EAGER: Exact Solutions to Multisite Microkinetic Models in Heterogeneous Catalysis

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

The design of heterogeneous catalysts for specific chemical reactions, along with ideal conditions for carrying out targeted reactions, is aided by a detailed understanding of the specific steps by which the reaction occurs on the catalyst surface. Such steps control the overall rate (i.e. kinetics) of the reaction, as well as the product selectivity in cases where multiple products are produced. Accurate kinetic models are crucial for research and development in heterogeneous catalysis. In recent years, there has been growing appreciation of the complexity of surface catalyzed reactions, thus prompting the evolution of microkinetic models (MKMs) as a tool to predict ideal combinations of catalyst design and reactor operating conditions. Two prevailing types of MKMs have emerged representing different levels of complexity and accuracy: 1) Mean Field (MF-MKMs) - built on a one-site basis, and 2) kinetic Monte Carlo (kMC) simulations with hundreds of sites. The project investigates a novel periodic tiling framework that retains the convenience of closed-form MF-MKM expressions, while accurately including complexities that have previously required kMC simulation. More broadly, the project will advance computational modeling across the full spectrum of heterogeneous catalysis, linking theory to experiment in a more robust catalyst and reaction engineering process, potentially scalable from the molecular to the process level. Tremendous progress has been made with simple mean-field microkinetic models (MF-MKMs) that ignore correlations between molecules on the catalyst surface. The other fruitful direction has been kinetic Monte Carlo (kMC) simulations that track every interaction and every detail of the catalytic process. MF-MKMs yield simple closed-form rate expressions. They are convenient for reactor design, process optimization, and for understanding trends in temperature, concentration, and barriers via derivative-based quantities like activation energies, reaction order, and degree of rate control. However, MF-MKMs cannot accurately describe reactions where adsorbates interact with each other and where surface diffusion is important. The current alternative kMC framework remains accurate for highly complex surface reactions but its statistical rate estimates are less convenient than a closed-form MF-MKM rate expressions for all of the aforementioned tasks. The project develops a generalizable way to partition the surface into linear periodic tiles, to automate the formulation of the master equation including adsorption, reaction, diffusion, and desorption steps (with adsorbate interactions of any strength), and to exactly solve the master equation. The new approach can yield exact solutions and closed-form rate expressions for complex surface reactions that are notoriously difficult for MF-MKMs. Preliminary results show that the tiling approach also yields rates that are essentially indistinguishable from numerically exact kMC results. The project applies sparse matrix tools and an automatic differentiation strategy to facilitate activation energies, reaction orders, degree of rate control, and data fitting / parameter estimation tasks. Maps will be created linking the linear tiles to conventional periodic surface models so that the new tiling models can be parameterized with ab initio calculations. This new framework should become a powerful alternative to kMC models in the frequently encountered situations where MF-MKMs are inadequate. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.