Macrohomogeneous model

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 ... 

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. 

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.)...

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... 

Therefore, the macrohomogeneous concept can also be adequately extended to the whole cell. For instance, a framework for macrohomogeneous modeling of porous SOFC electrodes is possible by taking into account multicomponent diffusion, multiple electrochemical and chemical reactions, and electronic and ionic conduction. The concept applies to both porous anodes and cathodes. The derivation of the model is illustrated by considering different chemical and electrochemical reaction schemes. The framework is general enough so that additional chemical and electrochemical reactions can be accounted for. 

Figure 2.8. Fltixes of water oxygen and protons in the CCL and boundary conditions to be used in the macrohomogeneous model of CCL performance and water balance.

In the past, studies of the macrohomogeneous model have explored the effects of thickness and composition on performance and catalyst utilization. The relevant solutions have been discussed in detail in Refs. [17-19,84]. Here, we will briefly review the main results. Analytical relations for reaction rate... 

The fact which transport limitations prevails in the CCL depends on the composition. If it has insufficient porosity, but a well-developed network of polymer electrolyte, it will have severe gas transport limitations but good proton transport and the other way around. The macrohomogeneous model... 

In this chapter the scope of our discussion was restricted by the macrohomogeneous model of CL performance and its derivatives. The first numerical macrohomogeneous models of CCL for a PEM fuel cell were developed by Springer and Gottesfeld (1991) and by Bernard and Verbrugge (1991). These models included the diffusion equation for oxygen transport, the Tafel law for the rate of ORR and Ohm s law for the proton transport in the electrolyte phase. A similar approach was then used by Perry, Newman and Cairns (Perry et al., 1998) and by Eikerling and Kornyshev (1998) for combined numerical and analytical studies. 

An extension of the macrohomogeneous model, which takes into account the dependence of transport parameters on CCL composition, has recently been developed by Eikerling (2006). The model includes the dependence of species diffusivity on pore size distribution and incorporates a model of water management. 

This ambitious task raises complicated nano-scale problems of CL structure-composition-function relations (Promislow and Wetton, 2009). Nonetheless, thanks to their relative simplicity, in the foreseeable future, variants of macrohomogeneous models will play an important role in cell and stack modelling. 

We will discuss the main results of the macrohomogeneous model first. 

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