Effects of diffusion and particle size in a kinetic model of catalyzed reactions

TL;DR

This paper analyzes how diffusion and particle size influence catalytic reaction rates, revealing conditions that optimize turnover frequency and providing insights applicable to experimental and complex models.

Contribution

It introduces a kinetic model incorporating diffusion, desorption, and particle size effects, offering analytical insights into reaction dynamics on supported catalysts.

Findings

Enhanced diffusion or larger particles increase reactant flux and TOF.

A critical diffusion length ratio determines whether reactant flux to support dominates.

Small particles yield higher TOF when desorption energy exceeds diffusion and reaction energies.

Abstract

We study a model for unimolecular reaction on a supported catalyst including reactant diffusion and desorption, using analytical methods and scaling concepts. For rapid reactions, enhancing surface diffusion or increasing particle size favors the flux of reactants to the catalyst particles, which increases the turnover frequency (TOF). The reactant flux towards the support becomes dominant when the ratio of diffusion lengths in the catalyst and in the support exceeds a critical value. A peak in the TOF is obtained for temperature-dependent rates if desorption energy in the support (Ed) exceeds those of diffusion (ED) and reaction (Er). Significant dependence on particle size is observed when the gaps between those energies are small, with small particles giving higher TOF. Slow reactions (Er > Ed) give TOF monotonically increasing with temperature, with higher reactant losses in small particles. The scaling concepts can be extended to interpret experimental data and results of more complex models.