Small pore size and, consequently, large surface area contributes to the high catalytic activity of microporous catalysts like zeolites. However, small pore size limits the accessibility to the active sites. Considerable experimental efforts have been made to synthesize porous materials with a bimodal pore size distribution, so as to combine fast transport by introducing macro/mesoporosity with high catalytic activity in the micropores. Despite experimental and theoretical work on the design of porous materials, the question what the optimal bimodal pore structure should look like is still an open one, which we address here.

We compare monodisperse catalysts (only micropores or narrow mesopores) with bidisperse ones (which have the same micropore size, but, additionally, contain larger meso- or macropores of a certain size). The bidisperse structure is optimized with the aim to maximize yield, and compared to the monodisperse structure. Diffusion and reaction is modelled in a two-dimensional catalyst chip, but we expect similar results to hold in three dimensions. First-order irreversible kinetics, molecular and Knudsen diffusion are considered.

It is found that the optimal bidisperse structure can be more than one order of magnitude better than the monodisperse one, for diffusion-limited reactions. This could be attributed to the fact that the interior part of the catalyst is considerably more accessible to diffusing reactants in the bidisperse structure because of much more facile diffusion in macro/mesopores, while reactants are rapidly depleted in the surface layer of monodisperse catalysts. The diffusion coefficient in macro/mesopores is typically 3, 4 or even more orders of magnitude higher than that in micropores.

Our optimizations yield the optimal pore size and pore wall thickness of the large pore channels, an important piece of information for catalyst synthesis. Values depend on the reaction rate coefficient, the diffusivities, and the catalyst particle size. In general, however, the optimal pore wall thickness corresponds to the (critical) length scale at which diffusion limitations just start to disappear inside the pore wall, so that the local Thiele modulus is around 1. The optimal pore wall thickness typically varies from 100 nm to 1 mm for gas phase reactions, for rate constants between 1 and 1000 s-1, and micropore diffusivity between 10-9 to 10-12 m2/s. The optimal pore size is the smallest one at which Knudsen diffusion does not dominate the diffusion process; as a result, the typical optimal pore size should be 100 nm or slightly larger. It should be noted that these values are rather different from those currently pursued by most experimentalists, who seem to focus on (ordered) mesoporous materials with zeolitic microporous walls. As such, these modelling insights may provide useful information for catalyst synthesis.