  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.
