Entanglement and reversible gelation for polymers of different architectures

  • W. Burchard
Conference paper
Part of the Progress in Colloid & Polymer Science book series (PROGCOLLOID, volume 78)


Entanglement has been studied in the past mainly with flexible linear chains. Early predictions were based upon scaling theory which gave only data on exponents of power laws but no prefactors. Tests were strongly inhibited by ambiguities in the definition of the overlap concentration c*. The present study uses the thermodynamically well-defined scaling parameter X = A 2 M wc. Recent renormalization group theories succeeded in the derivation of an analytic expression for the osmotic modulus in terms of X. The osmotic modulus was measured by static light scattering at the scattering angle zero. Experimental data from polystyrene chains of different molecular weights and from many other linear polymers demonstrate a good agreement with theory up to values of X = 3–5. Beyond that point the osmotic modulus increases stronger than predicted. The final exponent is 1.40 ± 0.03 instead of the predicted. 1.25. Good agreement with the theoretical prediction by Carnahan and Starling is also found for impenetrable particles (spheres). As a third architecture the experimental curve for stiff chain molecules is shown for which no theory is available to date. The results can, however, be interpreted qualitatively in a consistent manner.

Many polymers show at moderately high concentrations pronounced deviations from the pure entanglement behavior. Three effects are observed: 1) a strong low-angle excess scattering is found; 2) the osmotic modulus shows a turnover and decreases again; and 3) a pronounced slow mode of motion becomes apparent. The three effects increase strongly with concentration. Finally, behavior is observed which indicates reversible gelation.

Key words

Polymer solution entanglement gelation light scattering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    De Gennes P-G (1979) Scaling Concepts in Polymer Physics. Cornell University Press, NYGoogle Scholar
  2. 2.
    Ohta T, Oono Y (1982) Physics Letters 89:460CrossRefGoogle Scholar
  3. 3.
    Freed KF (1983) J Chem Phys 79:6357CrossRefGoogle Scholar
  4. 4.
    Cherayil SJ, Bawendi MG, Miyake A, Freed KF (1980) Macromolecules 20:2770Google Scholar
  5. 5.
    Wiltzius P, Haller HR, Cannell DS, Schaefer DW (1983) PHys Rev Letters 51:1183CrossRefGoogle Scholar
  6. 6.
    Coviello T, Burchard W, Dentini M, Crescenzi V (1987) Macromolecules 20, in pressGoogle Scholar
  7. 7.
    Debye P (1947) J Colloid Phys Chem 51:18CrossRefGoogle Scholar
  8. 8.
    McQuarrie DA (1973) Statistical Mechanics. Harper & Row, New YorkGoogle Scholar
  9. 9.
    Carpenter DK (1970) Enzyclopedia of Polymer Science and Technology. Wiley New York, 12:626Google Scholar
  10. 10.
    Carnahan NF, Starling KE (1969) J Chem Phys 51:635CrossRefGoogle Scholar
  11. 11.
    des Cloizeaux J (1982) J Phys 36:281Google Scholar
  12. 12.
    Daoud M, Cotton JP (1982) J Phys 43:531Google Scholar
  13. 13.
    Miyake A, Freed KF (1983) Macromolecules 16:1228CrossRefGoogle Scholar
  14. 14.
    Oono M, Baldwin PR, Ohta T (1984) Phys Rev Letters 53:2149CrossRefGoogle Scholar
  15. 15.
    Wiltzius P, Haller HR, Cannell DS, Schaefer DW (1984) Phys Rev Letters 53:834CrossRefGoogle Scholar
  16. 16.
    Batchelor GKJ (1976) J Fluid Mech 52:245CrossRefGoogle Scholar
  17. 17.
    Hess W, Klein R (1976) Physica A 85:509CrossRefGoogle Scholar
  18. 18.
    Eisele M, Burchard W, Manuscript in preparationGoogle Scholar
  19. 19.
    Wenzel M, Burchard W, Schätzel K (1986) Polymer 27:195CrossRefGoogle Scholar
  20. 20.
    Stadler R, Burchard W, Manuscript in preparationGoogle Scholar
  21. 21.
    Wachenfeld-Eisele E, Burchard W (1987) Proceedings of the 8th Networks Meeting, Ed O Kramer, Copenhagen, ElsevierGoogle Scholar
  22. 22.
    Lang P (1987) Diploma Thesis FreiburgGoogle Scholar
  23. 23.
    Koberstein JT, Picot C, Benoit H (1985) Polymer 28:673CrossRefGoogle Scholar
  24. 24.
    Gan JYS, Francoise J, Guenet H-M (1986) Macromolecules 19:173CrossRefGoogle Scholar

Copyright information

© Dr. Dietrich Steinkopff Verlag GmbH & Co. KG 1998

Authors and Affiliations

  • W. Burchard
    • 1
  1. 1.Institut für Makromolekulare ChemieUniversität FreiburgFreiburgF.R.G.

Personalised recommendations