Computational Optimization of Functionally Graded Electrodes for Solid Oxide Fuel Cells
Authors: Bain Aaron Thomas , Roberts Rory , Deiner Jay , Fellner Joseph 
Published: November 2022

Solid Oxide Fuel Cells (SOFCs) are widely considered to be an ideal power source across a range of industries in the near future due to their high efficiency, high power density, and fuel flexibility. However, for widespread usage of SOFCs to be feasible, certain disadvantages, such as their high operating temperature, electrochemical losses, and high cost of manufacturing, must be solved. In particular, the field of materials research occupies a unique position of being able to quickly and simultaneously solve many of these issues through the development of material compositions and structures that do not currently exist in the industry. Especially relevant to solid oxide fuel cells in particular, is the impact that the electrodes’ geometries and compositions have on the operating performance. The electrodes’ ability to quickly move reactants to the interface of the electrolyte and remove products to the bulk flow comes into play as the fuel cell operates at higher current densities and concentration losses become prominent. Therefore, the microstructures present throughout the electrodes’ depth plays a vital role in improving overall cell performance. However, current fuel cell research has not yet effectively captured and defined the connections of the microstructure parameters and measured their impact on cell behavior. Additionally, homogeneous electrode design and implementation have dominated the research and commercial space thus far. The technique of functional material grading, which has begun to see wide research and commercial usage for such problems as acoustic impedance matching, thermal control, and mechanical design will be leveraged for the enhancement of SOFC electrodes. Functionally graded electrodes have been used in solid oxide fuel cell research in recent years in an effort to improve the cell performance by altering the microstructure including porosity, particle size, and composition of electronic and ionic conductors near the triple phase boundary region. Normally the functional grading process adds additional fabrication steps making it less desirable as an optimization process and easy manufacturing method. However, by using an additive manufacturing process it eliminates the need for multiple discrete graded layers to be deposited to obtain a graded electrode functional layer. This study seeks to explore the correlations of geometry and structure parameters from the meso-scale through to the micro-scale level, together with mass transfer, ionic and electronic transport, and gas-surface electrochemical reactions inside the electrodes to guide future additive manufacturing of SOFCs. Outlined is the development of an effective medium model for simulating the performance of fuel cell microstructures as a function of specific operating ranges in temperature, pressure, and in fuels used. Smooth and continuous linear and nonlinear functional gradation profiles of porosity and material composition are studied within the framework of an effective medium boundary value problem where the electrochemical relations, such as the Butler-Volmer equation, percolating conduction paths, and gas diffusion are solved using the finite difference method. The form of these relations for homogeneous electrodes was analyzed by Costamagna, et. al [1], who also defined outstanding problems with regards to optimizing SOFC electrodes [2]. Globally optimal linear and nonlinear gradation profiles and cell parameters are derived as a function of particle sizes, ratio of conductivities, and desired operating conditions and scored based on their reduction of cell overpotentials.

[1] Costamagna, P., P. Costa, and V. Antonucci, Micro-modelling of solid oxide fuel cell electrodes. Electrochimica Acta, 1998. 43(3-4), pp.375-394.

[2] Costamagna, P., P. Costa, and E. Arato, Some more considerations on the optimization of cermet solid oxide fuel cell electrodes. Electrochimica Acta, 1998. 43(8), pp.967-972.

Figure 1