We demonstrate that the Langmuir–Hinshelwood formalism is an incomplete kinetic description and, in particular, that the Hinshelwood assumption (i.e., that adsorbates are randomly distributed on the surface) is inappropriate even in catalytic reactions as simple as A + A → A2. The Hinshelwood assumption results in miscounting of site pairs (e.g., A*–A*) and, consequently, in erroneous rates, reaction orders, and identification of rate-determining steps. The clustering and isolation of surface species unnoticed by the Langmuir–Hinshelwood model is rigorously accounted for by derivation of higher-order rate terms containing statistical factors specific to each site ensemble. Ensemble-specific statistical rate terms arise irrespective of and couple with lateral adsorbate interactions, are distinct for each elementary step including surface diffusion events (e.g., A* + * → * + A*), and provide physical insight obscured by the nonanalytical nature of the kinetic Monte Carlo (kMC) method—with which the higher-order formalism quantitatively agrees. The limitations of the Langmuir–Hinshelwood model are attributed to the incorrect assertion that the rate of an elementary step is the same with respect to each site ensemble. In actuality, each elementary step—including adsorbate diffusion—traverses through each ensemble with unique rate, reversibility, and kinetic-relevance to the overall reaction rate. Explicit kinetic description of ensemble-specific paths is key to the improvements of the higher-order formalism; enables quantification of ensemble-specific rate, reversibility, and degree of rate control of surface diffusion; and reveals that a single elementary step can, counter intuitively, be both equilibrated and rate determining.
|Original language||English (US)|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|State||Published - Feb 23 2021|
Bibliographical noteFunding Information:
ACKNOWLEDGMENTS. We thank Dr. Andrew Hwang for careful proofing, Dr. Brandon L. Foley for helpful discussion, Dr. Linh Bui for insightful technical advice, and the reviewers for their valuable comments. This work was funded by the US Department of Energy, Office of Basic Energy Science, Catalysis Science Program (Award DE-SC00019028).
© 2021 National Academy of Sciences. All rights reserved.
- Catalytic site ensembles
- Coverage-dependent rates
- Surface diffusion