1. MMC
  2. All Volumes and Issues
  3. Volume 4, Number 1, 2017
  4. Carbon monoxide oxidation on the Pt-catalyst: modelling and stability

Carbon monoxide oxidation on the Pt-catalyst: modelling and stability

MMC.
2017;
Volume 4, Number 1
: pp. 96-106
https://doi.org/10.23939/mmc2017.01.096
Received: August 30, 2017

Math. Model. Comput. Vol.4, No.1, pp.96-106 (2017)

Authors:
  1. I. Ryzha
  2. M. Matseliukh
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University

A two-dimensional mathematical model of carbon monoxide (CO) oxidation is investigated for the Langmuir-Hinshelwood mechanism on the surface of a Platinum (Pt) catalyst. The adsorbate-driven structural phase transition of catalytic surface is taken into account. The stability analysis of the model solutions is carried out. It is shown that the spatio-temporal periodic chemical oscillations of CO and oxygen (O) surface coverages and a fraction of the surface in the non-reconstructed $(1\times 1)$-structure occur. Conditions for Hopf and Turing bifurcation to arise are investigated.

reaction of catalytic oxidation
reaction-diffusion model
Hopf bifurcation
Turing bifurcation
  1. Sadeghi P., Dunphy K., Punckt C., Rotermund H. H. Inversion of pattern anisotropy during CO oxidation on Pt(110) correlated with appearance of subsurface oxygen. J. Phys. Chem. C. 116 (7), 4686–4691 (2012).
  2. Zaikin A. N., Zhabotinsky A. M. Concentration wave propagation in two-dimensional liquid-phase self-oscillating system. Nature. 225, 535–537 (1970).
  3. Rotermund H. H., Engel W., Kordesch M., Ertl G. Imaging of spatio-temporal pattern evolution during carbon monoxide oxidation on platinum. Nature. 343, 355–357 (1990).
  4. Jakubith S., Rotermund H. H., Engel W., von Oertzen A., Ertl G. Spatiotemporal concentration patterns in a surface reaction: Propagating and standing waves, rotating spirals, and turbulence. Phys. Rev. Lett. 65, 3013–3016 (1990).
  5. Nettesheim S., von Oertzen A., Rotermund H. H., Ertl G. Reaction diffusion patterns in the catalytic CO oxidation on Pt(110): Front propagation and spiral waves.  J. Chem. Phys. 98, 9977–9985 (1993).
  6. Kim M., Bertram M., Pollmann M., von Oertzen A., Mikhailov A. S., Rotermund H. H., Ertl G. Controlling chemical turbulence by global delayed feedback: Pattern formation in catalytic CO oxidation on Pt(110). Science. 292, 1357–1360 (2001).
  7. Wolff J., Papathanasiou A. G., Kevrekidis I. G., Rotermund H. H., Ertl G. Spatiotemporal addressing of surface activity. Science. 294, 134–137 (2001).
  8. Slin'ko M. M., Jaeger N. I. Oscillating Heterogeneous Catalytic Systems (Studies in Surface Science and Catalysis). Eds. Amsterdam: Elsevier; Vol. 86 (1994).
  9. Baxter R. J., Hu P. Insight into why the Langmuir-Hinshelwood mechanism is generally preferred.  J. Chem. Phys. 116 (11), 4379–4381 (2002).
  10. Wilf M., Dawson P. T. The adsorption and desorption of oxygen on the Pt(110) surface; a thermal desorption and LEED/AES study. Surf. Sci. 65, 399–418 (1977).
  11. Gomer R. Diffusion of adsorbates on metal surfaces.  Rep. Prog. Phys. 53 (7), 917–1002 (1990).
  12. Kellogg G. L. Direct observations of the $(1\times2)$ surface reconstruction on the Pt(110) plane. Phys. Rev. Lett. 55, 2168–2171 (1985).
  13. Gritsch T., Coulman D., Behm R. J., Ertl G. Mechanism of the CO-induced $(1\times 2)-(1\times 1)$ structural transformation of Pt(110).  Phys. Rev. Lett. 63, 1086–1089 (1989).
  14. Krischer K., Eiswirth M., Ertl G. Oscillatory CO oxidation on Pt(110): Modeling of temporal self-organization. J. Chem. Phys. 96, 9161–9172 (1992).
  15. Bär M., Eiswirth M., Rotermund H. H., Ertl G. Solitary-wave phenomena in an excitable surface-reaction.  Phys. Rev. Lett. 69 (6), 945–948 (1992).
  16. Gasser R. P. H., Smith E. B.  A surface mobility parameter for chemisorption.  Chem. Phys. Lett. 1 (10), 457–458 (1967).
  17. Bertram M., Mikhailov A. S.  Pattern formation on the edge of chaos: Mathematical modeling of CO oxidation on a Pt(110) surface under global delayed feedback.  Phys. Rev. E. 67, 036207:1-11 (2003).
  18. Bzovska I. S., Mryglod I. M.  Chemical oscillations in catalytic CO oxidation reaction.  Condens. Matter Phys. 13 (3), 34801:1–5 (2010).
  19. Connors K. A.  Chemical Kinetics: The Study of Reaction Rates in Solution.  New York, VCH Publishers (1990).
  20. Suchorski Y.  Private comunication.
  21. Korn G. A., Korn T. M.  Mathematical handbook for scientists and engineers.  Courier Corporation (2000).
  22. Kuznetsov Y.  Elements of applied bifurcation theory.  New York, Springer (1995).
  23. Bzovska I. S., Mryglod I. M.  Surface patterns in catalytic carbon monoxide oxidation reaction.  Ukr. Phys. J. 61 (2), 134–142 (2016).
  24. Hoyle R.  Pattern Formation.  New York, Cambridge University Press (2006).