Polarization Curve Fitting

Note The second row shows relative humidities of the anode and cathode in die format RHA RHC. Cell temperature is 353 K and pressure is 1 bar. 

FIGURE 5.9 Points experiment (Dobson et al. 2012). Lines Equation 5.60 with r]Q given by Equation 5.74. The experimental conditions and oxygen diffusion coefficients are listed in Table 5.5. Common for all the curves, fitting parameters are collected in Table 5.4. 

For both curves, fitting yields very close values of the exchange current density of k — 10 A cm (Table 5.5). This value of i is nearly two orders of magnitude less than the one obtained in Dobson et al. (2012) from the same set of curves using a flooded agglomerate model. Note that, as discussed in Dobson et al. (2012), their value is an order of magnitude higher than expected thus, the values of i indicated in Table 5.5 could be closer to reality. 

The GDL oxygen diffiisivity is fairly constant 0.026 and 0.023 cm s for curves 1 and 2, respectively (Table 5.5). Taking the oxygen diffusivity in air in the order of Dfree = 0.2 cm s , and using the equation for Bruggemann correction Db = 

Dfree GDL DL porosity, one obtains gdl — 0.26. This low value suggests that the GDL is partially flooded. 

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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. 

Using the value obtained for cpfh and the known value of a, and considering the diffusion length Lp as a fitting parameter, one can obtain good agreement of the theory with experiment for the entire polarization curve (Fig. 9)... 

Photocurrent measurements permit the determination of the hole diffusion length Lp. As was already noted, comparison of measured and calculated polarization curves allows Lp to be determined by a fitting procedure. For example, Butler (1977) and Wilson (1977) obtained for W03 and TiOz the values of Lp equal to 0.5 x 10-4 and 4 x 10-4 cm, respectively. 

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].)... 

Mathematically, geometric parameters can be described by using the Fourier Series in polar coordinates (p,9). Thus, given a set of boundary points (x, y) from an object of interest, they can be transformed into the polar coordinates with respect to its geometric center (x, y). A curve fitting technique in polar coordinates can be used to fit this set of points into a Fourier Series such that any point p(0) on this boundary can be expressed by... 

Figure 16. Concept of using a Fourier Series to represent the boundary of an object. The (x,y) coordinates of the boundary points of an object is transformed to polar coordinates. Each point on the boundary p(0) can be expressed by a Fourier Series obtained from curve fitting of the boundary points. (X,Y) are the coordinates of the center of gravity.

Fig. 2 distinguishes the domains of immunity, corrosion and passivity. At low pH corrosion is postulated due to an increased solubility of Cu oxides, whereas at high pH protective oxides should form due to their insolubility. These predictions are confirmed by the electrochemical investigations. The potentials of oxide formation as taken from potentiodynamic polarization curves [10] fit well to the predictions of the thermodynamic data if one takes the average value of the corresponding anodic and cathodic peaks, which show a certain hysteresis or irreversibility due to kinetic effects. There are also other metals that obey the predictions of potential-pH diagrams like e.g. Ag, Al, Zn. 

In addition to the form of in first-layer absorption, its magnitude is also of significance as regards validity or relative importance of Model 2. Here it is assumed that Model 2 may be based on dispersion forces with polarizations to produce larger than normal first-layer adsorbate-adsorbent potentials (the a term in Equation 6b) and longer than normal range adsorbate-adsorbate repulsions. One may evaluate a and b by curve fitting as follows ... 

Ahn et al. have developed fibre-based composite electrode structures suitable for oxygen reduction in fuel cell cathodes (containing high electrochemically active surface areas and high void volumes) [22], The impedance data obtained at -450 mV (vs. SCE), in the linear region of the polarization curves, are shown in Figure 6.22. Ohmic, kinetic, and mass transfer resistances were determined by fitting the impedance spectra with an appropriate equivalent circuit model. 

D. Outka et al. have studied the orientation of several Langmuir-Blodgett monolayers on oxidized Si(111) (16). By very detailed curve fitting and polarization dependence analysis they determined that arachidic acid (CH3(CH2)lgC02H) was not ordered, Cd arachidate was ordered normal to the substrate surface, and Ca arachidate was tilted 33° from the surface normal. 

The polarization curves for concentrations higher than 6 pM can be fit by Equations (5) and (6) and Figure 1.9 shows the S- and P-polarized harmonic data for the lO-pM solution. Similar results have been reported for SHG experiments on the rfaodamine dyes at various interfaces. The best fit is obtained by introducing a phase difference, rj, between the parameters A and B consistent with the complex nature of tiie susceptibilities on resonance. A plot of the concentration dependence of the A/B, given in Figure 1.10, shows that a relatively sharp transition takes place in the structure of the interface at an aqueous dye concentration of ca. 6 pM. 

The value of k was obtained by curve-fitting experimental infinite dilution activity coefficients of paraffins, olefins, and aromatics in several polar solvents. The value of k for each hydrocarbon group is given in Table IV. The values for Ai are taken from plots (28). The method for calculating r4 is also available (28). 

J. V. PETROCELLI I most certainly agree with your comment. I pointed out that my presentation was oversimplified, and 1 am glad that you brought this up. One must know the exact polarization curves for each system. There have been several systems reported in the literature, however, that fit Tafel plots very closely. 

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