Experimental polarization curves

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. 

Experimental validation of SOFC models has been quite scarce. Khaleel and Selman °° presented a comparison of 1-D electrochemical model calculations with experimental polarization curves for a range of... 

A perfect prototype of an ideally cation-permselective interface is a cathode upon which the cations of a dissolved salt are reduced. Experimental polarization curves measured on metal electrodes fit the theory very closely. Since in dimensional units the limiting current is proportional to the bulk concentration, the polarization measurements on electrodes may serve for determining the former. This is the essence of the electrochemical analytical method named polarography. (For the theory of polarographical methods see [28]—[30].)... 

Validation is performed in two steps first an experimental polarization curve, obtained with a fixed inlet gas flow rate, is compared with the calculated values, thus allowing the determination of some unknown parameter values (model calibration). Afterwards, three polarization curves, obtained at constant fuel and oxygen utiliza-... 

In Fig. 3.5, the experimental polarization curve for a PEM stack of 500 W is reported together with the output power supplied by the stack in the experimental conditions indicated in the caption. This stack is constituted by 32 individual fuel... 

In the electrochemical benchmark monograph by Bockris and Reddy (B R) (Ref. 3, p. 1001), these authors developed, based upon the quasiequilibrium approximation, transfer coefficients, as, in terms of mechanistic parameters. Their analysis demonstrated how such as, obtained from experimental polarization curves, can give information directly, enabling elucidation of reaction mechanisms. Their transfer coefficients are written as... 

The following problem is designed to provide understanding of Tafel plots for individual half-cell reactions and the form of experimental polarization curves to be expected based on the theory. Assume that for a given metal, M,... 

The earlier sections of this chapter discuss the mixed electrode as the interaction of anodic and cathodic reactions at respective anodic and cathodic sites on a metal surface. The mixed electrode is described in terms of the effects of the sizes and distributions of the anodic and cathodic sites on the potential measured as a function of the position of a reference electrode in the adjacent electrolyte and on the distribution of corrosion rates over the surface. For a metal with fine dispersions of anodic and cathodic reactions occurring under Tafel polarization behavior, it is shown (Fig. 4.8) that a single mixed electrode potential, Ecorr, would be measured by a reference electrode at any position in the electrolyte. The counterpart of this mixed electrode potential is the equilibrium potential, E M (or E x), associated with a single half-cell reaction such as Cu in contact with Cu2+ ions under deaerated conditions. The forms of the anodic and cathodic branches of the experimental polarization curves for a single half-cell reaction under charge-transfer control are shown in Fig. 3.11. It is emphasized that the observed experimental curves are curved near i0 and become asymptotic to E M at very low values of the external current. In this section, the experimental polarization of mixed electrodes is interpreted in terms of the polarization parameters of the individual anodic and cathodic reactions establishing the mixed electrode. The interpretation then leads to determination of the corrosion potential, Ecorr, and to determination of the corrosion current density, icorr, from which the corrosion rate can be calculated. 

The concepts associated with an analysis of Fig. 4.15 are reemphasized by examining the information derivable from experimental polarization curves (i.e., E versus log Iex curves). In general, the following are available from measurements or calculations E x, E M, the cathodic polarization curve, the anodic polarization curve, and Ecorr from asymptotic values of the polarization curves as Iex red — 0 and I x — 0. The... 

Fig. 4.29 Representative, experimental polarization curves for metal M in a deaerated acid solution...

Fig. 6.2 Schematic experimental polarization curves (solid curves) assuming Tafel behavior for the individual oxidation and cathodic-reactant reduction polarization curves (dashed curves)...

Tafel Curve Modeling (Ref 4, 5). Equation 6.5 provides the form of the experimental polarization curve when the anodic and cathodic reactions follow Tafel behavior. The equation accounts for the curvature near Ecorr and Icorr, which is observed experimentally. Physically, the curvature is a consequence of both the anodic and cathodic reactions having measurable effects on Iex at potentials near Ecorr. Tafel-curve modeling uses experimental data taken within approximately 25 mV of Ecorr where the corrosion process is less disturbed by induced corro-... 

The numerical methods [32, 33, 34, 35, 36, 37] developed for the analysis of experimental polarization curves described by the current-voltage characteristic (2) with the aim of determining the electrochemical parameters a, /3 and h, are of considerable importance in the field of basic research as well as in corrosion rate monitoring. They permit, in fact, a more objective evaluation of these quantities with reference to a given potential difference interval AE, removing the degree of subjectivity that is inherent in the graphic determination of the Tafel slopes. 

Among the factors that may determine the geometric shape of an experimental polarization curve and the region where the validity of the Tafel law begins to be evident, are the quantities a and fi. The influence these parameters exert on the graphic shape of a polarization curve is discussed in some studies [37, 38]. 

When an experimental polarization curve is performed, the overvoltage is applied from the outside between the points A and D of the dipole. Consequently, the true polarization, which coincides with the potential difference between B and D and determines the kinetics of the electrode process, generally differs from the measured value. 

Figure 7, concerning the behaviour of the SA 213 grade T22 low alloy steel in a solution containing 100 g/1 of EDTA at pH 6 and a temperature of 100 °C, gives a very effective representation of this mathematical concept because it clearly shows the difference in shape between the experimental polarization curve (Ra—Q ft) and the curve closest to the ideal evolution of the corrosion process (1 ,=1.1 ft). In the case under examination... 

Examination of figure 7 shows that the trend of the experimental polarization curve markedly differs from that of the curve corrected using the expression (10). It also reveals that the exposed surface area of the specimen plays a determinant role when, to attain a given overvoltage, use must be made of a high-intensity external current. In the present case, the difference in width (about 400 mV) between the two AE and AE intervals shows that, in some situations, the relevant contribution of the ohmic drop makes it difficult to perform significant measurements. 

Finally, it is important to note that, since the quantity (a + /3) refers to the ideal polarization curve, the computed value of may differ sensibly from the real one if no correction factor is used in analysing an experimental polarization curve. 

A numerical study of the influence of the ohmic drop on the evaluation of electrochemical quantities has been conducted, for example, over the AE interval [-20, 20] mV by means of the IRCOM program, which makes use of a polynomial of the sixth degree, considering some experimental polarization curves and taking the values of the electrochemical parameters obtained by the NOLI method. The examples examined have shown that the representation of experimental data by a polynomial of the sixth degree is very good and that the evaluation of the correct order of magnitude of the corrosion current density, in the presence of an ohmic contribution to the electrode potential, requires that the actual values of the Tafel slopes be known. 

The effect of area ratio is handled with experimental polarization curves in a similar fashion to that shown for schematic Evans diagrams in Fig. 11. Figure 13 shows experimental polarization curves for metals... 

This expression was derived in Chapter 1.3. An experimental polarization curve, such as that shown in Fig. 3(b), can be fitted by nonlinear least squares fitting to this expression. Such a fit will yield values for the corrosion rate, corrosion potential, and anodic and cathodic Tafel slopes. Most modern software packages for analysis of corrosion data have this capability. 

Fig. 6.6 Experimental polarization curve for Fe in 0.01 N HCl/EtOH with and without IR-drop compensation [2]...

Fig. 8.15 Calculated and experimental polarization curves (Source [183] reproduced with permission of Elsevier)...

In general, it is possible to obtain good agreement between the predieted and the experimental polarization curves with most models. Even the earlier one-dimensional model of the MEA developed by Bemadi and Verbrugge [45, 46] or the two-dimensional model developed by Siegel et al. [51], resulted in excellent agreement between eaeh model and experiment with the adjustment of some parameters. In the model presented here, all the parameters are within physical limits and since no parameters needed to be adjusted, this will help to conduct a systematic study on the importance of each single parameter on the fuel eell performanee. 

Figure 3. 4. Comparison of three-dimensional simulation with an experimental polarization curve.

The extrapolation of an experimental polarization curve, measured from the Tafel region to the reversible potential, reveals the exchange current density (Figure 4.9). The reciprocal of the slopes of the straight lines yield the Tafel coefficients and P. ... 

One major goal of fuel-cell models is to match the experimental polarization curve for the operating conditions considered. The simplest approach is to treat the MEA as a reactive boundary between the anode and cathode sides. With increasing complexity, the two catalyst layers can be described separately as an effective boundary, a quasi-three-dimensional layer which is partially flooded with... 

---