The optimal design of catalyst layer (CL) sub-component is critical for achieving commercialization of polymer electrolyte fuel cells (PEFCs). Typically, a CL is designed as a heterogeneous porous composite of Platinum catalyst over carbon support, void space, and polymer electrolyte membrane (PEM) materials, through which heat & mass transport processes occur with electrochemical reaction. To overcome performance limitations within the CL, a detailed understanding of these transport and reaction processes is required. Especially, an accurate modeling & optimization tool that establishes relationship between CL micro-structures to overall PEFC performance can significantly expedite experimental efforts towards developing tailored CL structures. The non-homogeneous media theories [1-3] estimate the effective molecular transport coefficients through averaged phase hold-up and/or tortuosity parameters which do not account for the microscopic structural information. On the other hand, detailed sub-continuum theories may account for detailed CL structural geometry, they however, may not be suitable for systems level analysis.
In our earlier study , we successfully constructed a compact modeling and optimization framework comprising a macro-/meso-scale CL agglomerate model capturing essential features transport & reaction processes and linked to our in house state-of-the-art interior point optimization algorithm, IPOPT . This framework was further exploited to examine PEFC model and optimization sensitivity for various CL agglomerate shapes (sphere, cylinder, and plate) and sizes .
Here, we analyze a generalized class of spherical shell agglomerate models originating from the approach by Aris , with a goal of providing a basis for realistic CL structures, and amenable to systems analysis.
First, we introduce non-homogeneity in distribution of triple phase boundaries (required for electrochemical reaction) by solving multi-zone spherical agglomerate reaction-diffusion problem, possessing radial variation in reaction rates. We examine sensitivity to PEFC performance in both simulation and optimization results for different zone thicknesses. Second, instead of the heuristic ‘shape-factor’ approach in Aris , we derive effectiveness of a spherical shell from first principles by introducing a Robin boundary condition, expressed in terms of Biot number (Bi), which plays an important role in estimating the effectiveness of CL layer. This generalized model gives a good agreement with Aris  for various values of shell thickness as Bi values approach to zero. Also, the case Bi = 0 for a solid sphere reduces to our previous model . The optimization based on maximum current density is obtained in detail for different shell thicknesses and various values of Bi. We examine how Bi influences the critical system design parameters including the I-V characteristics.
- J. C. Maxwell, A Treatise on Electricity and Magnetism (Clarendon, Oxford, 1881), Vol. 1, p. 435.
- D.A.G. Brugemann, Ann. Phys., 24, 637 (1935).
- J. Wang, J. K. Carson, M. F. North, D. J. Cleland, Int. J. Heat Mass Tran., 49, 3075 (2006).
- P. Jain, L.T. Biegler, and M.S. Jhon, Electrochem. Solid St., 11, B193 (2008).
- A. Wächter, L.T. Biegler, Math. Program., 106, 25 (2006).
- P. Jain, L.T. Biegler, and M.S. Jhon, J. Electrochem. Soc., 157, B1222 (2010).
- R. Aris, Chem. Eng. Sci., 6, 262 (1957).
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