Abstract
The article examines consistent mathematical micro- and macro-level models of CO oxidation on platinum-group metals. New mechanisms responsible for the excitation of oscillations are studied in detail by simulation. Micro-level oscillations may arise in parameter-space regions where the corresponding macro model has a limiting cycle, a bistability, or a unique stable steady-state solution. In the latter case, necessary conditions for the excitation of oscillations include fluctuations in the concentration of adsorbed particles, which are characteristic of micro models of small-volume systems, and a special arrangement of the macro-model trajectories on the phase plane producing sensitivity to small perturbations or excitability of the medium.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
T. Engel and G. Ertl, in: The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis,Vol. 4, Elsevier, Amsterdam (1982), p. 73.
G. Ertl, P. R. Norton, and J. Rustig, Phys. Rev. Lett., 49, No. 2, 171 (1982).
S. Ladas, R. Imbihl, and G. Ertl, Surf. Sci., 197, 153 (1988).
G. Ertl, Adv. Catal., 37, 213 (1990).
A. Hopkinson, J. M. Bradley, X. C. Guo, M. Gruyters, and D. A. King, Phys. Rev. Lett., 71, 1597 (1993).
N. I. Jaeger, K. Moller, and P. J. Plath, J. Chem. Soc. Faraday Trans., Pt. II, 82, 3315 (1986).
M. M. Slinko, N. I. Jaeger, and P. Svensson, J. Catal., 118, 349 (1989).
M. R. Basset and R. Imbihl, J. Chem. Phys., 93, 811 (1990).
J. E. Turner, B. C. Sales, and M. B. Maple, Surf. Sci., 103, 54 (1981).
J. E. Turner, B. C. Sales, and M. B. Maple, Surf. Sci., 109, 591 (1981).
B. C. Sales, J. E. Turner, and M. B. Maple, Surf. Sci., 114, 381 (1982).
M. Gruyters, T. Ali, and D. A. King, J. Chem. Phys., 100, 14417 (1996).
E. S. Kurkina, N. V. Peskov, M. M. Slin'ko, and M. G. Slin'ko, Dokl. Akad. Nauk, 351, No. 4, 497 (1996).
E. S. Kurkina, S. M. Makarova, and M. M. Slin'ko, Matem. Modelirovanie, 2, No. 1, 14 (1990).
V. P. Zhdanov, Surf. Sci., 426, 345 (1999).
V. I. Elokhin and E. I. Latkin, Dokl. Akad. Nauk, 344, No. 1, 56 (1995).
A. L. Vishnevskii, E. I. Latkin, and V. I. Elokhin, Surf. Rev. Lett., 2, No. 4, 459 (1995).
A. P. J. Jansen and R. M. Nieminen, J. Chem. Phys., 106, 2038 (1997).
K. Binder (ed.), Monte-Carlo Methods in Statistical Physics [Russian translation], Mir, Moscow (1982).
I. Langmuir, J. Amer. Chem. Soc., 37, 1139 (1915).
P. A. Redhead, Vacuum 12, No. 4, 203 (1962).
H. Eyring, S. H. Lin, and S. M. Lin, Basic Chemical Kinetics [Russian translation], Mir, Moscow (1983).
A. G. Makeev and N. L. Semendyaeva, Matem. Modelirovanie, 8, No. 8, 76 (1996).
Rights and permissions
About this article
Cite this article
Kurkina, E.S., Semendyaeva, N.L. Oscillation-Generating Mechanisms in Stochastic and Deterministic Models of a Catalytic Reaction. Computational Mathematics and Modeling 14, 319–333 (2003). https://doi.org/10.1023/A:1024499227068
Issue Date:
DOI: https://doi.org/10.1023/A:1024499227068