Distribution in an Electrochemical Cell

Primary and secondary current distributions in electrochemical cells are governed by the Laplace equation.[8] Consider a rectangular geometry governed by the following equation [9] 

Note that this geometry is of finite dimension in x (L) and semi-infinite in y. The following transformation is used to combine the variable  

Example 4.11 is solved in Maple below. The program used for example 4.10 can be modified to solve this example. Only the variable transformation (equation (4.21)) has to be modified. The following results are obtained  

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The situation is fundamentally different near an interface due to a significant redistribution of charge. Consider, for example, the potential distribution in an electrochemical cell at open circuit. Consider that a potential can be applied between the two metal electrodes such that no current flows. A situation like this is described in Section 5.1. The electrodes can be considered to be ideally polarized since a potential can be applied without passage of current. 

The phenomenon of charge transport, which is unique to all electrochemical processes, must be considered along with mass, heat, and momentum transport. The charge transport determines the current distribution in an electrochemical cell, and has far-reaching implications on the current efficiency, space-time yield, specific energy consumption, and the scale-up of electrochemical reactors. 

The term R0I is called the ohmic drop.2 Figure 3.3 shows the schematic potential distribution in an electrochemical cell. At the anode a potential drop Ua occurs, which is given by the sum of the equilibrium potential U and the anodic over potential r]a. An analogous situation takes place at the cathode. Note that the electromotive force of the cell is U0 = Uejj a + Uej/ C. In practical applications of Equation (3.19), one has to pay attention to the sign convention attributed to the various quantities. 

Figure 3.3 Potential distribution in an electrochemical cell (see text for definitions of the different physical quantities).

In spite of its limitations for complex systems, the Wagner number gives a good qualitative idea of the current distribution in an electrochemical cell. Indeed, when the Wagner number is small (W << 1), the influence of overpotentials can be neglected and the current distribution is nearly the primary distribution. For larger values (- 0.01 < W < 100), the... 

Popov KI, Zecevic SK, Pesic SM (1995) The current distribution in an electrochemical celL Part I the currtait voltage relationship fra a cell with parallel plate electrodes. J Serb Chtan Soc 60 307-316... 

Popov KI, Pesic SM, Kostic TM (1999) The current distribution in an electrochemical cell. Part V the determination of the depth of the ciurent line penetration between the edges of the electrodes and the side walls at the cell. J Serb Chem Soc 64 795-800... 

The spatial variation on the electrode of current density i is often referred to as the current distribution. Since the current density is related to reactirai rate through Faraday s law, the current distribution is thus a manner of expressing the variation of reaction rate within an electrochemical cell. As for traditional chemical reactors, nonuniformities in reaction rate may be anticipated if the fluid flow is inadequate to prevent concentration gradients. However, electrical field effects also influence the current distribution in an electrochemical cell, and thus reaction rates can be nonuniform even if perfect mixing is achieved in the reactor. Electrochemical cells of course have two electrodes, and sometimes optimizing a current distribution of one electrode is more important than the other. Depending on the proximity of the two electrodes, the current distributions of the electrodes may or may not influence each other. 

Electron Configuration distribution of electrons into different shells and orbitals from the lower to higher energy levels Electronegativity measure of the attraction of an element for a bonding pair of electrons Electroplating process where a metal is reduced on to the surface of an object, which serves as the cathode in an electrochemical cell... 

Salt Bridge concentrated solution of electrolyte used to complete the circuit in an electrochemical cell that helps to equalize charge distribution in each half cell Saltpeter potassium nitrate, KNO3 Saponification conversion of a fat to soap by reacting with an alkali Saturated solution that contains the maximum amount of solute under a given set of conditions... 

Ag2 Silver sulfide can attain a small metal excess, y 0.0025 at 300 C. The relatively small Ag" " ions are distributed statistically on many sites in the rigid lattice, and are very mobile. Therefore the activity and chemical potential of the Ag+ ions is virtually constant at varied chemical potential of Ag. The variation of /u-Ag can be conducted in an electrochemical cell ... 

The relative distribution of the mechanical and chemical components of adhesion were assessed via cathodic chargingl. In this approach, the electrolessly-metallized specimen was employed as the cathode in an electrochemical cell containing a sulfuric acid/arsenic trioxide electrolyte. The adhesion component values were gleaned from peel strength/coulomb curves before and after the final heat treatment. 

We arrive at the unusual conclusion that the macroscopic band profile is no longer determined by the electronic distribution as in traditional semiconductors but by the properties of the mobile ionic carriers, which, in fact, are the majority carriers. Then the electrolyte inserted in an electrochemical cell, under open circuit conditions, can be simply represented as a rigid reference frame (Fig.5). The Fermi level is principally determined at the surfaces by the local distribution of electrons among surface states. According to eq. (16) the cell voltage is simply related to the difference between these Fermi levels at the electrodes ... 

FIGURE 1.7. Voltage distribution in an electrochemical reactor = cell voltage E = anodic electrode potential 1 = voltage drop in anolyte = voltage drop in diaphragm = voltage drop in catholyte = cathodic overpotential. 

The equivalent circuit of an electrochemical cell is shown in Fig. 5.6. It can be represented by a capacitive divider consisting of Cw and CAux connected in series. Figure out how the voltage V and charge Q are distributed across this divider when the resistances are (a) finite (b) infinite. 

The Birch and Benkeser reactions of some unsaturated organic compounds [318 and references therein], which consist of a reduction by sodium or lithium in amines, can be mimicked electrochemically in the presence of an alkali salt electrolyte. The cathodic reaction is not the deposition of alkali metal on the solid electrode but the formation of solvated electrons. Most of the reactions described were performed in ethylenediamine [319] or methylamine [308,320]. A feature of these studies is variety introduced by the use of a divided or undivided cell. In a divided cell, the product distribution appears to be the same as that in the classic reduction by metal under similar conditions. In contrast, in an undivided cell the corresponding ammonium salt is formed at the anode it plays the role of an in situ generated proton donor. Under such conditions, the proton concentration... 

Mench, M.M. Wang, C.Y. An in situ method for determination of current distribution in PEM fuel cells applied to a direct methanol fuel cell. J. Electrochem. Soc. 2003,150 (1), A79-A85. 

In order to characterize the gold reference electrode and to estimate the potential distribution in the single-pellet cell, an electrochemical cell identical to that shown in Figure 1, but having all three electrodes made of gold, was used. A good reference electrode for the purposes of electrochemical promotion experiments must be catalytically inert in all experimental conditions, and it must have an invariant potential defined by a (preferably reversible) redox couple. Nevertheless, a... 

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