Low-current polarization curve

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 ... 

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... 

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... 

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)... 

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 ). 

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) . 

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... 

An analysis of Eq. (6.13) show that for n = 1 and P = 0.5 and for current densities less than 4% of t the polarization is very low (less than 1 mV) and can practically be neglected. The linear section of the polarization curve extends up to current densities which are 40% of f. At current densities higher than 4f, the semilogarith-mic polarization relation is observed. 

The current is recorded as a function of time. Since the potential also varies with time, the results are usually reported as the potential dependence of current, or plots of i vs. E (Fig.12.7), hence the name voltammetry. Curve 1 in Fig. 12.7 shows schematically the polarization curve recorded for an electrochemical reaction under steady-state conditions, and curve 2 shows the corresponding kinetic current 4 (the current in the absence of concentration changes). Unless the potential scan rate v is very low, there is no time for attainment of the steady state, and the reactant surface concentration will be higher than it would be in the steady state. For this reason the... 

It can be seen from Fig. 14.7 that the polarization curve for this reaction involving p-type germanium in 0.1 M HCl is the usual Tafel straight-line plot with a slope of about 0.12 V. For -type germanium, where the hole concentration is low, the curve looks the same at low current densities. However, at current densities of about 50 AJvcF we see a strong shift of potential in the positive direction, and a distinct limiting current is attained. Thus, here the first reaction step is inhibited by slow supply of holes to the reaction zone. 

Often, it will be found that currents for a given reaction cannot be measured at all metals at the same value of potential. At some metals the currents would be too low for a reliable, sufficiently accurate determination at others they might be too high for a satisfactory experimental realization. A comparison will then be possible only after an extrapolation of data obtained in a different region of potentials, to the value of selected for comparison. This extrapolation may not be sufficiently reliable where the Tafel section of the polarization curve is too short or indistinct. 

Applying the Tafel equation with Uq, we obtain the polarization curves for Pt and PtsNi (Fig. 3.10). The experimental polarization curves fall off at the transport limiting current since the model only deals with the surface catalysis, this part of the polarization curve is not included in the theoretical curves. Looking at the low current limit, the model actually predicts the relative activity semiquantitatively. We call it semiquantitative since the absolute value for the prefactor on Pt is really a fitting parameter. 

In order to prove the S-shaped character of the polarization curve, the system was studied galvanostatically. The model predicts that the sandwiched branch of the polarization curve should be stable, and therefore measurable under galvanostatic conditions. Figure 6.10 shows the results of the experiment depending on the scan rate, an S-shaped curve can be observed in the back scan, i.e., from high to low current. At low... 

It was experimentally found that the polarization curves of the investigated air gas-diffusion electrodes in a semi-logarithmic scale at low current densities (below 10 mA/cm2) are straight lines, which can be treated as Tafel plots. At these low current densities the transport hindrances in the air electrode are negligible so that activation hindrances only are available. 

Ultimately, the catalyst performance of a real fuel cell is of the greatest importance. The DEFC polarization curves for the two PtSn anode catalysts are tested and shown in Fig. 15.9. The characteristic data are summarized in Table 15.4. The PtSn-1 catalyst shows a strongly enhanced electron-oxidation reaction (EOR) activity and much better performance in both the activation-controlled region (low-current density region) and... 

The performance of a fuel cell is most often reported in the form of a polarization curve. Such a curve is shown in Figure 3. Roughly speaking, the polarization curve can be broken down into three main regions. At low currents, the behavior of a fuel cell is dominated by kinetic losses. These losses... 

Steady-State Kinetics, There are two electrochemical methods for determination of the steady-state rate of an electrochemical reaction at the mixed potential. In the first method (the intercept method) the rate is determined as the current coordinate of the intersection of the high overpotential polarization curves for the partial cathodic and anodic processes, measured from the rest potential. In the second method (the low-overpotential method) the rate is determined from the low-overpotential polarization data for partial cathodic and anodic processes, measured from the mixed potential. The first method was illustrated in Figures 8.3 and 8.4. The second method is discussed briefly here. Typical current—potential curves in the vicinity of the mixed potential for the electroless copper deposition (average of six trials) are shown in Figure 8.13. The rate of deposition may be calculated from these curves using the Le Roy equation (29,30) ... 

The individual polarization curves for the metals are often modified as a result of interactions resulting from codeposition. If the alloy deposition occurs at low polarization, the nobler metal will be deposited preferentially (Cu in Example 11.1). All factors, however, that increase polarization during electrodeposition, such as high current density, low temperature, and quiescent solution—factors that increase concentration polarization—will favor the deposition of the less noble metal (Zn in Example 11.1). 

Equation 1.7 for the reduction of protons at a mercury surface in dilute sulphuric add is followed with a high degree of accuracy over the range -9 Tafel plot i.s shown in Figure 1.5. At large values of the overpotential, one reaction dominates and the polarization curve shows linear behaviour. At low values of the overpotential, both the forward and back reactions are important in determining the overall current density and the polarization curve is no longer linear. 

Consider first the polarization curve (i.e., Tafel plot) for the anodic halfreaction occurring in corrosion of stainless steels (Fig. 16.8). The diagram for the active region is much the same as has been seen for other anodes (Figs. 15.4 to 15.7). As Eh is increased to a certain specific value, however, a sudden and dramatic drop in the anodic current density i occurs, corresponding to formation of an oxide film. At higher Eh, i remains constant at a very low level (the horizontal scale in Fig. 16.8 is logarithmic), and the metal has become passive, that is, effectively immune from corrosion. 

A cell with a capacity of 1 L was made of mild steel. An amorphous carbon rod (diameter 25 mm length 15 cm) was used as anode, the inside wall of the cell as cathode and a platinum wire was used as reference electrode. The anode compartment of the cell was separated from the cathode compartment by a skirt of steel welded to the cell cover. The anode gas was passed through a tube filled with tablets of NaF to absorb anhyd HF gas and then led to a gas sampler. Fluorine was detected with K.I soln. After the starting material was added into the molten KIIF2/HF salt, the electrolyte was pre-electrolyzed at a low current density until NF2 was detected, and then current efficiency of each product and polarization curves by galvanostatic or potential sweep method were determined (Table 1). At optimum conditions the current efficiency of NF3 was 55%. 

---