Current distribution uniformity

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]. 

Current distributions refer to the spatial variations of reaction rate on an electrode. T3q)ically, current distribution uniformity increases with decreasing size of the electrode. In general concentration and electrical fields govern current distributions. While detailed simulations are feasible, back of the envelope calculations can often allow for rapid estimates of whether a ncaiuniform current distribution is anticipated. 

Thus for reactors with small interelectrode gaps uniformity of current distribution is maintained. Keeping current distribution uniform becomes difficult, however, when reactor dimensions are eomparable or when no one dimension eontrols reactor behavior. 

Figure 2. Examples of numerical solutions for the cathodic current distribution on a plate electrode immersed in a cell with the counter electrode at the bottom. Three cases are compared (a) (/ column) completely reversible kinetics (primary distribution) (b) center) irttermedrate kinetics (Ub 0.2) (c) (right column) irreversible kinetics (Wa 10). The top row provides a comparison of the current distribution or the deposit profile on the cathode (cross-hatched region). The center row provides the current distribution along the electrode ( stretched ). The bottom row provides the corresponding poterrtial distributions. It is evident that the current distribution uniformity increases as the electrode kinetics become more passivated (Cell-Design software simulations ).

When a battery produces current, the sites of current production are not uniformly distributed on the electrodes (45). The nonuniform current distribution lowers the expected performance from a battery system, and causes excessive heat evolution and low utilization of active materials. Two types of current distribution, primary and secondary, can be distinguished. The primary distribution is related to the current production based on the geometric surface area of the battery constmction. Secondary current distribution is related to current production sites inside the porous electrode itself. Most practical battery constmctions have nonuniform current distribution across the surface of the electrodes. This primary current distribution is governed by geometric factors such as height (or length) of the electrodes, the distance between the electrodes, the resistance of the anode and cathode stmctures by the resistance of the electrolyte and by the polarization resistance or hinderance of the electrode reaction processes. 

Cell geometry, such as tab/terminal positioning and battery configuration, strongly influence primary current distribution. The monopolar constmction is most common. Several electrodes of the same polarity may be connected in parallel to increase capacity. The current production concentrates near the tab connections unless special care is exercised in designing the current collector. Bipolar constmction, wherein the terminal or collector of one cell serves as the anode and cathode of the next cell in pile formation, leads to gready improved uniformity of current distribution. Several representations are available to calculate the current distribution across the geometric electrode surface (46—50). 

For large Wa, the current distribution is uniform. For example, when electroplating (qv) an object, usually a uniform deposit is desirable. Equation 35 suggests that a larger piece, ie, low Wa, would be more difficult to plate uniformly than a smaller one. 

Charge Transport. Side reactions can occur if the current distribution (electrode potential) along an electrode is not uniform. The side reactions can take the form of unwanted by-product formation or localized corrosion of the electrode. The problem of current distribution is addressed by the analysis of charge transport ia cell design. The path of current flow ia a cell is dependent on cell geometry, activation overpotential, concentration overpotential, and conductivity of the electrolyte and electrodes. Three types of current distribution can be described (48) when these factors are analyzed, a nontrivial exercise even for simple geometries (11). 

Electrolytic plating rates ate controUed by the current density at the metal—solution interface. The current distribution on a complex part is never uniform, and this can lead to large differences in plating rate and deposit thickness over the part surface. Uniform plating of blind holes, re-entrant cavities, and long projections is especiaUy difficult. 

In a d.c. system the current distribution through the cross-section of a current-canying conductor is uniform as it consists of only the resistance. In an a.c. system the inductive effect caused by the induced-electric field causes skin and proximity effects. These effects play a complex role in determining the current distribution through the cross-section of a conductor. In an a.c. system, the inductance of a conductor varies with the depth of the conductor due to the skin effect. This inductance is further affected by the presence of another current-carrying conductor in the vicinity (the proximity effect). Thus, the impedance and the current distribution (density) through the cross-section of the conductor vaiy. Both these factors on an a.c. system tend to increase the effective... 

For installations with several storage tanks and a protection current of several tens of an mA, uniform protection current distribution should be the goal, so that the current injection occurs via a number of anodes distributed over the site or via a more distant anode bed. Dividing up the protection current over several anodes avoids large local anodic voltage cones and therefore effects on neighboring installations. 

The life of the magnesium anodes with a current content of about 1.2 A a for 10 mA according to Table 6-4 was calculated from Eq. (6-9) as 120 years. This assumes that the protection current is equally distributed over both anodes. The calculated life would certainly not be reached because uniform anode current distribution cannot be achieved over a long period of time. It would, however, be substantially longer than the minimum required life of 25 years. For this length... 

In this case, impressed current protection with several anodes was chosen on the one hand to achieve uniform current distribution with the relatively high protection current density, and on the other hand to avoid large anode voltage cones. A transformer-rectifier with a capacity of 10 V/1 A was chosen. 

The anode mountings are welded to lap joints in the yard, and the anodes are installed at a minimum distance of 30 cm from the structure to achieve the most uniform current distribution [1-3]. Nonuniform potential distribution occurs even with this distance. 

Cathodic protection of enamelled tanks with Mg anodes has long been the state of the art, with potential-controlled equipment being used with increasing frequency in recent years. A high-resistance coating with limited defects according to Ref. 4 enables uniform current distribution to be maintained over the whole tank. 

As an example of potential distribution, Fig. 20-8 shows the potential on the vertical axis in a 300-liter electric storage reservoir. The water had an extremely low conductivity of x (20°C) = 30 fiS cm l A Mg rod anode served for cathodic protection it reached to just above the built-in heating element to give uniform current distribution. This was confirmed by the measurements. 

Cathodic protection of uncoated objects in the soil is technically possible however, the high current requirement, as well as measures for the necessary uniform current distribution and for //f-free potential measurement, result in high costs. In determining the costs of cathodic protection of pipelines, it has to be remembered that costs will increase with increases in the following factors ... 

A particular advantage of impressed current systems is the ability to control the output voltage of the rectifier. Also, there are the comparatively low installation costs and relatively uniform current distribution. The costs of impressed current protection compared with aluminum anodes are 0.8 1. With ships this ratio depends on the length of the ship with larger ships it is 1 2.5 since the calculation is made in comparison with zinc and aluminum anodes. The order of magnitude of the annual costs depends on the structure and the investment costs. 

With an uncoated pipe or one with very poor coating and many defects close together, uniform current distribution for the pipeline can be assumed in the soil even at quite short distances from it (see Section 3.6.2.2, case b). 

The generally applicable relations for a two-conductor model are derived in the following section. For simplicity, local potential uniformity is assumed for one of the two conductor phases. Relationships for the potential and current distributions, depending on assumed current density-potential functions, are derived for various applications. 

Impressed current systems are normally based upon anodes of silicon iron, platinised titanium or platinised niobium. The method of anode installation is usually by suspension. The anode configuration and number must be such as to ensure uniform current distribution. Considerable use is made of wire-type platinised-titanium, and niobium anodes which offer minimal weight and relative ease of mounting/suspension. 

Fig. 11.13 Methods of securing more uniform current distribution...

Accurate control of potential, stability, frequency response and uniform current distribution required the following low resistance of the cell and reference electrode small stray capacitances small working electrode area small solution resistance between specimen and point at which potential is measured and a symmetrical electrode arrangement. Their design appears to have eliminated the need for the usual Luggin capillary probe. 

Naoi and co-workers [55], with a QCM, studied lithium deposition and dissolution processes in the presence of polymer surfactants in an attempt to obtain the uniform current distribution at the electrode surface and hence smooth surface morphology of the deposited lithium. The polymer surfactants they used were polyethyleneglycol dimethyl ether (molecular weight 446), or a copolymer of dimethylsilicone (ca. 25 wt%) and propylene oxide (ca. 75 wt%) (molecular weight 3000) in LiC104-EC/DMC (3 2, v/v). 

The molten salt, sodium aluminum chloride, fulfills two other tasks in the cell system. The ceramic electrolyte "-alumina is sensitive to high-current spots. The inner surface of the ceramic electrolyte tube is completely covered with molten salt, leading to uniform current distribution over the ceramic surface. This uniform current flow is one reason for the excellent cycle life of ZEBRA batteries. 

In this example the current density distribution is nonuniform in the vertical, since at all heights x the sums of ohmic potential drops and polarization of the two electrodes must be identical. In the top parts of the electrodes, where the ohmic losses are minor, the current density will be highest, and it decreases toward the bottom. The current distribution will be more uniform the higher the polarization. 

The rotating hemispherical electrode (RHSE) was originally proposed by the author in 1971 as an analytical tool for studying high-rate corrosion and dissolution reactions [13]. Since then, much work has been published in the literature. The RHSE has a uniform primary current distribution, and its surface geometry is not easily deformed by metal deposition and dissolution reactions. These features have made the RHSE a complementary tool to the rotating disk electrode (RDE). 

The primary current distribution is uniform on the hemisphere. Numerical calculations using the potential theory have shown that the current distribution is essentially uniform on the RHSE if the current density is less than 68% of the average limiting current density [47]. 

In electrochemistry, spherical and hemispherical electrodes have been commonly used in the laboratory investigations. The spherical geometry has the advantage that in the absence of mass transfer effect, its primary and secondary current distributions are uniform. However, the limiting current distribution on a rotating sphere is not uniform. The limiting current density is highest at the pole, and decreases with... 

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