Primary current distributions equipotential surfaces

Isopotential lines are parallel to the electrode surfaces for what is known as the primary current distribution (no interfacial electrode polarization, or zero polarization resistance). Said another way, the solution adjacent to an electrode surface is an equipotential surface (1). This primary current distribution applies to the case of extremely fast electrochemical reactions (e.g., nonpolar-izable electrode reactions). This current distribution situation is only of interest to the corrosion engineer in cases where high current densities might be flowing (i.e., in relatively nonpolarizable cells). 

Again, the problem with such a primary current distribution solution is that the pipe-solution interface is assumed to be an equipotential surface. Instead, we... 

Consider first the primary current distribution, which represents the distribution when the surface overpotentials (activation and concentration) are neglected, and the electrode is taken as an equipotential surface. For a disk electrode of radius ri embedded in a large insulating plane with a counter electrode at infinity, the potential distribution under such conditions is as shown in Figure 9.3.9. The current flows in a direction perpendicular... 

As was shown in Fig. 2.5, the primary current distribution is only uniform when all points on the electrode surface are strictly equivalent and the current density is low. This is possible only with two reactor designs, a parallel-plate reactor having electrodes of equal area and occupying opposite walls and the concentric-cylinder reactor. There will be a variation of potential and current density over the surface for all other electrode arrangements an example is shown in Fig. 2.16(a) where the broken lines join equipotential points and the current densities are inversely proportional to the lengths of the arrowed lines. The highest current density is between the points closest together on the two electrodes and almost no current flows on the reverse side of the anode. 

Fig. 2.16(a) Primary current distribution for the electrode geometry shown. The broken lines show equipotential contours. The current density is inversely proportional to the length of the arrows. Note that almost no current flows to the anode surface which faces away from the cathode. 

Under the assumption that the concentrations are uniform within the electrolyte, potential is governed by Laplace s equation (5.52). Under these conditions, the passage of current through the system is controlled by the Ohmic resistance to passage of current through the electrolyte and by the resistance associated with reaction kinetics. The primary distribution applies in the limit that the Ohmic resistance dominates and kinetic limitations can be neglected. The solution adjacent to the electrode can then be considered to be an equipotential surface with value o- The boundary condition for insulating surfaces is that the current density is equal to zero. 

Some electrochemical systems can be described as blocking electrodes for which no Faradaic reaction can occur. At steady state, the current density for such a system must be equal to zero. The transient response of a blocking electrode is due to the charging of the double layer. At short times or high frequency, the interfacial impedance tends toward zero, and the solution adjacent to Ihe electrode can then be considered to be an equipotential surface. The short-time or high-frequency current distribution, therefore, follows the primary distribution described in the... 

An important result regarding current and potential distributions at disk electrodes, pointed out by Newman,i63- les is that owing to the ohmic potential drop, a uniform current density and a uniform double-layer potential caimot coexist. First, consider the primary potential and current distribution where the electrolyte potential at the electrode constitutes an equipotential surface. The primary current density is given 5 by... 

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