(406e) Ab Initio Population Balance Model of TiCl4 Grafting on Amorphous Silica

Ab initio calculations have significantly advanced our understanding of many homogeneous and crystalline heterogeneous catalysts. In contrast, many important amorphous catalysts remain poorly understood. These catalysts are difficult to model because they exhibit a quenched distribution of sites with different structures and activities. For atomically dispersed catalysts on amorphous supports, the distribution depends on the support synthesis conditions, on the catalyst grafting/impregnation protocol, and sometimes on subsequent initiation/activation steps. Silica is the one of the most commonly used supports for atomically dispersed catalysts in the industry. Understanding the arrangement of silanol groups [≡SiOH] on the surface of amorphous silicas is critical in understanding the reactivity of amorphous catalysts. We use DFT to explore the grafting kinetics and equilibrium populations of (≡SiO)TiCl₃ and (≡SiO)₂TiCl₂ sites on amorphous silica. We show that the structure of the silica site has a significant effect on the structure and properties of the grafted Titanium species. We use sites carved from amorphous silica models to construct a population balance model for the grafting process. Finally, the equilibrium solution of the population balance model is compared with outcomes of EXAFS and elemental analysis experiments.