A mesoscale simulation is developed to simulate transport and electrochemistry in a small section of a proton exchange membrane fuel cell ͑PEMFC͒ cathode catalyst layer. Oxygen, proton, and electron transport are considered in the model. Many simulations are run with a wide variety of different parameters on stochastically reconstructed microstructures with a resolution of 2 nm. Knudsen diffusion plays an important role in limiting the transport of oxygen through the catalyst layer. Using larger carbon spheres in the catalyst layer increases the effective diffusivity of oxygen through the catalyst layer. The effective proton conductivity increases when larger spheres are used, a normal distribution of spheres is used, or a higher overlap tolerance is used. Increasing the overlap tolerance or overlap probability results in an increase in the effective electron conductivity. When electrochemical reactions are considered in a part of the catalyst layer that is close to the gas diffusion layer, the critical parameter that determines oxygen consumption is the carbon sphere radius. Oxygen consumption at a given carbon volume fraction is larger in microstructures containing spheres with smaller radii, because there is more surface area available for electrochemical reactions.Catalyst layers in proton exchange membrane fuel cells ͑PEM-FCs͒ have a complex structure due to the presence of carbon, platinum, ionomer, and pores. Carbon provides a pathway for electron conduction, platinum is used as a catalyst for electrochemical reactions, the ionomer allows for the conduction of protons, and oxygen or hydrogen travel through pores to reaction sites. It is difficult to make experimental observations of the catalyst layer, because its thickness is close to 10 m. To obtain a greater understanding of the transport properties and electrochemistry in the catalyst layer, numerical simulation can be used. Several different approaches have been used to model the catalyst layer in fuel cell models. In simulations which consider the entire fuel cell, the catalyst layer is often treated as an infinitely thin interface. 1-4 Alternatively, some have modeled the catalyst layer using porous electrode models 5-8 or agglomerate models. 9-15 These models do not resolve the porous structure of the catalyst layer, but rather rely on a bulk-averaged representation of the porous media in conjunction with the prescription of effective transport parameters. While this approach allows computationally efficient simulations of larger scale models, there are challenges in the determination of the effective transport parameters.There have been several efforts to simulate catalyst layer transport and reactions at the nanoscale level. A two-dimensional finite difference simulation of oxygen, proton, and electron transport along with electrochemical reactions through a regular microstructure was done by Wang. 16 This model was later extended to three dimensions and applied to a regular microstructure 17 and a random microstructure. 18 In the three-dimension...

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In this paper, we demonstrate how the principles of the freedom, actuation, and constraint topologies (FACT) approach may be applied to the synthesis, analysis, and optimization of microstructural architectures that possess extreme or unusual thermal expansion properties (e.g., zero or large negative-thermal expansion coefficients). FACT provides designers with a comprehensive library of geometric shapes, which may be used to visualize the regions wherein various microstructural elements can be placed for achieving desired bulk material properties. In this way, designers can rapidly consider and compare a multiplicity of microstructural concepts that satisfy the desired design requirements before selecting the final concept. A complementary analytical tool is also provided to help designers rapidly calculate and optimize the desired thermal properties of the microstructural concepts that are generated using FACT. As a case study, this tool is used to calculate the negative-thermal expansion coefficient of a microstructural architecture synthesized using FACT. The result of this calculation is verified using a finite element analysis (FEA) package called ale3d.

The three-dimensional structure of a PEMFC catalyst layer (CL) was obtained using a dual beam Focused Ion Beam/Scanning Electron Microscope (FIB/SEM). Lower order statistical functions such as porosity and two point correlation functions calculated from the FIB/SEM data were used in the numerical reconstruction of a multi-phase CL domain. A 'carbon-sphere-based' initial seed structure, when optimized by simulated annealing, produced a structure for which the two point correlation function matched with the FIB/SEM data with very high fidelity. The reconstructed CL domain with its phase-resolved nano-structure was used to perform numerical simulation and predict effective transport properties. The coupled partial differential equations governing the reactive transport of charged and neutral species in the CL were discretized based on the finite volume method and solved implicitly using parallel computing. The simulated values of the effective oxygen and water vapor diffusivity, proton and electron conductivity, and thermal conductivity were in reasonable agreement with measured data reported in the literature. A parametric study was performed to investigate the impact of inaccessible pores-a feature that is not resolved experimentally. The simulations indicate that the properties most sensitive to the presence of inaccessible pores are the effective O 2 and H 2 O diffusivities and the effective proton conductivity.

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Numerical aspects of a pore scale model are investigated for the simulation of catalyst layers of polymer electrolyte membrane fuel cells. Coupled heat, mass and charged species transport together with reaction kinetics are taken into account using parallelized finite volume simulations for a range of nanostructured, computationally reconstructed catalyst layer samples. The effectiveness of implementing deflation as a second stage preconditioner generally improves convergence and results in better convergence behavior than more sophisticated first stage pre-conditioners. This behavior is attributed to the fact that the two stage preconditioner updates the preconditioning matrix at every GMRES restart, reducing the stalling effects that are commonly observed in restarted GMRES when a single stage preconditioner is used. In addition, the effectiveness of the deflation preconditioner is independent of the number of processors, whereas the localized block ILU preconditioner deteriorates in quality as the number of processors is increased. The total number of GMRES search directions required for convergence varies considerably depending on the preconditioner, but also depends on the catalyst layer microstructure, with low porosity microstructures requiring a smaller number of iterations. The improved model and numerical solution strategy should allow simulations for larger computational domains and improve the reliability of the predicted transport parameters. The preconditioning strategies presented in the paper are scalable and should prove effective for massively parallel simulations of other problems involving nonlinear equations.