Catalyst layer porous-electrode theory

Porous-electrode theory has been used to describe a variety of electrochemical devices including fuel cells, batteries, separation devices, and electrochemical capacitors. In many of these systems, the electrode contains a single solid phase and a single fluid phase. Newman and Tiedemann reviewed the behavior of these flooded porous electrodes [23]. Many fuel-cell electrodes, however, contain more than one fluid phase, which introduces additional complications. Typical fuel cell catalyst layers, for example, contain both an electrolytic phase and a gas phase in addition to the solid electronically conducting phase. An earher review of gas-diffusion electrodes for fuel cells is provided by Bockris and Srinivasan [24]. 

Even among the models that employ porous-electrode theory, there have been differences in how the various models choose to describe the electrode. For example, consider the catalyst layer in a state-of-the-art PEM fuel cell containing a supported-platinum-on-carbon (or platinum-alloy-on-carbon) catalyst, a polymeric membrane material, and, in some cases, a void volume. Whether this void volume is considered explicitly, or whether gas- and liquid-phase transport is simply described via permeability through the ionomer is one of the key differences between the various models. 

Going from planar to porous electrode introduces another length scale, the electrode thickness. In the case of a PEM fuel cell catalyst layer, the thickness lies in the range of IcL — 5-10 pm. The objective of porous electrode theory is to describe distributions of electrostatic potentials, concentrations of reactant and product species, and rates of electrochemical reactions at this scale. An accurate description of a potential distribution that accounts explicitly for the potential drop at the metal/electrolyte interface would require spatial resolution in the order of 1 A. This resolution is hardly feasible (and in most cases not necessary) in electrode modeling because of the huge disparity of length scales. The simplified description of a porous electrode as an effective medium with two continuous potential distributions for the metal and electrolyte phases appears to be a consistent and practicable option for modeling these stmctures. 

A timeline of major developments in porous electrode theory that led to the current approaches in catalyst layer modeling is depicted in Figure 3.3. 

FIGURE 3.3 A timeline of developments in porous electrode theory and catalyst layer modeling. 

The species diffusivity, varies in different subregions of a PEFC depending on the specific physical phase of component k. In flow channels and porous electrodes, species k exists in the gaseous phase and thus the diffusion coefficient corresponds with that in gas, whereas species k is dissolved in the membrane phase within the catalyst layers and the membrane and thus assumes the value corresponding to dissolved species, usually a few orders of magnitude lower than that in gas. The diffusive transport in gas can be described by molecular diffusion and Knudsen diffusion. The latter mechanism occurs when the pore size becomes comparable to the mean free path of gas, so that molecule-to-wall collision takes place instead of molecule-to-molecule collision in ordinary diffusion. The Knudsen diffusion coefficient can be computed according to the kinetic theory of gases as follows... 

At a critical value of the fraction of objects of one type, these objects would form an extended cluster that connects the opposite external faces of the sample. At this so-called percolation threshold, the corresponding physical property represented by the connected objects would start to increase above zero. Thereby percolation theory establishes constitutive relations between composition and structure of heterogeneous media and their physical properties of interest. For porous electrodes or catalyst layers in PEFC, these properties are electrical conductivities of electrons and protons, diffiisivities of gaseous reactants and water vapor, and liquid water permeability. 

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