Journal of Statistical Physics

, Volume 83, Issue 5–6, pp 1241–1253 | Cite as

Critical exponents for numbers of differently anchored polymer chains on fractal lattices with adsorbing boundaries

  • Sunčica Elezović-Had zić
  • Milan Kne zević
  • Sava Milošević
  • Ivan Zivić
Short Communications

Abstract

We study the problem of polymer adsorption in a good solvent when the container of the polymer-solvent system is taken to be a member of the Sierpinski gasket (SG) family of fractals. Members of the SG family are enumerated by an integerb (2≤b≤∞), and it is assumed that one side of each SG fractal is an impenetrable adsorbing boundary. We calculate the critical exponents γ1, γ11, and γ s , which, within the self-avoiding walk model (SAW) of the polymer chain, are associated with the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing impenetrable boundary, respectively. By applying the exact renormalization group (RG) method for 2≤b≤8 and the Monte Carlo renormalization group (MCRG) method for a sequence of fractals with 2≤b≤80, we obtain specific values for these exponents. The obtained results show that all three critical exponents γ1, γ11, and γ s , in both the bulk phase and crossover region are monotonically increasing functions withb. We discuss their mutual relations, their relations with other critical exponents pertinent to SAWs on the SG fractals, and their possible asymptotic behavior in the limitb→∞, when the fractal dimension of the SG fractals approaches the Euclidean value 2.

Key Words

Polymer adsorption fractals exact and Monte Carlo renormalization group 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Bouchaud and J. Vannimenus,J. Phys. (Paris)50:2931 (1989).Google Scholar
  2. 2.
    V. Bubanja, M. Knezević, and J. Vannimenus,J. Stat. Phys. 71:1 (1993).Google Scholar
  3. 3.
    S. Kumar and Y. Sing,Phys. Rev. E 48:734 (1993).Google Scholar
  4. 4.
    S. Kumar, Y. Sing, and D. Dhar,J. Phys. A 26:4835 (1993).Google Scholar
  5. 5.
    I. Zivić, S. Milošević, and H. E. Stanley,Phys. Rev. E,49:636 (1994).Google Scholar
  6. 6.
    V. Miljković, S. Milošević, and I. Zivić,Phys. Rev. E, to appear.Google Scholar
  7. 7.
    S. Elezović, M. Knezević, and S. Milošević,J. Phys. A 20:1215 (1987).Google Scholar
  8. 8.
    I. Zivić and S. Milošević,J. Phys. A 26:3393 (1993).Google Scholar
  9. 9.
    D. Dhar,J. Phys. (Paris)49:397 (1988).Google Scholar
  10. 10.
    D. Dhar,J. Math. Phys. 19:5 (1978).Google Scholar
  11. 11.
    S. Milošević and I. Zivić,J. Phys. A 24:L833 (1991).Google Scholar
  12. 12.
    S. Milošević and I. Zivić,J. Phys. A 27:7739 (1994).Google Scholar
  13. 13.
    K. De'Bell and T. Lookman,Rev. Mod. Phys. 65:87 (1993).Google Scholar
  14. 14.
    A. J. Guttman and G. M. Torrie,J. Phys. A 17:3539 (1984).Google Scholar
  15. 15.
    B. Duplantier,Phys. Rev. Lett. 57:941 (1986).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Sunčica Elezović-Had zić
    • 1
  • Milan Kne zević
    • 1
  • Sava Milošević
    • 1
  • Ivan Zivić
    • 2
  1. 1.Faculty of PhysicsUniversity of BelgradeBelgradeSerbia
  2. 2.Faculty of Natural Sciences and MathematicsUniversity of KragujevacKragujevacSerbia

Personalised recommendations