Pore diameter dependence of catalytic activity: p-nitrobenzaldehyde conversion to an aldol product in amine-functionalized mesoporous silica.

The reaction yield for conversion of p-nitrobenzaldehyde (PNB) to an aldol product in amine-functionalized mesoporous silica nanoparticles (MSN) exhibits a 20-fold enhancement for a modest increase in pore diameter, d. This enhanced catalytic activity is shown to reflect a strong increase in the "passing propensity," P, of reactant and product species inside the pores. We find that P ≈ 0, corresponding to single-file diffusion, applies for the smallest d which still significantly exceeds the linear dimensions of PNB and the aldol product. However, in this regime of narrow pores, these elongated species must align with each other and with the pore axis in order to pass. Thus, P reflects both translational and rotational diffusion. Langevin simulation accounting for these features is used to determine P versus d. The results are also augmented by analytic theory for small and large d where simulation is inefficient. The connection with the catalytic activity and yield is achieved by the incorporation of results for P into a multi-scale modeling framework. Specifically, we apply a spatially coarse-grained (CG) stochastic model for the overall catalytic reaction-diffusion process in MSN. Pores are treated as linear arrays of cells from the ends of which species adsorb and desorb, and between which species hop and exchange, with the exchange rate reflecting P. CG model predictions including yield are assessed by Kinetic Monte Carlo simulation.