Title: "Modeling the preparation and activity of atomically dispersed catalysts on amorphous supports: method development and applications" 

Abstract: Several industrially important catalysts are single metals dispersed on amorphous supports. For example, Cr dispersed on amorphous SiO2 is used to catalyze polymerization of ethene and W dispersed on amorphous Al2O3 and SiO2 is used to catalyze metathesis of olefins. Despite their extensive use in the industry, these catalysts have largely been intractable to both, experimental and modeling investigations. In particular, they present the following challenges: (i) an unknown quenched disordered structure of the amorphous support, (ii) metal atoms attach to various surface grafting sites with different rates and have different activation and catalytic reaction kinetics, and (iii) only a small fraction of the sites are active. These challenges particularly render ab initio computational tools, routinely applied to study homogeneous and ordered heterogeneous catalysts, inefficient and impractical. The overarching goal of this thesis is developing computational tools to efficiently model the synthesis and activity of atomically dispersed catalysts on amorphous supports.

Atomically dispersed amorphous catalysts are synthesized by grafting organometallic complexes onto amorphous supports. We develop a machine learning parametrized population balance model to predict the evolving population of active sites during catalyst synthesis. The predictions of our method are benchmarked against thousands of brute force calculations on a model catalyst. Our algorithm, trained on just 100 sites, is able to predict the evolution of 20,000 sites during grafting. Additionally, we develop an Importance Learning (IL) algorithm to efficiently calculate the grafted catalyst’s site-averaged activation barrier. IL uses a combination of machine learning and importance sampling to discover rare and active catalytic sites. It converges to the correct site-averaged activation barrier with 3 orders of magnitude fewer samples than brute force sampling. We apply the population balance modeling framework to model the grafting of TiCl4 onto amorphous silica. The equilibrium predictions of the model agree with experimentally determined populations of grafted Ti sites.

A few studies in the past decade have generated atomistic models of amorphous silica supports and most studies have claimed that their models are representative of real silica materials. We compare models generated using different simulation protocols and show that different protocols lead to different structural features. We discuss the implications of these structural variations on the properties of grafted catalysts and outline experimental metrics that can be used to validate models in future studies. Finally, we present a site balance algebra to quantifying the amounts of different dispersed species in grafting experiments. This approach is used to quantify the amounts of [≡SiOTiCl3] and [(≡SiO)2TiCl2] sites obtained on grafting TiCl4 onto amorphous silica. We further demonstrate the application of this approach to spot erroneous experimental measurements.