Polarization curve modeling

Step 2 the static parameters obtained are all fed into the polarization curve model. Optimization on the basis of the experimental polarization curve enables us to determine the two remaining parameters 7 and/o. 

Figure 2.5 An example polar curve, modeled enthalpy of formation of H2 have most influ-from the preceding treatment of fuel cell ence entropy, internal currents, kinetic losses,...

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. 

Figure 6.8 S-shaped polarization curve observed in the CO oxidation model (for the exact model parameters, see Koperetal. [2001]). The thin line shows the cyclic voltammetry observed at a low scan rate of 2 mV/ s.

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... 

Spiro [27] has derived quantitative expressions for the catalytic effect of electron conducting catalysts on oxidation-reduction reactions in solution in which the catalyst assumes the Emp imposed on it by the interacting redox couples. When both partial reaction polarization curves in the region of Emp exhibit Tafel type kinetics, he determined that the catalytic rate of reaction will be proportional to the concentrations of the two reactants raised to fractional powers in many simple cases, the power is one. On the other hand, if the polarization curve of one of the reactants shows diffusion-controlled kinetics, the catalytic rate of reaction will be proportional to the concentration of that reactant alone. Electroless metal deposition systems, at least those that appear to obey the MPT model, may be considered to be a special case of the general class of heterogeneously catalyzed reactions treated by Spiro. 

The second part of the polarization curve is the ohmic regime. In this region, the potential varies linearly with the current density. This allows for Ohm s law to be used for modeling purposes... 

The last part of the polarization curve is dominated by mass-transfer limitations (i.e., concentration overpotential). These limitations arise from conditions wherein the necessary reactants (products) cannot reach (leave) the electrocatalytic site. Thus, for fuel cells, these limitations arise either from diffusive resistances that do not allow hydrogen and oxygen to reach the sites or from conductive resistances that do not allow protons or electrons to reach or leave the sites. For general models, a limiting current density can be used to describe the mass-transport limitations. For this review, the limiting current density is defined as the current density at which a reactant concentration becomes zero at the diffusion medium/catalyst layer interface. 

Figure 4. Model and experiment comparison of polarization curves for air or oxygen at different gas pressures and at 70 °C using eq 20. (Reproduced with permission from ref 12. Copyright 1995 The Electrochemical Society, Inc.)...

Figure 41. Comparison of localized polarization curves between experiments (a) and model predictions (b) for a 50 cm DMFC with an anode flow stoichiometry of 27 and a cathode air stoichiometry of 5 at 0.1 A/cm. ...

Difficulties in obtaining good quantitative agreement between predicted and measured distribution results are indicative that model refinements as well as an improved property database will be needed before accurate quantitative predictions of not only overall polarization curve but also detailed distributions within a DMFC may be obtained. 

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... 

Figure 26 exhibits the polarization curves in terms of the cathode overpotential variation with current density for the CL27 obtained from the 3-D, single-phase DNS model prediction,25,27 the experimental observation25,27 and the liquid water transport corrected 1-D macrohomogeneous model.27 The polarization curve refers to the cathode overpotential vs. current density curve in the... 

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-... 

Application to Strongly Absorbing Nonassociated Liquid V. Hat-Curved Model and Its Application for Polar Fluids... 

Section VI. It is possible to unblock the first drawback (i), if to assume a nonrigidity of a dipole—that is, to propose a polarization model of water. This generalization roughly takes into account specific interactions in water, which govern hydrogen-bond vibrations. The latter determine the absorption R-band in the vicinity of 200 cm-1. A simple modification of the hat-curved model is described, in which a dipole moment of a water molecule is represented as a sum of the constant (p) and of a small quasi-harmonic time-varying part p(/j. 

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