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Evolution of rheology during chemical gelation

  • H. H. Winter
Transient Networks
Part of the Progress in Colloid & Polymer Science book series (PROGCOLLOID, volume 75)

Abstract

Rheology is a sensitive measure of the evolving molecular structure in a crosslinking polymer. Dynamic mechanical experiments in small amplitude oscillatory shear give the storage modulus G′(ω, p) and the loss modulus G″(ω, p) as a function of frequency ω. The extent of crosslinking, p(t), changes with reaction time. Dynamic mechanical experiments allow detection of the gel point (GP) and give a macroscopic description of the critical gel state (network polymer at GP). This critical gel state is used as a reference for describing the entire evolution of rheology. The most surprising discovery of these experiments was that critical gels exhibit stress relaxation in a power law, i. e. the relaxation modulus is given as G()=St −n. The relaxation exponent, n, depends on network structure. The power law behavior is an expression of mechanical self similarity (fractal behavior). The range of self similarity is defined between an upper and a lower frequency limit. The lower frequency limit (reciprocal of characteristic relaxation time) corresponds to an upper scaling length, the correlation length, which is of the order of the linear size of the largest molecular cluster (of pre-gel) or of the largest remaining percolation cluster (of post-gel). High frequencies probe relaxation within single chains. The upper frequency limit corresponds to a lower scaling length, the glass length, which is given by the dimension of the molecular network units responsible for glassy behavior. The correlation length and, hence, the characteristic relaxation time increase in the approach of the gel point, diverge to infinity at the gel point, and then decrease again with increasing extent of crosslinking. The critical gel has no characteristic length or time scale. All observations are restricted to polymers at a temperature above the glass transition temperature and at frequencies much below the glass frequency.

Key words

Network polymers gel point polyurethane fractal critical phenomenon 

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References

  1. 1.
    Adam M, Delsanti M Durand D (1985) Macromolecules 18:2285CrossRefGoogle Scholar
  2. 2.
    Apicella A, Masi P, Nicolais L (1984) Rheol Acta 23:291CrossRefGoogle Scholar
  3. 3.
    ASTM D 1638-74Google Scholar
  4. 4.
    Bird RB, Armstrong R, Hassager O (1977) Dynamics of Polymeric Liquids, J Wiley, New YorkGoogle Scholar
  5. 5.
    Bistrup SA (1986) PhD Thesis, University MinnesotaGoogle Scholar
  6. 6.
    Castro JM, Macosko CW, Perry SJ (1984) Polym Com 25:82Google Scholar
  7. 7.
    Clerc CP, Tremblay AMS, Albinet G, Mitescu CD (1984) J Phys Lett 45:L913CrossRefGoogle Scholar
  8. 8.
    Clerc CP, Gireau G, Laugier JM, Luck JM (1985) J Phys A 18:2565CrossRefGoogle Scholar
  9. 9.
    Chambon F, Winter HH (1985) Polym Bull 13:499CrossRefGoogle Scholar
  10. 10.
    Chambon F, Petrovic ZS, MacKnight W, Winter HH (1986) Macromolecules 19:2146CrossRefGoogle Scholar
  11. 11.
    Chambon F, Winter HH (1987) J Rheol 31:683CrossRefGoogle Scholar
  12. 12.
    Chambon F (1986) Ph D Thesis, University MassachusettsGoogle Scholar
  13. 13.
    de Gernes PG (1979) Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, New YorkGoogle Scholar
  14. 14.
    Farris RJ, Lee C (1983) Polym Eng Sci 23:586CrossRefGoogle Scholar
  15. 15.
    Ferry JD (1980) Viscoelastic Properties of Polymers, J Wiley, New YorkGoogle Scholar
  16. 16.
    Fisher A, Gottlieb M (1986) Proc of Networks 86, Elsinore Denmark, Aug 1986Google Scholar
  17. 17.
    Flory PJ (1941) J Am Chem Soc 63:3083, 3091, 3096CrossRefGoogle Scholar
  18. 18.
    Flory PJ (1953) Principles of Polymer Chemistry, Cornell University Press, Ithaca, New YorkGoogle Scholar
  19. 19.
    Gordon M (1962) Proc R Soc, London Ser A 268:240CrossRefGoogle Scholar
  20. 20.
    Harran D, Laudouard A (1986) J Appl Polym SciGoogle Scholar
  21. 21.
    Lipshitz S, Macosko CW (1976) Polym Eng Sci 16:803CrossRefGoogle Scholar
  22. 22.
    Macosko CW, Miller DR (1976) Macromolecules 9:199, 206; (1979) Polym Eng Sci 19:272CrossRefGoogle Scholar
  23. 23.
    Macosko CW, Saam JC (1986) The Hydrosilation Cure of Polyisobutene, to be publishedGoogle Scholar
  24. 24.
    Muthukumar M (1985) J Chem Phys 83:3161CrossRefGoogle Scholar
  25. 25.
    Muthukumar M, Winter HH (1986) Marcromolecules 19:1284CrossRefGoogle Scholar
  26. 26.
    Stanley HE (1985) Introduction of Phase Transition and Critical Phenomena, 2nd Ed, Oxford University Press, New YorkGoogle Scholar
  27. 27.
    Stauffer D, Coniglio A, Adam M (1982) Adv Polym Sci 44:74Google Scholar
  28. 28.
    Stockmayer WH (1943) J Chem Phys 11:45; (1944) 12:125CrossRefGoogle Scholar
  29. 29.
    Winter HH, Chambon F (1986) J Rheol 30:367CrossRefGoogle Scholar
  30. 30.
    Winter HH, Morganelli P, Chambon F (1987) Macromolecules, submittedGoogle Scholar
  31. 31.
    Winter HH (1987) Polym Eng Sci, Dec 1987, in pressGoogle Scholar

Copyright information

© Dr. Dietrich Steinkopff Verlag GmbH & Co. KG 1987

Authors and Affiliations

  • H. H. Winter
    • 1
  1. 1.Max-Planck-Institut für PolymerforschungMainzF.R.G.

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