Pattern Formation in a Surface Reaction with Global Coupling

  • Harm Hinrich Rotermund
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 115)


Surface reactions exhibit unique features as model systems for nonlinear effects in chemical reactions. In addition they have an immense importance in heterogeneous catalysis in the chemical industry. Dynamic processes on surfaces, like the Pt — catalyzed CO-oxidation, can be described by a set of reaction-diffusion equations. For a certain range of reactants partial pressures and temperature of the sample, pattern formation like spiral waves, target patterns or solitary waves can be observed. When global coupling via the gas phase is introduced strong temporal oscillations may occur, sometimes exhibiting spatio-temporal patterns like standing waves, period doubling and chaotic behavior. The patterns mentioned were found under isothermal conditions. Of course, when increasing the reaction pressure, due to the exothermic nature of the CO-oxidation, temperature variations can be explored, observable with a sensitive InfraRed (IR) camera.


Surface Reaction Standing Wave Pattern Formation Spiral Wave Target Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M.G.T. FECHNER, Zur Elektrochemie; Ueber Umkehrungen der Polarität der einfachen Kette. Schweiggers J. der Chemie und Physik 1828, 53:129–151.Google Scholar
  2. [2]
    C.F. SCHöNBEIN, Archives de 1’ Electricité 1836, 5:267.Google Scholar
  3. [3]
    J.P. JOULE, On the Intermittend Character of the Voltaic Current in certain cases of Electrolysis; and on the Intensities of various Voltaic Arrangements. Phil. Mag. 1844, 24:106–115.Google Scholar
  4. [4]
    W. OSTWALD, ere Geschichte der Lehre der Berührungswirkungen. Dekanatsschrift Leibzig 1898.Google Scholar
  5. [5]
    A. LOTKA, Contribution to the Theory of periodic Reactions. Journal of Physical Chemistry 1910, 14:271–274.CrossRefGoogle Scholar
  6. [6]
    A. LOTKA, Analytical note on certain rhythmic relations in organic systems. Proceedings of the National Adademy of Science of the U.S. 1920, 6:410–415..CrossRefGoogle Scholar
  7. [7]
    J.W. DöBEREINER, Beiträge zur pneumatischen Chemie 1824, 4:.Google Scholar
  8. [8]
    J.W. DöBEREINER, Schweiggers J. der Chemie und Physik 1827, 39:159.Google Scholar
  9. [9]
    J.W. DöBEREINER, Vermischte Erfahrungen ueber Platina Gährungschemie. Schweiggers J. der Chemie und Physik 1828, 54:412–426.Google Scholar
  10. [10]
    P.J. PLATH, JENSEITS DES MOLEKüLS, Raum und Zeit in der Chemie (Vieweg, Braunschweig/Wiesbaden, 1997).Google Scholar
  11. [11]
    P. HUGO, Möglichkeiten und Grenzen der Berechnung des Diffusionseinflusses in porösen Katalysatoren. Chem. Ing. Tech. 1969, 41:400.CrossRefGoogle Scholar
  12. [12]
    M. JAKUBITH, Isotherme Oszillationen bei der CO-oxidation am Pt-Netz. Chem. Ing. Tech. 1970, 14:943–944.Google Scholar
  13. [13]
    P. HUGO, Stabilität und Zeitverhalten von Durchfluss-Kreislauf-Reaktoren. Ber. Bunsenges. Phys. Chem. 1970, 74:121.Google Scholar
  14. [14]
    E. WICKE, Instabile Reaktionszustände bei der Heterogenen Katalyse. Chemie-Ing.-Techn. 1974, 46:365–404.CrossRefGoogle Scholar
  15. [15]
    S.P. SINGH-BOPARAI AND D.A. KING, Proc. 4th Int. Congr. Sol. Surf., Suppl. Rev. Le Vide 1980, 403–406.Google Scholar
  16. [16]
    G. ERTL, P.R. NORTON AND J. RüSTIG, Kinetic oscillations in the platinum-catalysed oxidation of CO. Phys. Rev. Lett. 1982, 49:177–180.CrossRefGoogle Scholar
  17. [17]
    Oxidation of Carbon Monoxide, 4, Eds.T. Engel and G. Ertl (Elsevier, Amsterdam, 1982).Google Scholar
  18. [18]
    P.A. THIEL, R.J. BEHM, P.R. NORTON AND G. ERTL, Mechanism of an adsorbate-induced surface phase transformation: CO on Pt(100). Surf. Sci. 1982, 121:L553–L560.CrossRefGoogle Scholar
  19. [19]
    T.E. JACKMAN, J.A. DAVIES, D.P. JACKSON, W.N. UNERTL AND P.R. NORTON, The Pt(110) phase transition: a study by Rutherford backscattering, nuclear microanalysis, LEED and Thermal Desorption Spectroscopy. Surf. Sci. 1982, 120:389–412.CrossRefGoogle Scholar
  20. [20]
    P.A. THIEL, R.J. BEHM, P.R. NORTON AND G. ERTL, The interaction of CO and Pt(100). II. Energetic and kinetic parameters. J. Chem. Phys. 1983, 78:7448–7458.CrossRefGoogle Scholar
  21. [21]
    G. ERTL, Kinetics of chemical processes on well-defined surfaces. In Catalysis: Science and Technology, Eds. J.R. Anderson and M. Boudart. Heidelberg: Springer-Verlag, 1983:209–282.Google Scholar
  22. [22]
    M.P. Cox, G. ERTL, R. IMBIHL AND J. RüSTIG, Non-equilibrium surface phase transitions during the catalytic oxidation of CO on Pt(100). Surf. Sci. 1983, 134:L517–L523.Google Scholar
  23. [23]
    R.J. BEHM, P.A. THIEL, P.R. NORTON AND G. ERTL, The interaction of CO and Pt(100). I. Mechanism of adsorption and Pt phase transition. J. Chem. Phys. 1983, 78:7437–7447.CrossRefGoogle Scholar
  24. [24]
    V.V. BARELKO AND Y.E. VOLODIN, Electrothermographic méthode in heterogenous catalysis. Kinetika i Kataliz 1976, 17:112–117.Google Scholar
  25. [25]
    V.V. BARELKO, I.I. KURACHKA, A.G. MERZHANOV AND K.G. SHKADINSKII, Investigation of travelling waves on catalytic wires. Chem. Eng. Sci. 1978, 33:805–811.CrossRefGoogle Scholar
  26. [26]
    S.A. ZHUKOV AND V.V. BARELKO, Spatially nonhomogeneous Stationary States of a Catalyst in Oxidation Reactions on a Platinum Filament. Sov. J. Chem. Phys. 1982, 4:883–891.Google Scholar
  27. [27]
    P. PAWLICKI AND R.A. SCHMITZ, Spatial Effects on Supported Catalysts. Chem. Eng. Prog. 1987, 83:40–45.Google Scholar
  28. [28]
    G.A. CORDONIER AND L.D. SCHMIDT, Chemical Engineering Science 1989, 44:1983.CrossRefGoogle Scholar
  29. [29]
    L. LOBBAN AND D. Luss, Spatial temperature oscillations during hydrogen oxidation on a nickel foil. J. Chem. Phys. 1989, 93:6530–6533.CrossRefGoogle Scholar
  30. [30]
    J.C. KELLOW AND E.E. WOLF, Thermographie studies of catalytic reactions. Chem. Eng. Sci 1990, 45:2597–2602.CrossRefGoogle Scholar
  31. [31]
    D. Luss, Temperature fronts and pulses on catalytic ribbons. Physica 1992, 188A:68–77.Google Scholar
  32. [32]
    M.P. Cox, G. ERTL AND R. IMBIHL, Spatial self-organization of surface structure during an oscillating catalytic reaction. Phys. Rev. Lett. 1985, 54: 1725–1728.CrossRefGoogle Scholar
  33. [33]
    H.H. ROTERMUND, G. ERTL AND W. SESSELMANN, Scanning photoemission microscopy of surfaces. Surf. Sci. 1989, 217:L383–L390.CrossRefGoogle Scholar
  34. [34]
    H.H. ROTERMUND, S. JAKUBITH, A.V. OERTZEN AND G. ERTL, Imaging of spatial pattern formation in an oscillatory surface reaction by scanning photoemission microscopy. J. Chem. Phys. 1989, 91:4942–4948.CrossRefGoogle Scholar
  35. [35]
    H.H. ROTERMUND, W. ENGEL, M. KORDESCH AND G. ERTL, Imaging of spatio-temporal pattern evolution during carbon monoxide oxidation on platinum. Nature 1990, 343:355–357.CrossRefGoogle Scholar
  36. [36]
    W. ENGEL, M.E. KORDESCH, H.H. ROTERMUND, S. KUBALA AND A.V. OERTZEN, UHV-compatible photoelectron emission microscope for applications in surface science. Ultramicroscopy 1991, 36:148–153.CrossRefGoogle Scholar
  37. [37]
    J.J. CARROLL AND A.J. MELMED, Ellipsometry-LEED study of the adsorption of oxygen on (011) tungsten. Surf. Sci. 1969, 16:251–264.CrossRefGoogle Scholar
  38. [38]
    H.H. ROTERMUND, G. HAAS, R.U. FRANZ, R.M. TROMP AND G. ERTL, Imaging pattern formation in surface reactions from ultra-high vacuum to atmospheric pressures. Science 1995, 270:608–610.CrossRefGoogle Scholar
  39. [39]
    H.H. ROTERMUND, G. HAAS, R.U. FRANZ, R.M. TROMP AND G. ERTL, Imaging pattern Formation: Bridging the pressure Gap. Applied Physics A 1995, 61:569–574.CrossRefGoogle Scholar
  40. [40]
    H.H. ROTERMUND, Imaging of dynamic processes on surfaces by light. Surf. Sci. Reports 1997, 29:265–364.CrossRefGoogle Scholar
  41. [41]
    T. ENGEL AND G. ERTL, Elementary steps in the catalytic oxidation of carbon monoxide on Platinum metals. Adv. Catal. 1979, 28:1–77.CrossRefGoogle Scholar
  42. [42]
    K. KRISCHER, M. EISWIRTH AND G. ERTL, Oscillatory CO oxidation on Pt(110): Modeling of temporal self-organization. J. Chem. Phys. 1992, 96:9161–9172.CrossRefGoogle Scholar
  43. [43]
    T. GRITSCH, D. COULMAN, R.J. BEHM AND G. ERTL, Mechanism of the CO induced 1 × 2 → 1 × 1 structural transformation of Pt(110). Phys. Rev. Lett. 1989, 63:1086–1089.CrossRefGoogle Scholar
  44. [44]
    T. GRITSCH, D. COULMAN, R.J. BEHM AND G. ERTL, A scanning tunneling microscopy investigation of the 1 × 2-1 × 1 structural transformation of the Pt(110) surface. Appl. Phys. A 1989, 49:403–405.CrossRefGoogle Scholar
  45. [45]
    R. DUCROS AND R.P. MERRIL, The interaction of oxygen with Pt(110). Surf. Sci. 1976, 55:227–245.CrossRefGoogle Scholar
  46. [46]
    N. FREYER, M. KISKINOVA, G. PIRUG AND H.P. BONZEL, Oxygen adsorption on Pt(110)-(l × 2) and Pt(110)-(l × 1). Surf. Sci. 1986, 166:206–220.CrossRefGoogle Scholar
  47. [47]
    R. IMBIHL, M.P. COX, G. ERTL, H. MLLER AND W. BRENIG, Kinetic oscillations in the catalytic CO oxidation on Pt(100): Theory. J. Chem. Phys. 1985, 83:1578–1587.CrossRefGoogle Scholar
  48. [48]
    B.C. SALES, J.E. TURNER AND M.B. MAPLE, Oscillatory oxidation of CO over Pt, Pd and Ir catalysts: Theory. Surf. Sci. 1982, 114:381–394.CrossRefGoogle Scholar
  49. [49]
    S. LADAS, R. IMBIHL AND G. ERTL, Kinetic oscillations during the catalytic CO oxidation on Pd(110): the role of subsurface oxygen. Surf. Sci. 1989, 219:88–106.CrossRefGoogle Scholar
  50. [50]
    M.R. BASSETT AND R. IMBIHL, Mathematical modeling of kinetic oscillations in the catalytic CO oxidation on Pd(110): The subsurface oxygen model. J. Chem. Phys. 1990, 93:811–821.CrossRefGoogle Scholar
  51. [51]
    J. LAUTERBACH, G. HAAS, H.H. ROTERMUND AND G. ERTL, Spatio-temporal pattern formation on polycrystalline platinum surfaces during the catalytic CO oxidation. Surf. Sci. 1993, 294:116–130.CrossRefGoogle Scholar
  52. [52]
    S. JAKUBITH, H.H. ROTERMUND, W. ENGEL, A.V. OERTZEN AND G. ERTL, Spatiotemporal concentration patterns in a surface reaction: Propagating and standing waves, rotating spirals, and turbulence. Phys. Rev. Lett. 1990, 65:3013–3016.CrossRefGoogle Scholar
  53. [53]
    H.H. ROTERMUND, W. ENGEL, S. JAKUBITH, A.V. OERTZEN AND G. ERTL, Methods and application of UV photoelectron microscopy in heterogeneous catalysis. Ultramicroscopy 1991, 36:164–172.CrossRefGoogle Scholar
  54. [54]
    H.H. ROTERMUND, Imaging pattern formation in surface reactions from ultra-high vacuum up to atmospheric pressures. Surf. Sci. 1997, 386:10–23.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Harm Hinrich Rotermund
    • 1
  1. 1.Fritz-Haber-Institut der Max-Planck-GesellschaftBerlinGermany

Personalised recommendations