Microkinetic Models with Interacting Adsorbates and Langmuir–Hinshelwood Steps: Solving the Master Equation on Small Periodic Tiles

The most prevalent microkinetic modeling (MKM) techniques in catalysis assume mean-field coverages and noninteracting adsorbates (MF-MKMs) or use kinetic Monte Carlo (KMC) to explicitly track surface reactions on large numbers of sites. Between these extremes are models with mean-field adsorbate interactions, models with coverage-dependent adsorption and reaction energies, and models that invoke closures and truncations to account for correlated adsorbate positions. 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. We demonstrate the MKM construction for the reaction 2A_(g) ↔ 2A* → A_2(g) on a square lattice (with Greek cross tiling) and on a hexagonal lattice (with new “creamcups” tiling).