(45a) Model-Based Design of Hierarchically Structured Porous Catalysts

Nanoporous catalysts like zeolites have an extremely large internal surface area, which contributes to the high intrinsic catalytic activity. However, their small pore size leads to slow molecular transport and pore blocking, limiting the efficient use of the catalytic materials. This indicates that, apart from the nanopores (i.e., micropores and narrow mesopores) where reactions actually occur, a ?distribution? network of large mesopores and macropores is needed for molecules to quickly move in and out of the catalyst. The question is how this network should be designed to achieve optimal catalyst performance. Such a design is of considerably practical relevance, since it has become technically possible to control the hierarchical structure of porous catalysts, containing both nanopores and a distribution network, thanks to tremendous progress in (nano)materials science.

Inspired by the fractal design of leaves and lungs, which differs so strongly from that of typical catalysts, we studied whether broad, perhaps scaling hierarchical pore networks would perform better than those where the large pore channels are all of the same size. This optimization problem differs from those in which the nanopore size is varied, and is highly practical in view of the fact that the features at the nanoscale typically determine the (given) intrinsic kinetics, which we would like to preserve. Therefore, the texture at all length scales larger than the narrowest pores should be optimized, with regard to efficient molecular transport through the distribution network.

Remarkably, the optimal catalyst performance is found to be essentially the same regardless of whether a broad distribution of large pore channel diameters is allowed (bimodal) or not (bidisperse). This is because, in the optimal hierarchical structures, irrespective of the distribution of large diameters around the optimal average channel diameter, the minimized diffusion limitations exist to the same extent in a principle direction (e.g., a radial direction for a spherical catalyst particle), while they essentially disappear in a direction perpendicular to this principle direction. It is also found that one Thiele modulus governs the optimal catalyst performance when this Thiele modulus is defined in a way analogous to the generalized Thiele modulus (Froment and Bischoff, 1990), but using the molecular diffusivity in the large pore channels, rather than the effective diffusivity in the nanopores. This study calls for the synthesis of hierarchically structured porous catalysts with an optimized, approximately bidisperse pore size distribution, thanks to its easier synthesis and an identical performance as compared to those with a bimodal pore size distribution, especially given the allowed variance around the average.