Diffusion and reaction in percolating pore networks

Abstract

We address the problem of diffusion and reaction in porous catalysts subjected to percolation disorder. The results with an idealized pore network indicate that the fractal characteristics of the void space can have a remarkable influence on the transport and reactive properties of the system. Within a specific range of length scales, we observe scaling behavior relating the catalytic effectiveness of the network and the diffusion-reaction ratio J-${\mathrm{bar}}_{\mathrm{N}}$∝(D/K${)}^{1\mathrm{/}{\mathrm{d}}_{\mathrm{R}}}$. In addition, the exponent ${\mathrm{d}}_{\mathrm{R}}$ is consistently in the range ${\mathrm{d}}_{\mathrm{w}}$${\mathrm{d}}_{\mathrm{R}}$${\mathrm{d}}_{\mathrm{w}}^{|\mathrm{I}\mathrm{H}}$, where ${\mathrm{d}}_{\mathrm{w}}$ is the two-dimensional random walk exponent on the incipient infinite cluster and ${\mathrm{d}}_{\mathrm{w}}^{|\mathrm{I}\mathrm{H}}$ is the corresponding diffusion exponent which includes all clusters of the system at the percolation threshold. Moreover, in contrast with diffusion under ``inert'' conditions, where the ``dangling'' bonds in the percolating cluster do not play any role in transport, these elements become active zones due to the reaction mechanism. We also outline some specific guidelines to demonstrate the relevance of these results in the context of design and characterization problems in heterogeneous catalysis.