Theory of Polymers on Fractal Lattices

  • Apurba Kumar Roy
  • Alexander Blumen
Part of the NATO ASI Series book series (NSSB, volume 258)


Nowadays, There is much interest in the statistics of polymers (both of linear chain type and also branched) in good solvents1. The most salient feature of real polymers is the “excluded-volume” effect: the physical fact that no two different monomers composing the polymer can occupy the same spatial position at the same time. In the case of a linear chain polymer without the excluded-volume constraint the chain is Markovian (Gaussian) and can be modelled as a random walk (RW); whereas with inclusion of this constraint the chain becomes non-Markovian and corresponds to a self-avoiding random walk (SAW). In the case of branched polymers we call the analogous case excluded-volume-branched-polymers (EVB) and distinguish them from simple randomly branched polymers (RB), where no such restrictions apply. The statistical properties of SAW and EVB on several kinds of fractal lattices have been extensively discussed in recent years2–7. The motivation for analysing the statistical features of polymers on fractals comes from the wish to understand the controversial (and much studied) problem of establishing the critical behaviour of saw on random media8–10.


Random Walk Configurational Entropy Simple Random Walk Fractal Lattice Sierpinski Gasket 
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  1. 1.
    P. G. de Gennes, in Scaling Concepts in Polymer Physics (Cornell University, Ithaca, New York, 1979).Google Scholar
  2. 2.
    R. Rammal, G. Toulouse and J. Vannimenus, J. Phys. (Paris) 45, 389 (1984).CrossRefGoogle Scholar
  3. 3.
    A. Aharony and A. B. Harris, J. Stat. Phys. 54, 1091 (1989).CrossRefGoogle Scholar
  4. 4.
    M. Knezevic and J. Vannimenus, Phys. Rev. B 35, 4988 (1987).CrossRefGoogle Scholar
  5. 5.
    A. K. Roy and A. Blumen, J. Stat. Phys. 59, 1581 (1990).CrossRefGoogle Scholar
  6. 6.
    A. K. Roy and A. Blumen, J. Chem. Phys., submitted (1990).Google Scholar
  7. 7.
    A. K. Roy, B. K. Chakrabarti and A. Blumen, J. Stat. Phys., submitted (1990).Google Scholar
  8. 8.
    A. K. Roy and B. K. Chakrabarti, J. Phys. A 20, 215 (1987).CrossRefGoogle Scholar
  9. 9.
    S. B. Lee and H. Nakanishi, Phys. Rev. Lett. 61, 2022 (1988).CrossRefGoogle Scholar
  10. 10.
    Y. Meir and A. B. Harris, Phys. Rev. Lett. 63, 2819 (1989).CrossRefGoogle Scholar
  11. 11.
    J. Isaacson and T. C. Lubensky, J. Phys. (Paris) 41, L 469 (1980).Google Scholar
  12. 12.
    D. Lhuillier, J. Phys. (Paris) 49, 705 (1988).CrossRefGoogle Scholar
  13. 13.
    D. Stauffer, in Introduction to Percolation Theory, (Taylor and Francis, London, 1985).CrossRefGoogle Scholar
  14. 14.
    H. E. Stanley, in On Growth and Form, H. E. Stanley and N. Ostrowsky, eds. (NATO ASI Series E, No. 100, 1986).Google Scholar
  15. 15.
    T. Vilgis, J. Phys. (Paris) 49, 1481 (1988).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Apurba Kumar Roy
    • 1
  • Alexander Blumen
    • 2
  1. 1.Santipur CollegeNadiaIndia
  2. 2.Physikalisches Institut and BIMFUniversity of BayreuthBayreuthFederal Republic of Germany

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