Modeling the Structural Heterogeneity of Vicinal Silanols and Its Effects on TiCl₄Grafting onto Amorphous Silica

Molecular metal complexes such as MCl_xreact readily with hydroxyl-terminated surfaces to produce some of the "single-atom" catalysts used in important large-scale commercial reactions, including olefin metathesis, polymerization, and epoxidation. While the local oxide environment can vary at each metal site, the manner and degree to which these differences impact the catalytic activities of individual sites are poorly understood. In this work, we develop a computational framework to model the grafting of metal complexes onto amorphous supports and apply the framework to examine TiCl₄grafting onto amorphous silica. We use density functional theory (DFT) to calculate free energies for TiCl₄reactions at vicinal silanol sites. The kinetics and thermodynamics depend on the dihedral angle between the silanols. Vicinal silanol pairs with small dihedral angles are predicted to yield bipodal [(SiO)₂TiCl₂] sites initially, but they react further with TiCl₄vapor to give vicinal pairs of monopodal sites, [ SiOTiCl₃]. In contrast, silanol pairs with large dihedral angles yield vicinal pairs of monopodal Ti sites directly. The DFT results were used to construct a population balance model to describe the kinetics of TiCl₄grafting onto nonuniform sites of an atomistic model for amorphous silica. The solution of the population balance model predicts that the majority of the vicinal pairs graft as bipodal [(SiO)₂TiCl₂] sites first and then slowly convert to monopodal [SiOTiCl₃] sites. The predictions provide a plausible explanation for the variability in the populations of monopodal and bipodal sites previously reported for TiCl₄grafting.