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Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes

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Reactive Flows, Diffusion and Transport

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Summary

Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. It can be derived rigorously for low-pressure conditions from the microscopic model, which is characterized as a moderately interacting many-particle system, in the limit as the particle number tends to infinity. Also the mesoscopic model is given by a many-particle system. However, the particles move on a lattice, such that in contrast to the microscopic model the spatial resolution is reduced. The derivation of deterministic limit equations is in correspon-dence with the successful description of experiments under low-pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena of stochastic origin can be observed in experiments. The models include a new approach to the platinum phase transition, which allows for a unification of existing models for Pt(100) and Pt(110). The rich nonlinear dynamical behavior of the macroscopic reaction kinetics is investigated and shows good agreement with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pat-tern formation, which has not been captured by earlier models, can be reproduced in stochastic simulations with the mesoscopic model.

This work has been supported by the German Research Foundation (DFG) through SFB 359 (Project B3) at the University of Heidelberg.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Heidelberg, Heidelberg

    J. Starke & K. Oelschläger

  2. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR), Universität Heidelberg, Heidelberg

    J. Starke & C. Reichert

  3. Fritz-Haber-Institut der Max Planck Gesellschaft, Berlin

    M. Eiswirth

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  1. J. Starke
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  4. K. Oelschläger
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  1. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR), Universität Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Willi Jäger , Rolf Rannacher  & Jürgen Warnatz ,  & 

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Starke, J., Reichert, C., Eiswirth, M., Oelschläger, K. (2007). Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes. In: Jäger, W., Rannacher, R., Warnatz, J. (eds) Reactive Flows, Diffusion and Transport. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28396-6_13

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