Advertisement

On the number of contacts of two polymer chains situated on fractal structures

Article

Abstract.

We study the critical behavior of the number of monomer-monomer contacts for two polymers in a good solvent. Polymers are modeled by two self-avoiding walks situated on fractals that belong to the checkerboard (CB) and X family. Each member of a family is labeled by an odd integer b, \(3\le b\le\infty\). By applying the exact Renormalization Group (RG) method, we establish the relevant phase diagrams whereby we calculate the contact critical exponents \(\varphi\) (for the CB and X fractals with b = 5 and b = 7). The critical exponent \(\varphi\) is associated with power law of the number of sites at which the two polymers are touching each other.

Keywords

Polymer Phase Diagram Polymer Chain Renormalization Group Critical Exponent 
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.
    M. Rubinstein, R. Colby, Polymer Physics (Oxford University Press, New York, 2003)Google Scholar
  2. 2.
    C. Vanderzande, Lattice Models of Polymers (Cambridge University Press, Cambridge, 1998)Google Scholar
  3. 3.
    E. Bouchaud, J. Vannimenus, J. Phys. A 50, 2931 (1989)Google Scholar
  4. 4.
    A. Lapp, M. Mottin, D. Broseta, L. Leibler, J. Phys. II France 2, 1247 (1992)CrossRefGoogle Scholar
  5. 5.
    N. Posharnowa, A. Schneider, M. Wünsch, V. Kuleznew, B.A. Wolf, J. Chem. Phys. 115, 9536 (2001)CrossRefGoogle Scholar
  6. 6.
    K. Kumeta, I. Nagashima, S. Matsui, K. Mizoguchi, J. Appl. Polym. Sci. 90, 2420 (2003)CrossRefGoogle Scholar
  7. 7.
    P.G. de Gennes, J. Phys. Lett. 40, 69 (1979)Google Scholar
  8. 8.
    Ch. Kappeler, L. Schäfer, T. Fukuda, Macromolecules 24, 2715 (1991)Google Scholar
  9. 9.
    M. Benmouna, T.A. Vilgis, M. Daoud, M. Benhamou, Macromolecules 27, 1172 (1994)Google Scholar
  10. 10.
    L. Schäfer, Ch. Kappeler, J. Phys. France 46, 1853 (1985)Google Scholar
  11. 11.
    M. Benhamou, A. Derouiche, A. Bettachy, J. Chem. Phys. 106, 2513 (1997)CrossRefGoogle Scholar
  12. 12.
    S. Müller, L. Schäfer, Eur. Phys. J. B 2, 351 (1998)CrossRefGoogle Scholar
  13. 13.
    T.A.S. Haddad, R.F.S. Andrade, S.R. Salinas, J. Phys. A 37, 1499 (2004)CrossRefMATHGoogle Scholar
  14. 14.
    K.F. Freed, J. Phys. A 18, 871 (1985)CrossRefMathSciNetGoogle Scholar
  15. 15.
    A. Sariban, K. Binder, J. Chem. Phys. 86, 5859 (1987)CrossRefGoogle Scholar
  16. 16.
    P. Leoni, C. Vanderzande, L. Vandeurzen, J. Phys. A 34, 9777 (2001)CrossRefMathSciNetMATHGoogle Scholar
  17. 17.
    E. Orlandini, F. Seno, A.L. Stella, Phys. Rev. Lett. 84, 294 (2000)CrossRefGoogle Scholar
  18. 18.
    M. Baiesi, E. Carlon, E. Orlandini, A.L. Stella, Phys. Rev. E 63, 041801 (2001)CrossRefGoogle Scholar
  19. 19.
    E. Orlandini, S.M. Bhattacharjee, D. Marenduzzo, A. Maritan, F. Seno, J. Phys. A 34, L751 (2001)Google Scholar
  20. 20.
    D. Marenduzzo, S.M. Bhattacharjee, A. Maritan, E. Orlandini, F. Seno, Phys. Rev. Lett. 88, 028102 (2002)CrossRefGoogle Scholar
  21. 21.
    Y. Kafri, D. Mukamel, L. Peliti, Eur. Phys. J. B 27, 135 (2002)CrossRefGoogle Scholar
  22. 22.
    M. Baiesi, E. Carlon, E. Orlandini, A.L. Stella, Eur. Phys. J. B 29, 129 (2002)CrossRefGoogle Scholar
  23. 23.
    S. Kumar, Y. Singh, J. Phys. A 26, L987 (1993)Google Scholar
  24. 24.
    S. Kumar, Y. Singh, J. Stat. Phys. 89, 981 (1997)MATHGoogle Scholar
  25. 25.
    I. Živić, S. Milošević, J. Phys. A 31, 1365 (1998)Google Scholar
  26. 26.
    S. Kumar, Physica A 292, 422 (2001)CrossRefMathSciNetMATHGoogle Scholar
  27. 27.
    S. Elezović-Hadžić, S. Milošević, J. Phys. A 25, 4095 (1992)MathSciNetGoogle Scholar
  28. 28.
    S. Milošević, I. Živić, V. Miljković, Phys. Rev. E 55, 5671 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Faculty of PhysicsUniversity of BelgradeBelgradeSerbia
  2. 2.Faculty of Natural Sciences and MathematicsUniversity of KragujevacKragujevacSerbia

Personalised recommendations