Current and potential distributions

Current and potential distributions are affected by the geometry of the system and by mass transfer, both of which have been discussed. They are also affected by the electrode kinetics, which will tend to make the current distribution uniform, if it is not so already. Finally, in solutions with a finite resistance, there is an ohmic potential drop (the iR drop) which we minimise by addition of an excess of inert electrolyte. The electrolyte also concentrates the potential difference between the electrode and the solution in the Helmholtz layer, which is important for electrode kinetic studies. Nevertheless, it is not always possible to increase the solution conductivity sufficiently, for example in corrosion studies. It is therefore useful to know how much electrolyte is necessary to be excess and how the double layer affects the electrode kinetics. Additionally, in non-steady-state techniques, the instantaneous current can be large, causing the iR term to be significant. An excellent overview of the problem may be found in Newman s monograph [87]. 

A commonly employed method to minimise ohmic potential drop effects is to place the reference electrode very close to the working electrode by means of a Luggin capillary. The disadvantage of very close placement, which may be unacceptable, is disturbance of the fluid flow. To avoid this, other methods are sometimes used. For example, a rotating disc electrode has been described in which the reference electrode is placed in a tiny compartment within the rotating electrode assembly and linked to the solution via a tiny orifice (0.7 mm) drilled in the centre of the disc [88]. 

One of the principal reasons for the extensive use of the rotating disc electrode is its uniform accessibility. However, if the solution conductivity is not sufficiently high, it does not have a uniform current distribution. Experimental investigations have provided criteria for the concentration of inert electrolyte necessary to add to ensure uniformity [89]. Current 

Studies have also been conducted into the current distribution at tubular electrodes [94]. At the DME, it is non-uniformity of current and potential distributions, during drop growth, which is one of the causes of polarographic maxima [Sect. 2.3.5(d)]. 

Detailed expositions of the practical use of hydrodynamic electrodes can be found in various references, e.g. refs. 95—97. A commonly heard criticism of hydrodynamic electrodes is that they, and often the associated flow systems, are difficult to construct. We do not believe the difficulty to be so great and if judicious care is taken, it is perfectly possible to make the electrodes in most research laboratories. 

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These four equations, using the appropriate boundary conditions, can be solved to give current and potential distributions, and concentration profiles. Electrode kinetics would enter as part of the boundary conditions. The solution of these equations is not easy and often involves detailed numerical work. Electroneutrahty (eq. 28) is not strictly correct. More properly, equation 28 should be replaced with Poisson s equation... 

Fig. 3-24 Current and potential distribution in the neighborhood of a local anode on a buried pipeline (explanation in the text).

A check on the cathodic protection of the pipeline should be carried out annually according to Section 10.4, where, of course, only the on potential should be measured. This value should also be compared with the values of the measurements in Section 10.4. If there are no changes in the on potentials and the protection current densities for the individual sections of the pipeline, it can be concluded that the off potential has not changed. The values can easily be compared using computers and represented in plots. If the protection current and potential distribution have changed, or in any case every 3 years, the off potentials as well as the on potentials should be measured. 

By using only a single reference electrode in the object to be protected, the potential can be determined only in the vicinity of this electrode and not in more remote areas. Section 3.3.1 together with Eq. (3-27) provides further explanation of this. To improve the current and potential distribution, the number and location of the anodes must suit the geometry of the object to be protected. Occasionally, additional reference electrodes are required for potential control [2]. The optimum nominal potential for potential control can be found by this method by considering remote IR errors. 

Nonuniform current and potential distribution is usually to be expected with uncoated objects to be protected. The distribution can be considerably improved by coatings (see Section 20.1.3). In enamelled tanks, the current and potential distribution of cathodic protection is very good. By arranging the anode centrally, IR errors from equalizing currents in the switching-off phase can be ignored. The anode potential in the switching-off phase can be evaluated from the information... 

The grounding resistance that is given by the current and potential distribution in the electrolyte and that will be considered in detail in what follows. 

Two different functions J U) are introduced into Eq. (24-89). After integration the following equations concerning current and potential distribution result ... 

Several cell configurations are common in electrochemical research and in industrial practice. The rotating disk electrode is frequently used in electrode kinetics and in mass-transport studies. A cell with plane parallel electrodes imbedded in insulating walls is a configuration used in research as well as in chemical synthesis. These are two examples of cells for which the current and potential distributions have been calculated over a wide range of operating parameters. Many of the principles governing current distribution are illustrated by these model systems. 

J. Nonuniform Current and Potential Distributions to Polarization Resistance Probes... 

It is useful now to describe a few rules pertinent to current and potential distributions prior to discussing specific geometries (1). 

Isopotential lines may vary with electrode position for the secondary and tertiary current and potential distributions, where interfacial polarization of various types is considered. The variation of local true potential across the electrochemical interface with electrode position is of great interest in galvanic corrosion, cathodic protection, etc., since this true potential drives electrochemical reactions. 

Current distribution problems are often categorized according to the process that limits or determines the current and potential distribution (1,6). 

A. Current and Potential Distributions for the Rotating Cylinder Electrode... 

C. Current and Potential Distribution for the Flow Channel with Parallel Plates... 

B. Current and Potential Distributions at the Entrance to a Circular Pipe... 

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