(198g) Optimal Bidisperse Pore Structure of Heterogeneous Catalysts, and Its Application to Denox

Small pore size and, consequently, large surface area contributes to the high catalytic activity of microporous catalysts like zeolites. However, the 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 nanopores. 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, and apply to the example of deNOx catalysis.

We compare monodisperse catalysts (only nanopores, i.e., 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. First-order irreversible kinetics and molecular diffusion are considered.

It is found that the optimal bidisperse structure is typically about 4 to 400 times better than the monodisperse one, for diffusion-limited first-order reactions. The effectiveness factor of the optimal bidisperse structure, η, is governed by the bidisperse Thiele modulus, φ, defined as φ=L*sqrt(k/D_m), where L is a measure for the catalyst size, D_m is the molecular diffusivity, and k is the rate constant. Introduction of macropores can remove diffusion limitations effectively when φ<1. Particularly, η approaches unity when φ<0.1. However, depletion also happens in optimal bidisperse structure when φ>5; the characteristic thickness of the skin where depletion occurs is independent of L. Production in the skin accounts for 97% of that of the entire catalyst when the skin thickness L_s=2*sqrt(D_m/k), and 99.5% when L_s=3*sqrt(D_m/k). The asymptote η~1/φ is observed when φ>5. In other words, similar results hold for the optimized bidisperse catalysts as for monodisperse catalysts, if φ is defined in the above way, on the basis of the diffusivity in the large pore channels. This is because all the concentration gradients inside the optimal structure are essentially in the macropores, while the nanoporous material is used as efficiently as is physically possible, at the concentrations present in the immediately neighboring macropores.

Optimization also yields useful information for material synthesis. The optimal macropore wall thickness is found to be any value less than 0.2*sqrt(D_e/k), where D_e is the effective diffusivity in the nanopores and typically much smaller than D_m. The optimal macroporosity is a function of φ only and never exceeds 0.5.

These theoretical insights are readily applied to design deNOx catalysts for a power plant. Overall catalytic activity in a mesoporous catalyst with 3 nm pores could be increased by a factor of about 4 just by introducing, and optimizing a macropore network, for the same intrinsic kinetics and mesopore size. In this case, the optimal macropore wall thickness should be anywhere from 8 to 44 μm. The optimal macropore size should be a quarter of the optimal macropore wall thickness, i.e., from 2 to 11 μm. In practice, this would correspond to a deNOx catalyst consisting of mesoporous particles of 8-44 μm, and pores in between them of around 2-11 μm. Information like this is immediately applicable to practical catalyst synthesis.