Traditional mean-field rate equations of chemical kinetics for spatially uniform systems1−3 and the corresponding reaction−diffusion equations describing spatial heterogeneity4−6 have proved immensely useful in elucidating catalytic processes. However, it is well-recognized that standard mean-field rate expressions neglect spatial correlations in the reactant and/or product distribution. It is less well appreciated that the standard treatment of diffusion is generally applicable only at low concentrations and in unrestricted environments.

This article describes an advanced physical chemistry lab experiment on dynamic NMR (DNMR) of intramolecular exchange processes in EDTA (the disodium salt of ethylenediaminetetraacetic acid) complexes of Sc3+, Y3+, and La3+. This lab experiment is intended for chemistry and biochemistry undergraduates, who have finished or are in the process of completing the physical chemistry course sequence. Three six-hour laboratory sessions, covering the synthesis of the EDTA complexes, the NMR experiment, and the calculation of the DNMR lineshapes are assigned for this lab experiment. This lab experiment is an integration of analytical chemistry, physical chemistry, instrumental analysis, NMR spectroscopy, and computational skills. It provides a challenging hands-on experience for students to use this comprehensive technique to study chemical exchanges. Rate constants at different temperatures and activation energies of the nitrogen inversion processes for these EDTA complexes are obtained in this lab experiment.

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.