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  4. Stability of carbon monoxide oxidation process on gold nanoparticles

Stability of carbon monoxide oxidation process on gold nanoparticles

MMC.
2021;
Volume 8, Number 1
: pp. 116–124
https://doi.org/10.23939/mmc2021.01.116
Received: October 16, 2020
Revised: February 01, 2021
Accepted: February 04, 2021

Mathematical Modeling and Computing, Vol. 8, No. 1, pp. 116–124 (2021)

Authors:
  1. P. P. Kostrobij
  2. I. A. Ryzha
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University

The stability conditions for mathematical models of carbon monoxide oxidation on the surface of gold nanoparticles are investigated.  The cases of reaction mechanisms of one-step and step-by-step transformation of reagents are consecutively considered.  Using the stability analysis by Lyapunov method, it is shown that models which take into account the possibility of structural changes of the catalyst surface can predict the occurrence of oscillatory mode in the system as a result of Hopf instability.

reaction of catalytic oxidation
modeling of CO oxidation
gold nanoparticles
  1. Freund H.-J., Meijer G., Scheffler M., Schlogl R., Wolf M.  CO oxidation as a prototypical reaction for heterogeneous processes.  Angewandte Chemie International Edition. 50 (43), 10064–10094 (2011).
  2. Krischer K., Eiswirth M., Ertl G.  Oscillatory CO oxidation on Pt(110): Modeling of temporal self-organization.  Journal of Chemical Physics. 96 (12), 9161–9172 (1992).
  3. Haruta M., Kobayashi T., Sano H., Yamada N.  Novel gold catalysts for the oxidation of carbon monoxide at a temperature far below  0◦C.  Chemistry Letters. 16 (2), 405–408  (1987).
  4. Valden M., Lai X., Goodman D. W.  Onset of catalytic activity of gold clusters on titania with the appearance of nonmetallic properties.  Science. 281 (5383), 1647–1650 (1998).
  5. Ryzha I., Matseliukh M.  Carbon monoxide oxidation on the Pt-catalyst: modelling and stability.  Mathematical Modeling and Computing. 4 (1), 96–106  (2017).
  6. Kostrobij P., Ryzha I., Markovych B.  Mathematical model of carbon monoxide oxidation: influence of the catalyst surface structure.  Mathematical Modeling and Computing. 5 (2), 158–168 (2018).
  7. Kuznetsov Y. A.  Elements of Applied Bifurcation Theory. Springer, New York (1995).
  8. Hoyle R.  Pattern Formation. Cambridge University Press, New York (2006).
  9. Imbihl R., Ertl G.  Oscillatory kinetics in heterogeneous catalysis.  Chemical Reviews. 95 (3), 697–733 (1995).
  10. Gritsch T., Coulman D., Behm R. J., Ertl G.  Mechanism of the CO-induced  1×2→1×1 structural transformation of Pt(110).  Physical Review Letters. 63 (10), 1086–1089  (1989).
  11. Slinko M. M., Jaeger N. I.  Oscillating Heterogeneous Catalytic Systems (Studies in Surface Science and Catalysis). Vol.86. Elsevier Science: Amsterdam (1994).
  12. Qiao L., Li X., Kevrekidis I. G., Punckt C., Rotermund H. H.  Enhancement of surface activity in CO oxidation on Pt(110) through spatiotemporal laser actuation.  Physical Review E. 77 (3), 036214 (2008).
  13. Uchiyama T., Yoshida H., Kuwauchi Y., Ichikawa S., Shimada S., Haruta M., Takeda S.  Systematic morphology changes of gold nanoparticles supported on CeO2 during CO oxidation.  Angewandte Chemie International Edition. 50 (43), 10157–10160 (2011).
  14. Elsgolts L.  Differential Equations and the Calculus of Variation. Kniga po Trebovaniju, Moskva (2012), (in Russian).
  15. Zhdanov V. P.  Kinetic models of CO oxidation on gold nanoparticles.  Surface Science. 630, 286–293 (2014).
  16. Reichert C., Starke J., Eiswirth M.  Stochastic model of CO oxidation on platinum surfaces  and deterministic limit.  Journal of Chemical Physics. 115 (10), 4829–4838 (2001).
  17. Korn G. A., Korn T. M.  Mathematical Handbook for Scientists and Engineers: Deffinitions, Theorems and Formulas for Reference and Review. Dover Publications (2000).