Macrohomogenization

At macroscopic level, the overall relations between structure and performance are strongly affected by the formation of liquid water. Solution of such a model that accounts for these effects provides full relations among structure, properties, and performance, which in turn allow predicting architectures of materials and operating conditions that optimize fuel cell operation. For stationary operation at the macroscopic device level, one can establish material balance equations on the basis of fundamental conservation laws. The general ingredients of a so-called "macrohomogeneous model" of catalyst layer operation include ... 

Main Results of Macrohomogeneous Catalyst Layer Models... 

The macrohomogeneous model was exploited in optimization studies of the catalyst layer composition. The theory of composifion-dependent performance reproduces experimental findings very well. - The value of the mass fraction of ionomer that gives the highest voltage efficiency for a CCL with uniform composition depends on the current density range. At intermediate current densities, 0.5 A cm < jo < 1.2 A cm , the best performance is obtained with 35 wt%. The effect of fhe Nation weight fraction on performance predicted by the model is consistent with the experimental trends observed by Passalacqua et al. ... 

The other type of model is the macrohomogeneous model. These models are macroscopic in nature and, as described above, have every phase defined in each volume element. Almost all of the models used for fuel-cell electrodes are macrohomogeneous. In the literature, the classification of macrohomogeneous models is confusing and sometimes contradictory. To sort this out, we propose that the macrohomogeneous models be subdivided on the basis of the length scale of the model. This is analogous to dimensionality for the overall fuel-cell models. 

In this section, the reactions and general equations for the catalyst layers are presented first. Next, the models are examined starting with the interface models, then the microscopic ones, and finally the simple and embedded macrohomogeneous ones. Finally, at the end of this section, a discussion about the treatment of flooding is presented. 

These models are essentially macrohomogeneous versions of the single-gas-pore models. 

The final simple macrohomogeneous porous-electrode models are the ones that are more akin to thin-film models. In these models, the same approach is taken, but instead of gas diffusion in the catalyst layer, the reactant gas dissolves in the electrolyte and moves by diffusion and reaction. The... 

Figure 12. Comparison of simple macrohomogeneous agglomerate (solid line) and thin-film (dashed line) cathode models to experimental data (diamonds). Data are adapted from ref 34.

Figure 13. Plot of cathode potential as a function of current density for a macrohomogeneous embedded model where the proton conductivity is assumed to be uniform (0.044 S/m), curve a, or varies with water production (changing humidity) across the catalyst layer, curve b. (Reproduced with permission from ref 98. Copyright 2002 The Electrochemical Society, Inc.)...

Figure 25. Adler s ID macrohomogeneous model for the impedance response of a porous mixed conducting electrode. Oxygen reduction is viewed as a homogeneous conversion of electronic to ionic current within the porous electrode matrix, occurring primarily within a distance A from the electrode/electrolyte interface (utilization region). (Adapted with permission from ref 28. Copyright 1998 Elsevier.)...

Figure 28. Svensson s macrohomogeneous model for the i— 1/characteristics of a porous mixed-conducting electrode, (a) The reduction mechanism assuming that both surface and bulk diffusion are active and that direct exchange of oxygen vacancies between the mixed conductor and the electrolyte may occur, (b) Tafel plot of the predicted steady-state i— V characteristics as a function of the bulk oxygen vacancy diffusion coefficient. (Reprinted with permission from ref 186. Copyright 1998 Electrochemical Society, Inc.)...

Figure 48. Kenjo s ID macrohomogeneous model for polarization and ohmic losses in a composite electrode, (a) Sketch of the composite microstructure, (b) Description of ionic conduction in the ionic subphase and reaction at the TPB s in terms of interpenetrating thin films following the approach of ref 302. (c) Predicted overpotential profile in the electrode near the electrode/electrolyte interface, (d) Predicted admittance as a function of the electrode thickness as used to fit the data in Figure 47. (Reprinted with permission from refs 300 and 301. Copyright 1991 and 1992 Electrochemical Society, Inc. and Elsevier, reepectively.)...

This estimate could prove to be valuable input for more accurate representation of the pore blockage effect in the macroscopic two-phase fuel cell models. Figure 24 shows the variation of the effective oxygen diffusivity with liquid water saturation from the correlation in Eq. (29) along with the typical macrohomogeneous correlation with m = 1.5 and b = 1.5 otherwise used arbitrarily in the macroscopic fuel cell modeling literature. 

With the evaluated site coverage and pore blockage correlations for the effective ECA and oxygen diffusivity, respectively, and the intrinsic active area available from the reconstructed CL microstructure, the electrochemistry coupled species and charge transport equations can be solved with different liquid water saturation levels within the 1-D macrohomogeneous modeling framework,25,27 and the cathode overpotential, q can be estimated. 

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... 

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