Current secondary distribution

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. 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

Seconday Current Distribution. When activation overvoltage alone is superimposed on the primary current distribution, the effect of secondary current distribution occurs. High overpotentials would be required for the primary current distribution to be achieved at the edge of the electrode. Because the electrode is essentially unipotential, this requires a redistribution of electrolyte potential. This, ia turn, redistributes the current. Therefore, the result of the influence of the activation overvoltage is that the primary current distribution tends to be evened out. The activation overpotential is exponential with current density. Thus the overall cell voltages are not ohmic, especially at low currents. 

Tertiay Current Distribution. The current distribution is again impacted when the overpotential influence is that of concentration. As the limiting current density takes effect, this impact occurs. The result is that the higher current density is distorted toward the entrance of the cell. Because of the nonuniform electrolyte resistance, secondary and tertiary current distribution are further compHcated when there is gas evolution along the cell track. Examples of iavestigations ia this area are available (50—52). 

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... 

Mehdizadeh et al. exploited the separability of current distribution on different scales to model the macroscopic current distribution on patterns made up of lines or points distributed over a large workpeice [136], They solved the secondary distribution of the superficial current density sup using a boundary condition which captures the density of small features but not their geometry. The boundary condition is based on a smoothly varying parameter representing the Faradaically active fraction of surface area. 

Working within a similar scheme, DeBecker and West introduced a treatment of feature scale effects on the overall current distribution which they call the hierarchical model [138]. Rather than represent the features as a smoothly varying density of active area, they retain the features, but simplify their representation in the global model. An integral current for each feature is assigned to the geometric center of the feature to provide a simplified boundary condition for the secondary current distribution. This boundary condition captures a part of the ohmic penalty paid when current lines converge onto features. It thus contains more information than the active area approximation but still less than a fully matched current distribution on the two levels. 

Secondary current distribution is related to current production sites inside the porous electrode itself. The... 

However, there is another kind of influence on current distribution that may even the score. This is called secondary current distribution and describes the resistances set up at the interface of the working electrodes in a cell in which the interface tends to be polarizable. For example, it was shown [Eq. (7.36)] that when f) < RT/F, the interfacial resistance per unit area is RT/igF. If i0 is very small (e.g., 10-10 A cm-2, hence, an interfacial resistance cm-2 of 2.6 x 10 ohms), it is this interfacial resistance and not the ohmic resistance in the bulk solution that detennines the current distribution. Thus, in an extreme case of high solution concentration (low solution resistance) and low i q, a substantial fraction of the length of the pores in a porous electrode remains active.34 Considerations such as these, together with resistance effects at edges, all count in cell design. 

There are other cases in practical electrochemical devices in which current distribution is important. Because of the interplay of interfacial and electrolyte resistance effects (primary and secondary current distribution, respectively , the detailed calculation involve much mathematics. Electroplating deep into crevices of the object to be plated is an example of where current distribution considerations often dominate behavior. Throwing power is a term that describes the degree of penetration of the current— hence the plating—into fissures and irregularities in electrodeposition. 

Current distribution Distribution of reaction rates on an electrode surface. Primary current distribution is calculated by considering only electric field effects both overpotential and concentration gradients are neglected. Secondary current distribution takes both field effects and surface overpotential into account. Tertiary current distribution takes field effects, surface overpotential, and concentration gradients into account. 

Wagner number Dimensionless ratio of polarization resistance to electrolyte resistance. A low value is characteristic of a primary current distribution a high value corresponds to a secondary current distribution. 

Secondary current distribution. Both field effects and the effects of sluggish reaction kinetics are considered. 

The complexity of a model increases as we proceed from the primary to the tertiary distribution and as the number of spatial dimensions that are considered increases. Essentially all published solutions have been reduced to one or two dimensions, and most include only simulations of the primary and secondary current distributions. For the special case in which only mass transport is limiting, a large number of correlations for the current distribution are available. 

The secondary current distribution is calculated by including the effects of the ohmic drop in the electrolyte and the effects of sluggish electrode kinetics. While the secondary distribution may be a more realistic approximation, its calculation is more difficult therefore, we need to assess the relative importance of electrode kinetics to determine whether we can neglect them in a simulation. 

FIGURE 8 Secondary current distribution. When surface overpotential governs the current distribution, small differences in solution resistance (represented by smaller resistors) can be neglected, and the current distribution becomes more uniform. 

FIGURE 10 Current distribution on a disk electrode. The primary current distribution approaches infinity at the junction of the electrode and the coplanar insulator. The secondary current distribution is more uniform. Average current density is /aVg and the electrode radius r0. 

Channel flow between plane parallel electrodes is shown in Fig. 11. This geometry is similar to that of the disk in that an electrode and an insulator intersect in the same plane. Because of many geometric similarities, the general characteristics of the primary and secondary current distributions are similar. At the edges the local current density is infinite for the primary current distribution (Fig. 12). Increasing the kinetic limitations tends to even out the current distribution. The significant contrasts appear in a comparison of the tertiary current distributions. In channel flow, the fluid flows across the electrode rather than normal to it. Consequently, the electrode is no... 

FIGURE 12 Current distribution on plane parallel electrodes. Primary and secondary current distributions are symmetric about a centerline plane. When the reactant concentration is considered, an unsymmetric current distribution results. 

Numerical simulations reveal that this effective value Rif differs form Re if the measured (simulated) Rif is smaller than Rsw (Fig. 21a). These deviations are connected with the inhomogeneous potential distribution in the vicinity of a microelectrode yielding laterally varying electrode overvoltages for small electrode resistances (Fig. 21b). In microelectrode experiments, however, the ratio Reef / Rm is often large (cf. Sec. 3.4) and hence Ra x R f is usually a reasonable approximation. In liquid electrochemistry, similar effects are discussed in the context of primary (Rei = 0) and secondary (Re > 0) current distributions [268, 269]. 

A dimensionless parameter known as the Wagner number is useful for qualitatively predicting whether a current distribution will be uniform or nonuniform (2,40,41). This parameter helps to answer the question, Which current distribution applies to my cell primary, secondary or tertiary ... 

The secondary current distribution Both ohmic factors and charge transfer controlled overpotential kinetic effects are considered. The potential across the electrochemical interface can vary with position on the electrode. 

---