Current Polarization Curve

To rationalize the effect of oxygen stoichiometry X on the potential loss, consider first the case of a small cell current. In this case, the local polarization curve is given by Equation 5.43. To calculate the polarization curve as a function of mean cell current density rjo (/), it is advisable to divide the terms under the logarithms in Equation 5.43 

This procedure does not change ijo, as the logarithms in Equation 5.54 appear with different signs. Suppose that ijo is independent of z (the rationale for this assumption is discussed below). From Equation 5.54, one can see that ijo is constant along z, provided that the ratio Jo/ch is independent of z. Note that in that case, both logarithms in Equation 5.54 are constant. 

Denoting o = ych, where y 0 is constant, substituting this relation into Equation 5.50, and solving the resulting equation yields Ch = exp (-yz/(A/)). Using Equation 5.53 to calculate y, one finally obtain (Kulikovsky, 2004) 

From Equations 5.55 and 5.56, it is clear that jo/Ch = fxJ- Using this in Equation 5.54, gives the integral polarization curve of the cathode side 

In PEFCs, the constancy of along z results from the following argumentation. Generally, the local cell voltage Eceii is 

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In the diode the cathode is usually a W filament which can be flashed and maintained as a reference electrode at a temperature above which adsorption occurs. The anode may be of similar construction or take the form of a metal film evaporated from an adjacent filament. Experimentally, current polarization curves are obtained, first for the clean anode surface A and then for the covered anode surface A. Alternatively, resistance-voltage characteristics are measured (SO). The potential difference comprises the applied polarization and the C.P.D. between the emitter and collector. For a given anode current j,... 

FIGURE 27.6S Potential-current polarization curves of H2.O2 fuel cells using Nafion 117 (thickness 180 p,m and 30% water uptake) and STA with and without thiophene (termed NASTATH and NASTA, respectively) (thickness about 175 p,m and 60% water uptake). Anode and cathode based on 0.35 mg cm Pt from 20% Pt C catalyst pressure ratio H2.O2 3 5 atm gas flow rates 2 = 0.8 L min H2= 1.2 L min . (Reprinted from Tazi, B. and O. Savadogo, O., Electrochim. Acta, 45, 4329, 2000. With permission from Elsevier.)... 

M and N drawn in terms of current. The curve for M is offset along the current axis showing the situation for M electrodes with three different areas. As the area of M increases, the couple potential (ignoring effects of ohmic potential drops) approaches the uncoupled corrosion potential for M in the given solution, which is the highest possible couple potential. Similarly, the lowest possible couple potential, found when the N M area ratio is very low, is the uncoupled corrosion potential for N in the environment. The corrosion current is given by the intersection of the two potential-current polarization curves, and the current densities are determined by dividing the current by the electrode areas. 

The preconcentration of trace metals by electrodeposition is an integral part of anodic-stripping voltammetry. The method consists of the preelectrolysis of the stirred solution with a small mercury drop or solid electrode as the cathode (112-114). The metals, which are deposited and dissolve in the mercury, are then stripped from the amalgam after a suitable rest period by a reversal of the electrode potential. The resulting current-polarization curve is characteristic of the metal and its concentration. Concentrations as low as 10 M of metal ions require a preelectrolysis of about 60 min or longer. Other electrodes such as mercury films, platinum, gold, silver, and various forms of carbon have been used (77 ). 

One of the goals of these above characterizations is the achievement of high and uniform fuel cell performance. These characterizations provide the necessary knowledge about what parameters should and ean be tailored in order to achieve higher performance. Once a good and uniform performance is consistently achieved, some or all of these characterizations can be eliminated. The best way to gauge the performance of an MEA is to collect voltage -current polarization curves. 

As stated above, Ejj and Eprot often dejiend strongly on the method by which they are determined and, therefore, do not uniquely define intrinsic material properties. The Eprof values determined from the scanning method can be complicated by scan rate, pit size or depth, vertex potential/current, polarization curve shape, and specimen geometry [86,87]. Investigators have found more consistent Eprof values after a critical charge has passed, while others report a single critical potential [85]. Often this potential is difficult to choose from E-I data and has been taken at various points on the reverse scan of a cyclic potentiodynamic polarization curve [89]. 

Electrochemical tests are rapid techniques to determine mechanisms, determine the effect of various parameters on corrosion rate, and screen out a large number of materials [43]. They usually involve measurement of corrosion potentials, corrosion currents, polarization curves, and electrochemical impedance. They are used to evaluate metals and alloys and the behavior of metallic, inorganic, and oiganic coatings. The simplest test involves the measurement of the corrosion potential and its use in conjunction with other measurements. A zero resistance ammeter (ZRA) is commonly used to measure corrosion currents between dissimilar metals and alloys. Controlled potentitd tests and anodic and cathodic polarization curves using potentiostats are the most commonly used electrochemical tests. These are powerful tools for investigating the effect of various parameters on corrosion behavior. These incorporate the use of cycUc polarization and polarization resistance for localized corrosion and corrosion rate measurements. Table 4 lists electrochemical tests that can be used for corrosion tests in the automobile industry. 

The high-current polarization curve of the CCL follows from Ek[. (2.54). Setting X = 0 in this equation we get... 

This relation determines the position of the intersection of the low- and high-current polarization curves (Figure 2.4). Note that for e -C 1 we have coth(l/e) 1 and the intersection is located at ejo = 2 (Figure 2.4, left plot) . 

Figure 2.10 Upper solid analytical high-current polarization curve for uniform loading. Crosses the exact numerical polarization curve for uniform loading. Lower solid polarization curve of the active layer with optimal shape of catalyst loading. Short-dashed curve nonuniform loading third and fourth order derivatives in Eq. (2.92) are taken into accoimt.

Consider first the low-current polarization curve for Tafel kinetics (2.29). In this equation we should replace... 

Making this substitution, we obtain the low-current polarization curve of the cathode side, which takes into account oxygen transport in the GDL ... 

Figure 3.2 The high-current polarization curve of the cathode side of a PEM fuel cell, Eq. (3.7). Note the limiting current density at j = jo-...

Consider first the low-current regime of CCL operation. The low-current polarization curve of a CCL is given by (2.44). To simplify calculations we will assume that parameter e (2.13) is large, so that coth(l/e) e (this situation is typical of PEFCs). Equation (2.44) then reduces to... 

This result should obey the normalization condition (4.134) calculating the integral we get the high-current polarization curve of a cell with variable catalyst loading ... 

Above we have neglected oxygen transport loss in the GDL. It is easy to show that accounting for this loss does not change the result (4.148). Consider the low-current polarization curve of the catalyst layer (4.140). In the presence of transport loss, the oxygen concentration in the catalyst layer cj is related to this concentration in the channel Ch by Elq. (3.2). In dimensionless variables this equation reads... 

To conclude this section, note that the low- and high-current polarization curves can be derived directly by dividing Equation 4.69 by Equation 4.70. This yields... 

Assuming, again, that rjo is independent of z (the section Why r]o is Nearly Constant along the Channel ), this can only be possible if the ratio jo/Ch is constant. Repeating the calculations in the section Low-current Polarization Curve leads to the cell polarization curve (Kulikovsky, 2011a)... 

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