing the concentration of the reacting ion and decreasing the concentration of the supporting electrolyte in a simple salt solution stimulates Ohmic control of the deposition process, but a large value of the exchange current density seems to be the most important for it (Figs. 9 and 10). 

The initiation of dendritic growth is followed by an increase of the deposition current density, and the overall current density will be larger than the limiting diffusion current on a flat active electrode. Based on the above discussion, the polarization curve equation in the Ohmic-controlled electrodeposition of metals can be determined now by 9... 

It is interesting to note that (67c) describes qualitatively the increase of the apparent current density over the value of the limiting diffusion current density after initiation of dendritic growth, since the quantitative treatment of the polarization characteristics in the presence of dendrite growth is simply impossible. This is because dendrites can have a variety of unpredictable structures. In this way, the results of Ibl and Schadegg,59 Diggle et al.,12 and Popov et al.,21 as well as the Ohmic-controlled deposition of tin,57 silver,7 and lead,58 could be explained qualitatively. 

Thus, instead of a limiting diffusion current density plateau, a curve inflection point or a short inclined plateau can be expected on the polarization curve in Ohmic-controlled electrodeposition of metals, as observed in the case of silver electrodeposition from nitrate solutions. The exchange current density of the silver reaction in nitrate electrolytes is sufficiently large to permit Ohmic-controlled deposition as well as dendritic growth at low overpotentials.27 After a linear increase of the deposition current density with increasing overpotential, an exponential increase after the inflection point appears, meaning the elimination of mass-transfer limitations due to the initiation of dendritic growth. 

At overpotentials larger than 175 my the current density is considerably larger than the one expected from the linear dependence of current on overpotential. The formation of dendritic deposits (Fig. 16d-f) confirms that the deposition was dominantly under activation control. Thus, the elimination of mass transport limitations in the Ohmic-controlled electrodeposition of metals is due to the initiation of dendritic growth at overpotentials close to that at which complete diffusion control of the process on the flat part of the electrode surface occurs. 

In practice, deposits with high roughness factor and good mechanical resistance are of particular interest. Dendrites have low mechanical resistance and they are unsuitable as electrocatalysts, but the elucidation of the Ohmic-controlled electrodeposition of metals due to the dendritic growth is of a great theoretical importance. 

Typical polarization curves are represented in Figure 10.15, corresponding to nanoscale membrane assemblies based on porous anodic alumina functioning in a Hj/Oj fuel cell (Bocchetta et al., 2007). In the region of low current, activation control predominates, whereas in the central, essentially linear region of the diagram, ohmic control exists. Finally, in the region of almost constant current, mass transfer... 

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