Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Freund, H.-J., Meijer, G., Scheffler, M., Schlogl, R., Wolf, M.: CO oxidation as a prototypical reaction for heterogeneous processes. Angew. Chem. Int. Ed. 50(43), 10064–10094 (2011). https://doi.org/10.1002/anie.201101378
Krischer, K., Eiswirth, M., Ertl, G.: Oscillatory CO oxidation on Pt(110): modeling of temporal self-organization. J. Chem. Phys. 96(12), 9161–9172 (1992). https://doi.org/10.1063/1.462226
Haruta, M., Kobayashi, T., Sano, H., Yamada, N.: Novel gold catalysts for the oxidation of carbon monoxide at a temperature far below \(0^\circ \text{ C }\). Chem. Lett. 16(2), 405–408 (1987). https://doi.org/10.1246/cl.1987.405
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). https://doi.org/10.1126/science.281.5383.1647
Ryzha, I., Matseliukh, M.: Carbon monoxide oxidation on the Pt-catalyst: modelling and stability. Math. Model. Comput. 4(1), 96–106 (2017). https://doi.org/10.23939/mmc2017.01.096
Kostrobij, P., Ryzha, I., Markovych, B.: Mathematical model of carbon monoxide oxidation: influence of the catalyst surface structure. Math. Model. Comput. 5(2), 158–168 (2018). https://doi.org/10.23939/mmc2018.02.158
Kuznetsov, Y.: Elements of Applied Bifurcation Theory. Springer, New York (1995)
Hoyle, R.: Pattern Formation. Cambridge University Press, New York (2006)
Imbihl, R., Ertl, G.: Oscillatory kinetics in heterogeneous catalysis. Chem. Rev. 95(3), 697–733 (1995). https://doi.org/10.1021/cr00035a012
Gritsch, T., Coulman, D., Behm, R.J., Ertl, G.: Mechanism of the CO-induced \(1 \times 2\rightarrow 1 \times 1\) structural transformation of Pt(110). Phys. Rev. Lett. 63(10), 1086–1089 (1989). https://doi.org/10.1103/physrevlett.63.1086
Slinko, M.M., Jaeger, N.I.: Oscillating Heterogeneous Catalytic Systems (Studies in Surface Science and Catalysis), vol. 86. Elsevier Science, Amsterdam (1994)
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. Phys. Rev. E 77(3), 036214 (2008). https://doi.org/10.1103/PhysRevE.77.036214
Uchiyama, T., Yoshida, H., Kuwauchi, Y., Ichikawa, S., Shimada, S., Haruta, M., Takeda, S.: Systematic morphology changes of gold nanoparticles supported on \({\text{ CeO }}_{2}\) during CO oxidation. Angew. Chem. Int. Ed. 50(43), 10157–10160 (2011). https://doi.org/10.1002/anie.201102487
Elsgolts, L.: Differential Equations and the Calculus of Variation. Kniga po Trebovaniju, Moskva (2012). (in Russian)
Zhdanov, V.P.: Kinetic models of CO oxidation on gold nanoparticles. Surf. Sci. 630, 286–293 (2014). https://doi.org/10.1016/j.susc.2014.08.025
Reichert, C., Starke, J., Eiswirth, M.: Stochastic model of CO oxidation on platinum surfaces and deterministic limit. J. Chem. Phys. 115(10), 4829–4838 (2001). https://doi.org/10.1063/1.1391255
Korn, G.A., Korn, T.M.: Mathematical Handbook for Scientists and Engineers: Definitions, Theorems and Formulas for Reference and Review. Dover Publications, New York (2000)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Kostrobij, P., Ryzha, I. (2021). Modeling of Carbon Monoxide Oxidation on Gold Nanoparticles: Is There Oscillatory Mode?. In: Shakhovska, N., Medykovskyy, M.O. (eds) Advances in Intelligent Systems and Computing V. CSIT 2020. Advances in Intelligent Systems and Computing, vol 1293. Springer, Cham. https://doi.org/10.1007/978-3-030-63270-0_34
Download citation
DOI: https://doi.org/10.1007/978-3-030-63270-0_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-63269-4
Online ISBN: 978-3-030-63270-0
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)