A Potential–dependent Thiele Modulus to Quantify the Effectiveness of Porous Electrocatalysts

Electrochemical reactors often employ high surface area electrocatalysts to accelerate volumetric reaction rates and increase productivity. While electrocatalysts can alleviate kinetic overpotentials, diffusional resistances at the pore-scale often prevent full catalyst utilization. The effect of intraparticle diffusion on the overall reaction rate can be quantified through an effectiveness factor expression governed by the Thiele modulus parameter. This analytical approach is integral to the development of catalytic structures for thermochemical processes and has previously been extended to electrochemical processes by accounting for the relationship between reaction kinetics and electrode overpotential. In this paper, we illustrate the method by deriving the expression for the potential-dependent Thiele modulus and using it to quantify the effectiveness factor for porous electrocatalytic structures. Specifically, we demonstrate the application of this mathematical framework to spherical microparticles as a function of applied overpotential across catalyst properties and reactant characteristics. The relative effects of kinetics and mass transport are related to overall reaction rates, revealing markedly lower catalyst utilization at increasing overpotential. Subsequently, we generalize the analysis to different catalyst shapes and provide guidance on the design of porous catalytic materials for use in electrochemical reactors.