Catalyst layers modeling domain

Recently, a new class of stochastic CL models has been developed (Mukherjee and Wang, 2006). These models simulate species transport in a small 3D domain of the catalyst layer. The domain is subdivided into elementary computational cells representing either a void space or an electrolyte/carbon phase. The structure of this domain is obtained by the stochastic reconstruction of micro-images of real catalyst layers. 

This section provides a comprehensive overview of recent efforts in physical theory, molecular modeling, and performance modeling of CLs in PEFCs. Our major focus will be on state-of-the-art CLs that contain Pt nanoparticle electrocatalysts, a porous carbonaceous substrate, and an embedded network of interconnected ionomer domains as the main constituents. The section starts with a general discussion of structure and processes in catalyst layers and how they transpire in the evaluation of performance. Thereafter, aspects related to self-organization phenomena in catalyst layer inks during fabrication will be discussed. These phenomena determine the effective properties for transport and electrocatalytic activity. Finally, physical models of catalyst layer operation will be reviewed that relate structure, processes, and operating conditions to performance. 

Figure 3.49. Slice of a PEM cell showing gas diffusion layer (A), catalyst layer (B) and membrane layer (C), at a magnification factor of 200 (a). Tunnelling electron microscope pictures of catalyst layer at a magnification factor of 500 (b), 18 400 (c) and in (d) 485 500. (From N. Siegel, M. EUis, D. Nelson, M.v.Spakovsky (2003). Single domain PEMFC model based on agglomerate catalyst geometry. J. Power Sources 115, 81-89. Used with permission from Elsevier.)...

The same authors developed this model further by transforming the volumetric catalyst layer source terms into interfacial boundary conditions for a full three-dimensional fuel-cell model [23]. The catalyst surface is represented as a two-dimensional plane, which is coupled to computational fluid dynamics (CFD) code. The modeling domain includes a channel pair with ribs and MEA. 

Fuel cell science is a rapidly growing field it includes overlapping domains of chemistry, physics and fluid mechanics. It is, therefore, hardly possible to discuss all the models and approaches used in FC studies under one heading. In this book we demonstrate the basic anal dical solutions describing coupled kinetic, transport and electric phenomena in catalyst layers, cells and stacks. 

This coarse-grained molecular dynamics model helped consolidate the main features of microstructure formation in CLs of PEFCs. These showed that the final microstructure depends on carbon particle choices and ionomer-carbon interactions. While ionomer sidechains are buried inside hydrophilic domains with a weak contact to carbon domains, the ionomer backbones are attached to the surface of carbon agglomerates. The evolving structural characteristics of the catalyst layers (CL) are particularly important for further analysis of transport of protons, electrons, reactant molecules (O2) and water as well as the distribution of electrocatalytic activity at Pt/water interfaces. In principle, such meso-scale simulation studies allow relating of these properties to the selection of solvent, carbon (particle sizes and wettability), catalyst loading, and level of membrane hydration in the catalyst layer. There is still a lack of explicit experimental data with which these results could be compared. Versatile experimental techniques have to be employed to study particle-particle interactions, structural characteristics of phases and interfaces, and phase correlations of carbon, ionomer, and water in pores. 

The modeling domain should be adjusted to numerically model the effects of using a multilayer electrode. In this case, the electrochemical reaction must occur at two different layers the inner and outer catalyst... 

The flow in the gas channels and in the porous gas diffusion electrodes is described by the equations for the conservation of momentum and conservation of mass in the gas phase. The solution of these equations results in the velocity and pressure fields in the cell. The Navier-Stokes equations are mostly used for the gas channels while Darcy s law may be used for the gas flow in the GDL, the microporous layer (MPL), and the catalyst layer [147]. Darcy s law describes the flow where the pressure gradient is the major driving force and where it is mostly influenced by the frictional resistance within the pores [145]. Alternatively, the Brinkman equations can be used to compute the fluid velocity and pressure field in porous media. It extends the Darcy law to describe the momentum transport by viscous shear, similar to the Navier-Stokes equations. The velocity and pressure fields are continuous across the interface of the channels and the porous domains. In the presence of a liquid phase in the pore electrolyte, two-phase flow models may be used to account for the interaction between the gas phase and the liquid phase in the pores. When calculating the fluid flow through the inlet and outlet feeders of a large fuel cell stack, the Reynolds-averaged Navier-Stokes (RANS), k-o), or k-e turbulence model equations should be used due to the presence of turbulence. 

A fully 2D model of the process has been developed by Ohs et al. (2011). The model takes into account water transport and gas permeation through the membrane and it resolves the catalyst layers. However, neither the details of the transition region between the D- and R-domains nor the distribution of local currents along the electrodes have been reported. 

This section considers a circular dead spot in the anode catalyst layer of a PEM fuel cell and solves a problem for the distribution of potentials and currents in and around the spot (Kulikovsky, 2013b). The spot is modeled as a circular domain with many orders of magnitude lower exchange current density of the HOR, which mimics much lower catalyst active surface. 

D model of a partial cross-section, yz-direction as defined in Figure 7-2, for analysis of fluxes and concentrations in the gas diffusion and catalyst layers. This is similar to the 1-D, but it is extended in two dimensions to include the effect of the "ribs" or "lands" between the channels. This domain may include only one side (either cathode or anode) or both sides. 

The modeling domain includes the membrane, the catalyst layer, and the gas diffusion layer, as shown in Figure 7-5. The conditions in the gas chamber are considered to be given and do not change in z-direction (or in any direction). 

For a 2-D modeling domain representing the gas diffusion layer above two halves of the channels and an entire rib between them (as shown in the figure below) representing a portion of an interdigitated flow field, write the governing equations and corresponding boundary conditions. Assume isothermal conditions. Also, assume that the catalyst layer has no thickness, that is, the reaction happens at the boundary between the gas diffusion layer and the catalyst layer. List the inputs (independent variables). 

The sol-gel method is also used to make very fine spherical particles of oxides. By structuring the solvent with surface-active solutes, other forms can also be realized during condensation of the monomeric reactant molecules to form a solid particle. Figure 8.16 shows that normal or inverse micelles or liquid crystals (liquids having long-distance order) can be formed in such solutes. Micelles are small domains in a liquid that are bounded by a layer of surface-active molecules. In these domains the solid is condensed and the microstructure of the precipitated solid is affected by the micelle boundaries. Monodisperse colloidal metal particles (as model catalyst) have been made in solvents that have been structured with surfactants. In the concentration domains where liquid crystals obtain highly porous crystalline oxides can be condensed. After calcination such solids can attain specific surface areas up to 1000 m /g. Micro-organisms use structured solutions when they precipitate calcite, hematite and silica particles. 

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