(569ei) Site-Averaged Polymerization Rates for the Phillips Catalyst: Silanol-Geometry Effects on Grafting Probabilities and Site-Specific Turnover Frequencies

Many industrial catalysts are single metal atoms on amorphous supports like silica and silica-alumina. At low dispersions, each active site must act independently. However, the disordered support makes the environment of each metal center different. Structural differences between sites can lead to important differences in activity, adsorption, selectivity, and even to different rate determining steps on different sites. Moreover, the structural disorder is an unknown, quenched, non-equilibrium distribution. We have developed (1) population balance models for the grafting reactions between catalyst precursors and the ensemble of different silanols, and (2) an importance learning method to compute site-averaged rates for the ensemble of sites with different geometries and barriers. We present ab initio calculations and population balances to model Phillips catalyst preparation by grafting of chromochlorate precursors on amorphous silica. We also present importance learning calculations for the site-averaged polymerization rate. Our results explain why higher temperatures during catalyst preparation lead to more active polymerization sites.