FROM TILINGS AND MASTER EQUATIONS TO MICROKINETIC MODELS

Adams, Kevin Christopher

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https://hdl.handle.net/2142/129949 Copy

Description

Title

FROM TILINGS AND MASTER EQUATIONS TO MICROKINETIC MODELS

Author(s)

Adams, Kevin Christopher

Issue Date

2025-07-18

Director of Research (if dissertation) or Advisor (if thesis)

Peters, Baron

Doctoral Committee Chair(s)

Peters, Baron

Committee Member(s)

• Gruebele, Martin
• Luthey-Schulten, Zaida
• Jackson, Nicholas

Department of Study

Chemistry

Discipline

Chemistry

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• microkinetic model
• heterogeneous catalysis
• master equation
• activation energy
• reaction order
• interacting adsorbates
• kinetic Monte Carlo

Abstract

The most prevalent microkinetic modeling (MKM) techniques in catalysis assume mean field coverages and non-interacting adsorbates (MF-MKMs) or use kinetic Monte Carlo (KMC) to explicitly track surface reactions on large numbers of sites. However, MF-MKMs cannot accurately describe reactions where adsorbates interact with each other or where surface diffusion is important, whereas kMC (while accurate) lacks the convenience and insight that comes from a closed-form rate expression. Across a wide range of situations, kMC makes accurate predictions, but they are generated one-condition-at-a-time as estimates with statistical noise. Moreover, finite difference formulas amplify the sampling noise in derivative quantities like the overall activation energy, the reaction order, and the degree of rate control. Using KMC results as a benchmark, we show that tilings corresponding to square and hexagonal lattices yield easily formulated, easily solved, and surprisingly accurate microkinetic models, even with interacting adsorbates and Langmuir-Hinshelwood steps. Additionally, we introduce a master equation microkinetic modeling (ME-MKM) approach that bridges the gap between MF-MKMs and kMC simulations. We describe a generalizable way to partition a 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. We demonstrate this method for examples that are notoriously difficult for MF-MKMs and obtain results which are essentially indistinguishable from numerically exact kMC results. We also demonstrate (using kMC data) that the analytic ME-MKM rate expression can be used “in reverse” to accurately estimate rate parameters and adsorbate interactions from data. Lastly, we also demonstrate the capabilities of the ME-MKM to calculate derivatives of steady-state rates with respect to temperature, concentration, or other variables using a closed-form expression with comparable accuracy to kMC results for systems MF-MKMs can’t describe. For a wide range of conditions across all systems explored, the ME-MKM predictions match the accuracy of kMC with lower computational cost and no statistical estimation errors.

Graduation Semester

2025-08

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/129949

Copyright and License Information

Copyright 2025 Kevin Adams

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