Potentials and overpotentials

In this case, the operating temperature of the fuel cell (used in the Nemst potential, and overpotential calculations) is assumed to be the outlet cathode gas temperature. Initial fuel cell parameters used in the various simulations are summarized in Table 8.5. 

Figure 3.2.4 The volcano for OER. The potential and overpotential for Ru02 is indicated by the circle and the arrow.

A variation in the i(f potential should also be manifest with varying pH of the solution since, in this case, a substantial change in the electrode potential with respect to the potential of zero charge occurs owing to the varying equilibrium potential and overpotential. For example, at i = 10"" Acm, a variation in pH from 0 to 5 corresponds to a variation in from -0.74 to -1.33 V, which leads to a shift of by -0.030 V, i.e., a decrease in dry/d pH by 0.006 V. A similar effect is to be expected when we consider the influence of the concentration of an indifferent salt, namely, a decrease in 5ry/a log C by several millivolts. Practically, if the Tafel slope is expressed as 2.3 RT/a F), where a is an effective factor differing from the true a because of the dependence of i/ri on then the derivatives of ry with respect to pH and log C will differ from the value of 0.059 V by a factor very close to (1 - a)/a. ... 

The symbol for the fuel cell and electrolysis cell is derived from the battery symbol the longer and shorter lines represent, respectively, the cathode and anode, and the dashed line represents the electrolyte. An arrow drawn in the direction of positive current flow points toward an electrolyte with negative charge carriers, as in the manner of the transistor symbol. Galvanic and electrolytic cells are distinguished by the location of the positive terminal a positive terminal at the cathode indicates a galvanic cell, while a positive terminal at the anode indicates an electrolytic cell. The outer box represents the system enclosure, which may or may not be open. The values of potential and overpotential are consistent with Table 2. 

Potentials AND Overpotentials in a Fuel Cell Planar Electrodes... 

Figure 5.37b shows the dependence of the cell potential and overpotentials for carbon and Ru corrosion on the fraction of the MD-domain. In this figure, the mean current in the cell is fixed at 100 mA cm . As can be seen, as long as the fraction of MD-domain is below 70%, the variation of the cell potential and overpotentials is not large. Thus, a very substantial methanol-depleted area manifests itself as a... 

FIGURE 5.37 (a) Overpotentials along the channel. For all the curves, = 0.01 and = 0.5168 V. (b) Cell potential and overpotentials for carbon and Ru corrosion versus the fraction of methanol-depleted domain. Note the dramatic drop of Eceii and growth of overpotentials when more than 80% of the channel length is methanol-depleted. The mean cell current density is 100 mA cm . ... 

Figure 18 shows the dependence of the activation barrier for film nucleation on the electrode potential. The activation barrier, which at the equilibrium film-formation potential E, depends only on the surface tension and electric field, is seen to decrease with increasing anodic potential, and an overpotential of a few tenths of a volt is required for the activation energy to decrease to the order of kBT. However, for some metals such as iron,30,31 in the passivation process metal dissolution takes place simultaneously with film formation, and kinetic factors such as the rate of metal dissolution and the accumulation of ions in the diffusion layer of the electrolyte on the metal surface have to be taken into account, requiring a more refined treatment. 

The autocorrelation distance is determined by the total overpotential (0Q) of the double layer, which is measured from the critical pitting potential and the coverage 0 of the passive film. From the experimental results which will be discussed later, the actual function form is determined as... 

The anodic overpotential r controls both the rate and degree of oxidation, which means that the opening of the compacted structure is faster the greater the anodic potential, and oxidation is not completed until a steady state is attained at every anodic potential. This overpotential is also included in the constant a, with a subsequent influence on the two terms of the chronoamperometric equation. Both experimental and theoretical results in Fig. 43 show good agreement. 

It must be emphasized that Equations (5.24) and (5.25) stem from the definitions of Fermi level, work function and Volta potential and are generally valid for any electrochemical cell, solid state or aqueous. We can now compare these equations with the corresponding experimental equations (5.18) and (5.19) found to hold, under rather broad temperature, gaseous composition and overpotential conditions (Figs. 5.8 to 5.16), in solid state electrochemistry ... 

The potential reversible potential and the overpotential,... 

The position of the 4-derived t2g band in the mixed oxides shifts from 0.8 eV for Ru02 to 1.5 eV for Ir02 proportional to the composition of the oxide. As a consequence of common 4-band formation the delocalized electrons are shared between Ir and Ru sites. In chemical terms, Ir sites are oxidized and Ru sites are reduced and electrochemical oxidation potentials are shifted. Oxidation of Ru sites to the VIII valence state is now prohibited. Thus corrosion as well as 02 evolution on Ru sites is reduced which explains the Tafel slope and overpotential behaviour. Most probably Ru sites function as Ir activators [83]. 

Alternatively, one may control the electrode potential and monitor the current. This potentiodynamic approach is relatively easy to accomplish by use of a constant-voltage source if the counterelectrode also functions as the reference electrode. As indicated in the previous section, this may lead to various undesirable effects if a sizable ohmic potential drop exists between the electrodes, or if the overpotential of the counterelectrode is strongly dependent on current. The potential of the working electrode can be controlled instead with respect to a separate reference electrode by using a potentiostat. The electrode potential may be varied in small increments or continuously. It is also possible to impose the limiting-current condition instantaneously by applying a potential step. 

Schuldiner (1959) studied the effect of H2 pressure on the hydrogen evolution reaction at bright (polished) Pt in sulphuric acid. The mechanism of the reaction was assumed to be as in equations (3.3) and (3.4). The step represented by equation (3.3) was assumed to be at equilibrium at all potentials and equation (3.4) represented the rate-determining step. The potentials were measured as overpotentials with respect to the hydrogen potential, i.e. the potential of the H +/H2 couple in the solution (0 V vs. RHE). 

The additional potential required to maintain a current flowing in a cell when the concentration of the electroactive species at the electrode surface is less than that in the bulk solution. In extreme cases, the cell current reaches a limiting value determined by the rate of transport of the electroactive species to the electrode surface from the bulk solution. The current is then independent of cell potential and the electrode or cell is said to be completely polarized. Concentration overpotential decreases with stirring and with increasing electrode area, temperature and ionic strength. 

The formation condition for PS can be best characterized by i-V curves. Figure 2 shows a typical i-V curve of silicon in a HF solution.56 At small anodic overpotentials the current increases exponentially with electrode potential. As the potential is increased, the current exhibits a peak and then remains at a relatively constant value. At potentials more positive than the current peak the surface is completely covered with an oxide film and the anodic reaction proceeds through the formation and dissolution of oxide, the rate of which depends strongly on HF concentration. Hydrogen evolution simultaneously occurs in the exponential region and its rate decreases with potential and almost ceases above the peak value. 

Electrochemistry is in many aspects directly comparable to the concepts known in heterogeneous catalysis. In electrochemistry, the main driving force for the electrochemical reaction is the difference between the electrode potential and the standard potential (E — E°), also called the overpotential. Large overpotentials, however, reduce the efficiency of the electrochemical process. Electrode optimization, therefore, aims to maximize the rate constant k, which is determined by the catalytic properties of the electrode surface, to maximize the surface area A, and, by minimization of transport losses, to result in maximum concentration of the reactants. 

Consequently, a wealth of information on the energetics of electron transfer for individual redox couples ("half-reactions") can be extracted from measurements of reversible cell potentials and electrochemical rate constant-overpotential relationships, both studied as a function of temperature. Such electrochemical measurements can, therefore, provide information on the contributions of each redox couple to the energetics of the bimolecular homogeneous reactions which is unobtainable from ordinary chemical thermodynamic and kinetic measurements. 

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