Current density distribution

This equation is the starting point for determination of the current-density distributions in many electrochemical cells. 

In such cases basket anodes are frequently used. These have a relatively large surface and work at a low driving voltage due to their special construction. A cylinder of platinized titanium-expanded metal serves as the basket to which a titanium rod is welded. This serves as the current lead and carrier, and ends in a plastic foot that contains the cable lead and at the same time serves as the mounting plate. The expanded metal anode exhibits a very uniform anode current density distribution, even at large dimensions, in contrast to the plate anode. The reason is the many comers and edges of the metal that make the point effect only evident at the outer edges of the anode. 

Good electrode geometry (i.e., even current-density distribution)... 

The constancy of the diffusion layer over the entire surface and thus the uniform current-density distribution are important features of rotating-disk electrodes. Electrodes of this kind are called electrodes with uniformly accessible surface. It is seen from the quantitative solution of the hydrodynamic problem (Levich, 1944) that for RDE to a first approximation... 

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. 

Mathematical calculations of the current-density distribution in a direction normal to the electrode are rather difficult hence, to discuss the major qualitative trends, we shall limit ourselves to reviewing the simplest cases. Consider the processes occurring in a porous electrode of thickness d operated unilaterally. The current density generated at depth x per unit volume will be designated as and it is obvious that iyj X ... 

We discuss the particular case where only ohmic potential drops are present concentration gradients are absent. The current-density distribution normal to the surface can be found by integrating the differential equation (18.12) with the boundary conditions... 

FIGURE 18.5 Current density distribution inside a porous electrode [according to Eq. (18.18)] for two values of electrode thickness dj = 0.33L , jj and dj =... 

Lithography With the STM Nonelectrochemical Methods. The prospect of atomic density information storage has spurred applications of the STM as a surface modification tool. In this application, the anisotropic current density distribution generated by an STM tip is exploited to "write" on a substrate surface. Features with critical dimensions < 5 nm have been written in UHV, in air, and under liquids. 

Lithography With the STM Electrochemical Techniques. The nonuniform current density distribution generated by an STM tip has also been exploited for electrochemical surface modification schemes. These applications are treated in this paper as distinct from true in situ STM imaging because the electrochemical modification of a substrate does not a priori necessitate subsequent imaging with the STM. To date, all electrochemical modification experiments in which the tip has served as the counter electrode, the STM has been operated in a two-electrode mode, with the substrate surface acting as the working electrode. The tip-sample bias is typically adjusted to drive electrochemical reactions at both the sample surface and the STM tip. Because it has as yet been impossible to maintain feedback control of the z-piezo (tip-substrate distance) in the presence of significant faradaic current (vide infra), all electrochemical STM modification experiments to date have been performed in the absence of such feedback control. 

Figure 9.9 illustrates a typical plot of current density distribution across the GDE width for various types of nickel net structures. With a current supply to the back of the electrode structure there is no limitation, in principle, placed on the electrode size, at least from the point of view of current distribution. However, size limitations still... 

Fig. 9.9 Current density distribution along the oxygen-depolarised cathode width for various types of nickel net.

Fig. 9.12 By an i ncrease in bias or doping density the round (a) or slightly faceted (b) cross-section of macropores becomes starshaped by branching (c, d) or spiking (e) along the (100) directions orthogonal to the growth direction, (f) The current density distribution at a pore tip. (g) SEM micrograph...

A local variation in porosity can be produced by an inhomogeneous illumination intensity. However, any image projected on the backside of the wafer generates a smoothed-out current density distribution on the frontside, because of random diffusion of the charge carriers in the bulk. This problem can be reduced if thin wafers or illumination from the frontside is used. However, sharp lateral changes in porosity cannot be achieved. 

Examples of cell constructions, which provide a uniform current density, will be shown in Sect. 2.5.2. A significant disturbance of the current density distribution can be produced by gas evolution, especially in case of vertical electrodes in the... 

Figure 19. Liquid saturation and current density of the cathode as a function of position for the case of dry air fed at 60 °C. (a) Liquid saturation in the gas-diffusion layer where the channel goes from x = 0 to 0.05 cm and the rib is the rest the total cathode overpotential is —0.5 V. (b) Current-density distributions for different channel/rib arrangements. (Reproduced with permission from ref 56. Copyright 2001 The Electrochemical Society, Inc.)...

Figure 21. Comparison of local current density distributions in a two-channel serpentine PEFC at Eceii — 0.4...

The effect of inlet stoichiometry on transport characteristics and performance of PEFC was also investigated by Pasaogullari and Wang. In Figure 24 the local current density distributions along the flow direction are displayed at a cell voltage of 0.65 V. As explained earlier, the membrane is hydrated much faster in lower flow rates, and therefore, the performance peak is seen earlier in lower stoichio-... 

To measure the current distribution in a hydrogen PEFC, Brown et al. ° and Cleghorn et al. ° employed the printed circuit board approach using a segmented current collector, anode catalyst, and anode GDL. This approach was further refined by Bender et al. ° to improve ease of use and quality of information measured. Weiser et al. ° developed a technique utilizing a magnetic loop array embedded in the current collector plate and showed that cell compression can drastically affect the local current density. Stumper et al."° demonstrated three methods for the determination of current density distribution of a hydrogen PEFC. First, the partial membrane elec-... 

Figure 29. Current density distributions in a fully humidified PEFC using 30 jum membrane (EW < 1000) under various cell voltages.

Figure 38. Current density distributions in a 50 cm DMFC for (a) high cathode air flow rate (stoichiometry of 85 at 0.1 A/cm ) and (b) low cathode air flow rate (stoichiometry of 5 at 0.1 A/cm ). ...

Having fixed the basic geometry and the required power, the algorithm iteratively identifies the current density distribution which maximizes the generated field while maintaining the necessary field homogeneity over a pre-defined volume. 

An example for the field cones and equipotential surface is shown in Fig. 3.9 for d = 1.2 mm and rt= 420 A. The vertical line represents a position of 5rt away from the tip. The field lines are drawn so that their density is proportional to the field strength. Field distributions and equipotential surfaces of other tip shapes have also been investigated, particularly as regards the field emission current density distribution,24,31 but will not be discussed here. 

Obviously the contribution of the pore walls—according to the current density distribution—to cathodic hydrogen evolution becomes negligible beyond 10 fim pore depth so that for a perfect, undivided Raney-nickel coating of 100 fim thickness, only 7 to 8% utilization is anticipated. This is the reason why the fissures and cracks, the so-called tertiary structure of the catalyst, formed in Raney-nickel coatings by the leaching process are so important for improving its utilization. 

Figure 9. Top HOR (less O2 crossover) current density distribution with respect to length scales of a local H2-starved region determines where H2 depletes. Bottom carbon corrosion current distribution with respect to length scales of a local H2-starved region shows how a fully starved region develops. The cell operates on neat H2/air at s 1.5 A/cm2 (80 °C, 150 kPaabs, 100% RHin).

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