Advertisement

Bulk mediated surface diffusion: the infinite system case

  • J. A. Revelli
  • C. E. Budde
  • D. Prato
  • H. S. Wio
Article

Abstract.

An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented. The time evolution of the effective probability distribution width on the surface is calculated and analyzed within an anomalous diffusion framework. The asymptotic behavior for large times shows a sub-diffusive regime for the effective surface diffusion but, depending on the observed range of time, other regimes may be obtained. Monte Carlo simulations show excellent agreement with analytical results. As an important byproduct of the indicated approach, we present the evaluation of the time for the first visit to the surface.

Keywords

Monte Carlo Simulation Asymptotic Behavior Excellent Agreement Large Time Distribution Width 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.H. Clint, Surfactant Aggregation (Chapman and Hall, New Jork, 1992)Google Scholar
  2. 2.
    H.E. Johnson, J.F. Douglas, S. Granick, Phys. Rev. Lett. 70, 3267 (1993)CrossRefGoogle Scholar
  3. 3.
    C.T. Shibata, A.M Lenhof, J. Colloid Interface Sci. 148, 469 (1992)Google Scholar
  4. 4.
    S. Kim, H. Yu., J. Phys. Chem. 96, 4034 (1992)Google Scholar
  5. 5.
    Y.L. Chen, S. Chen, C. Frank, J. Israelachvili, J. Colloid Interface Sci. 153, 244 (1992)Google Scholar
  6. 6.
    A.A. Sonin, A. Bonfillon, D. Langevin, Phys. Rev. Lett. 71, 2342 (1993)CrossRefGoogle Scholar
  7. 7.
    A.L. Adams, G.C. Fishe, P.C. Munoz, L. Vroman, J. Biomed. Meter. Res. 18, 643 (1984)Google Scholar
  8. 8.
    O. Bichuk, B. OShaughnessy, J. Chem. Phys. 101, 772 (1994)CrossRefGoogle Scholar
  9. 9.
    C. Tsallis, S.V.F. Levy, A.M.C. Souza, R. Maynard, Phys. Rev. Lett. 75, 3598 (1995) [Erratum: Phys. Rev. Lett. 27, 5442 (1996)]CrossRefGoogle Scholar
  10. 10.
    D. Prato, C. Tsallis, Phys. Rev. E. 60, 2398 (1999)CrossRefGoogle Scholar
  11. 11.
    M.A. Ré, C.E. Budde, D.P. Prato, Physica A 323, 9 (2003)Google Scholar
  12. 12.
    G.M. Zaslavsky, Physica D 76, 110 (1994)CrossRefMathSciNetGoogle Scholar
  13. 13.
    J. Klafter, A. Blumen, M.F. Shlesinger, Phys. Rev. A 35, 3081 (1987)CrossRefMathSciNetGoogle Scholar
  14. 14.
    A. Blumen, G. Zumofen, J. Klafter, Phys. Rev. A 40, 3964 (1989)CrossRefGoogle Scholar
  15. 15.
    G. Zumofen, A. Blumen, M.F. Shlesinger, J. Stat. Phys. 54, 1519 (1889)Google Scholar
  16. 16.
    N.G. Van Kampen, Stochastic Processes in Physics ans Chemistry (North-Holland, Amsterdam, 1981)Google Scholar
  17. 17.
    E.W. Montroll, B.J. West, in Fluctuation Phenomena, edited by E.W. Montroll, J.L. Lebowitz (North Holland, Amsterdam, 1979)Google Scholar
  18. 18.
    J.A. Revelli, C.E. Budde, D. Prato, H.S. Wio, Bulk Mediated Surface Diffusion: Finite System Case, to be submittedGoogle Scholar
  19. 19.
    J.A. Revelli, C.E. Budde, D. Prato, H.S. Wio, Bulk Mediated Surface Diffusion: Non Markovian Dynamics, to be submittedGoogle Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • J. A. Revelli
    • 1
  • C. E. Budde
    • 2
  • D. Prato
    • 2
  • H. S. Wio
    • 1
    • 3
  1. 1.Grupo de Física EstadísticaCentro Atómico Bariloche and Instituto BalseiroSan Carlos de BarilocheArgentina
  2. 2.Facultad de Matemáticas, Astronomía y FísicaUniversidad Nacional de CórdobaCórdobaArgentina
  3. 3.Departament de FísicaUniversitat de les Illes Balears and IMEDEAPalma de MallorcaSpain

Personalised recommendations