(323b) Grafting TiCl4 Onto Amorphous Silica: Modeling Effects of Silanol Heterogeneity

Metal complexes can react with amorphous silica to produce “single atom” catalysts for a variety of reactions, including metathesis, polymerization, and epoxidation. These catalysts are often envisaged as well-defined, uniform sites like those of an enzyme, or a homogeneous catalyst. However, the local silica environment at each grafting site is unique, and the manner and degree to which these differences impact the site activities is poorly understood. We develop a computational framework to model grafting of metal complexes to amorphous supports. Our method uses a machine learning parametrized population balance model to predict the evolving distribution of catalytic sites during grafting. We apply the framework to model the grafting of TiCl₄ onto amorphous silica. We show that the grafting kinetics and thermodynamics depend on the dihedral angle between the vicinal silanols. Sites with a small dihedral angle initially yield a bipodal [(≡SiO)₂TiCl₂] site and subsequently convert to a vicinal pair of monopodally-grafted Ti species [≡SiOTiCl₃]. Sites with a large dihedral angle directly yield the vicinal pair of monopodally-grafted Ti species. We use the DFT results to construct a population balance model for TiCl₄ grafting kinetics on the non-uniform sites of amorphous silica extracted from an atomistic silica model. The predictions of the population balance model agree with experiments.