Hierarchical Model of CCL Operation

Owing to the assumed spherical symmetry of agglomerates, the agglomerate structure can be represented by a unit cell that is repeated throughout the agglomerate. This 

FIGURE 4.11 (a) Schematic 2D cross-sectional view of an agglomerate of Pt/C that is sur- 

The macroscale model is almost identical to the MHM discussed in the section Macrohomogeneous Model with Constant Properties. In the electrochemical source term of the MHM Equation 4.5, a spatial variation in the agglomerate effectiveness factor must be accounted for 

The model of water-filled nanopores, presented in the section ORR in Water-Filled Nanopores Electrostatic Effects in Chapter 3, was adopted to calculate the agglomerate effectiveness factor. As a reminder, this model establishes the relation between metal-phase potential and faradaic current density at pore walls using Poisson-Nernst-Planck theory. Pick s law of diffusion, and Butler-Volmer equation 

In addition to the detailed treatment of CCL structure and processes, the model developed in Sadeghi et al. (2013b) employed a simple empirical description of pore blocking in GDL by liquid water. 

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The assumption of constant Ch+ fails in water-filled agglomerates, considered in the section Hierarchical Model of CCL Operation in Chapter 4 and in water-filled... 

As for the first assumption, the electrolyte phase must be treated as a mixed phase. It consists of a thin-film structure of ionomer at the surface of Pt/C agglomerates and of water in ionomer-free intra-agglomerate pores. The proton density is highest at the ionomer film (pH 1 or smaller), and it is much smaller in water-filled pores (pH > 3). However, the proton density distribution is not incorporated in the statistical utilization Tstat, but in an agglomerate effectiveness factor, defined in the section Hierarchical Model of CCL Operation. ... 

As concerns the second assumption, direct access to the gas pore network is not a stringent requirement for keeping the Pt surface active. The condensed phases of water and ionomer possess finite oxygen permeabilities, which will render oxygen concentrations finite at electrolyte-covered Pt particles. Again, this is an issue of nonuniform reaction rate distributions that will be dealt with in the section Hierarchical Model of CCL Operation. In that section, a two-scale performance model will be presented, which couples transport and distribution of protons and oxygen at the agglomerate level and at the macroscopic scale. 

In the section Hierarchical Model of CCL Operation, a hierarchical modeling framework will be presented it couples multiple effects of proton and oxygen transport at the mesoscopic scale of agglomerates and at the macroscopic scale of the layer. In that general case, the CL effectiveness factor can be defined by... 

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