(528j) A Potential-Dependent Thiele Modulus to Quantify the Effectiveness of Porous Electrocatalysts

Porous electrocatalysts have been strategically employed in heterogeneous catalytic processes to enhance the volumetric reaction rates by increasing active site density. However, there exists a trade-off with mass-transport through the porous catalyst, which impacts the effective use of these catalyst sites. Classical approaches in chemical reactor design and engineering introduce an effectiveness factor to assess the ratio between the observed reaction rate and the reaction rate if the entire catalyst surface area had been exposed to bulk concentration conditions. The dimensionless parameter, commonly termed the Thiele modulus, conveniently describes the relative balance between kinetic and mass transport resistances in the catalyst particle, quantifying the relation between catalyst particle size and activity.^[1-5] Historically, the Thiele modulus has been used to inform materials design for thermochemical processes, wherein relevant reactions are driven by temperature and pressure, supporting the development of porous media used in catalytic, separation, and adsorption technologies. This analytical approach can be extended to evaluate catalysts for electrochemical processes, but the potential-dependence of reaction rates requires a reformulation of the traditional effectiveness factor.

In this talk, we will describe a general framework to quantify the effectiveness factor as functions of particle and reactant properties, applying both Tafel and Butler–Volmer kinetics to one-dimensional reaction-diffusion through a porous sphere.^[6] Internal transport effects from diffusion through the catalyst pores and external transport effects resulting from reactant diffusion across the boundary layer surrounding the particle will be assessed. From this analysis, we will discuss design principles for electrocatalyst sizing based on desired utilization efficiency, and compute the interfacial current density with and without external transport as a function of applied overpotential. Our findings reveal markedly lower catalyst utilization for electrocatalysts in typical aqueous electrolytes, and the need to develop hierarchical structured electrocatalysts to mitigate diffusional pore-scale losses. To this end, we will extend the model to other common catalyst geometries using a simple shape factor analysis. Lastly, to highlight the utility and generalizability of the approach, we will apply the framework to the oxygen reduction reaction at a polymer electrolyte fuel cell, assessing the effect of ohmic and transport losses across multiple length scales on fuel cell performance. We anticipate that the framework presented is broadly applicable to porous electrocatalysts leveraged across a range of conditions encountered in electrochemical engineering applications.

References:

[1] Thiele, Industrial & Engineering Chemistry, 31, 916-920 (1939).

[2] Levenspiel, Chemical reaction engineering, 3^rd ed., Wiley, New York, (1999).

[3] Fogler, Elements of Chemical Reaction Engineering, Prentice Hall, Englewood-Cliffs, (1986).

[4] Froment et al., Fundamentals of Chemical Reaction Engineering, Wiley, New York, (1990).

[5] Davis et al., Fundamentals of Chemical Reaction Engineering, Courier Corporation, (2012).

[6] Wan et al., ChemRxiv Preprint, https://doi.org/10.26434/chemrxiv.14233244.v1, (2021).