Journal of Statistical Physics

, Volume 89, Issue 5–6, pp 981–995 | Cite as

Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent

  • Sanjay Kumar
  • Yashwant Singh


A model of two interacting (chemically different) linear polymer chains is solved exactly using the real-space renormalization group transformation on a family of Sierpinski gasket type fractals and on a truncated 4-simplex lattice. The members of the family of the Sierpinski gasket-type fractals are characterized by an integer scale factorb which runs from 2 to ∞. The Hausdorff dimensiond F of these fractals tends to 2 from below asb → ∞. We calculate the contact exponenty for the transition from the State of segregation to a State in which the two chains are entangled forb = 2-5. Using arguments based on the finite-size scaling theory, we show that forb→∞, y = 2 - v(b) d F, wherev is the end-toend distance exponent of a chain. For a truncated 4-simplex lattice it is shown that the system of two chains either remains in a State in which these chains are intermingled in such a way that they cannot be told apart, in the sense that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system, or in a State in which they are either zipped or entangled. We show the region of existence of these different phases separated by tricritical lines. The value of the contact exponenty is calculated at the tricritical points.

Key words

Segregation entanglement tricritical line contact exponent finite-size scaling fractals 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Kumar and Y. Singh,J. Phys. A, Math. Gen. 26:L987 (1993).CrossRefADSGoogle Scholar
  2. 2.
    R. Hilfer and A. Bluemen,J. Phys. A, Math. Gen. 17:L537 (1984).CrossRefADSGoogle Scholar
  3. 3.
    Z. Borjan, S. Elezovic, M. Knezevic, and S. Milosevic,J. Phys. A, Math. Gen. 20:L715 (1987); D. Dhar,J. Phys. A, Math. Gen. 21:2261 (1988).CrossRefADSGoogle Scholar
  4. 4.
    S. Elzovic, M. Knezevic, and S. Milosevic,J. Phys. A, Math. Gen. 20:1215 (1987).CrossRefADSGoogle Scholar
  5. 5.
    I. Zivic, S. Milosevic, and H. E. Stanley,Phys. Rev. E 49:636 (1994); S. Milosevic and I. Zivic,J. Phys. A, Math. Gen. 24:L833 (1991).CrossRefADSGoogle Scholar
  6. 6.
    D. Dhar,J. Phys. (Paris) 40:397 (1988).ADSMathSciNetGoogle Scholar
  7. 7.
    S. Kumar and Y. Singh,Phys. Rev. E. 51:579 (1995).CrossRefADSGoogle Scholar
  8. 8.
    S. Kumar, Y. Singh, D. Dhar,J. Phys. A, Math. Gen. 26:4835 (1993).CrossRefADSGoogle Scholar
  9. 9.
    D. Dhar and J. Vannimenus,J. Phys. A, Math. Gen. 20:199 (1987).CrossRefADSGoogle Scholar
  10. 10.
    S. Kumar and Y. Singh,Phys. Rev. E 48:734 (1993); E. Bouchand and J. Vannimenus,J. Phys. (Paris) 50:2931 (1989); E. Orlandine, F. Seno, A. L. Stella, and M. C. Tesi,Phys. Rev. Lett. 68:488 (1992).CrossRefADSGoogle Scholar
  11. 11.
    S. Kumar, Y. Singh, Y. P. Joshi,J. Phys. A, Math. Gen. 23:2987 (1990).CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    B. Duplantier and H. Saleur,Nuclear Physics B290:[FS 20], 291 (1987).ADSMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Sanjay Kumar
  • Yashwant Singh
    • 1
  1. 1.Department of PhysicsBanaras Hindu UniversityVaranasiIndia

Personalised recommendations