Distribution overpotential

Current distribution Overpotential-current relationship E = f(i) Polarization dE/di resistance term Wagner number... 

Based on a co-flow configuration, the effect of various parameters on cell performance has been studied systematically. The study covers the effect of (a) air flow rate, (b) anode thickness, (c) steam to carbon ratio, (d) specific area available for surface reactions, and (e) extend of pre-reforming on cell efficiency and power density. Though the model predicts many variables such as conversion, selectivity, temperature and species distribution, overpotential losses and polarization resistances, they are not discussed in detail here. In all cases calculations are carried for adiabatic as well as isothermal operation, fii calculations modeling adiabatic operation the outer interconnect walls are assumed to be adiabatic. All calculations modeling isothermal operation are carried out for a constant temperature of 800°C. Furthermore, in all cases the cell is assumed to operate at a constant voltage of 0.7 V. 

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. 

As the Nemst equation suggests, concentration variations in the electrolyte lead to potential differences between electrodes of the same kind. These potential differences are concentration polarizations or concentration overpotentials. Concentration polarizations can also affect the current distribution. Predicting these is considerably more difficult. If concentration gradients exist, equations 25 and 27 through 29 must generally be solved simultaneously. 

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). 

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). 

At low overpotentials, the silver electrode prepared according to Budev-ski et al. behaves as an ideal polarized electrode. However, at an overpotential higher than —6 mV the already mentioned current pulses are observed (Fig. 5.48A). Their distribution in the time interval r follows the Poisson relation for the probability that N nuclei are formed during the time interval x... 

The other potential losses required to drive an electrode reaction are the activation overpotential, rja, and concentration overpotential, r]conc. The problem of current distribution is then governed Eq. (57) as well as by the following equations ... 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

In many cases mass transfer is not the sole cause of unsteady-state limiting currents, observed when a fast current ramp is imposed on an elongated electrode. In copper deposition, in particular, as a result of the appreciable surface overpotential (see Section III,C) and the ohmic potential drop between electrodes, the current distribution below the limiting current is very different from that at the true steady-state limiting current. 

A mechanism which proceeds through surface reconstruction of the substrate has been identified for Ni deposition on Au(lll) [120, 121]. The process begins with place exchange of nickel into a particular position in the reconstructed Au(lll) surface, followed by deposition of Ni islands on top of the imbedded atom. At higher overpotentials, nucleation occurs instead at step edges, so that control of the potential allows control of the nucleation process and the distribution of Ni in the early stages of growth. In this instance, the nucleation process has been captured by STM on the atomic scale. 

Figure 6.4 Distributions Wox and Wred at equilibrium (left) and after application of a cathodic overpotential.

Their values depend on the overpotential. Show that for r) = 0 a+/3 / 1. This (small) error arises because the Fermi-Dirac distribution has been replaced by a step function. 

Typically the contributions of the two bands to the current are of rather unequal magnitude, and one of them dominates the current. Unless the electronic densities of states of the two bands differ greatly, the major part of the current will come from the band that is closer to the Fermi level of the redox system (see Fig. 7.6). The relative magnitudes of the current densities at vanishing overpotential can be estimated from the explicit expressions for the distribution functions Wled and Wox ... 

It is important to note that as early as 1931, the density of electronic states in metals, the distribution of electronic states of ions in solution, and the effect of adsorption of species on metal electrode surfaces on activation barriers were adequately taken into account in the seminal Gurney-Butler nonquadratic quantum mechanical treatments, which provide excellent agreement with the observed current-overpotential dependence. 

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.)...

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