Stochastic Reconstruction and Transport Simulation of PEFC Catalyst Layers

Understanding mass transport in polymer electrolyte fuel cells (PEFCs) is critical to improve reactant and water transport in catalyst layers. Numerical simulation techniques can be used to gain a detailed understanding of transport within the catalyst layer structure. The accuracy of these simulations is dependent on the accuracy of the physical domain and the mathematical models. While detailed mathematical models of mass, charge and energy transport have been presented in literature, there has been limited work in understanding the catalyst layer structure. Reconstructions of PEFC catalyst layers are therefore crucial to understand its microstructure and to obtain transport properties via simulation. Imaging techniques such as X-ray tomography (micro-CT) or scanning electron microscopy (SEM), even though informative, cannot easily be used to understand how different porous media parameters (e.g., pore sizes, connectivity) control its transport properties (e.g., effective diffusivity) as the structure is not mathematically characterized. The method of stochastic reconstruction on the other hand, uses geometry based statistical descriptors in order to create reconstructions. The statistical descriptors are related to the geometric properties of the porous media, e.g., the two point correlation function is related to the interface area and the chord length function is related to pore size. The method of stochastic reconstruction is cost and time efficient, can account for the stochastic nature of porous media, and provides a way to characterize the porous media by its statistical descriptors. Most of the fuel cell literature is composed of imaging based reconstructions [1,2]. A few catalyst layer stochastic reconstructions use either simple statistical descriptors, such as two-point correlation functions, or heuristic approach, e.g., creating the structure based on a sphere packing algorithm [3,4]. Due to the limited stochastic information and idealized building blocks, these reconstructions might not truly represent the complex microstructure of PEFC porous media, which consists of non-spherical fractal carbon particles [5]. The use of multiple correlation functions together with simulated annealing [6] could provide an improved method to reconstruct the complex PEFC porous media, and to analyze the relation between porous media structure and transport properties. In this work, a modified simulated annealing method based on one proposed by Yeong and Torquato [6] is used to reconstruct a three-dimensional and multi-phase microstructure representative of a catalyst layer (CL). A two dimensional version of the program was used to reconstruct a PEFC CL earlier [7]. The new improved method uses a multigrid hierarchical annealing technique to significantly reduce the reconstruction time and ascertains long range connectivity. The multigrid method performs reconstructions in sequential refinement stages and has been found to result in reconstruction time reduction by 2-3 orders of magnitude. The new method uses a biased pixel swapping method compared to conventional random swapping for faster and more accurate reconstruction. The biased pixel swapping has reduced the reconstruction time by almost an order of magnitude, while also improving the accuracy of the reconstructions by an order of magnitude. Multiple statistical descriptors are used in combination to generate a structure, which provides a better representation of the PEFC CL structure. An algorithm for automatically generating a computational mesh and a mathematical model of the transport process in the catalyst layer has also been developed. Mass and electron transport are simulated on the reconstructions using the open source package OpenFCST [8]. The effective transport properties of the reconstructions are close to the reference structure value, e.g., the ratio of difusibility values of the reconstructions to diffusibility values of reference was found to be in the range of 0.9-0.96. The new method allows us to reconstruct detailed high-resolution structures with high accuracy in practical amount of time, e.g., a reconstruction of size 300x300x300 can now be reconstructed in 24-30 hours instead of several weeks. The effect of different stochastic descriptors on the transport properties will also be studied in future. Overall, the current work provides a novel methodology to characterize and reconstruct PEFC porous media from statistical descriptors in a time and cost effective manner. [1] K. Lange et al. Electrochim. Acta. 2012, 85, 322-331 [2] W. Epting et al. Adv. Funct. Mater. 2012, 22, 555-560 [3] P. Mukherjee et al. J. Electrochem. Soc. 2006, 153, A840-A849 [4] K. Lange et al. J. Electrochem. Soc. 2010, 157, B1434-B1442 [5] D. Banham et al. J. Power Sources. 2011, 196, 5438–5445 [6] C. Yeong et al. Physical Review E. 1998, 57, 495-506 [7] L. Pant et al. Phys. Rev. E. 2014, 90, 023306 [8] Open Fuel Cell Simulation Toolbox (openFCST). Available at www.openfcst.org Figure 1

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