Advertisement

Branched Polymers and Gels

  • M. Daoud
Conference paper
Part of the Centre de Physique des Houches book series (LHWINTER, volume 10)

Abstract

Polymers are giant molecules that are made of millions of atoms. They are the repetition of an elementary unit called monomer. They are used as plastics, paints, adhesives, rubbers, and in some future, as batteries. They have changed completely our everyday life by superseding natural materials such as wood, iron, etc. Our understanding of the structure of synthetic polymers has increased tremendously these last 20 years. They may be either linear or branched. In the former case, one makes react divalent monomers, that may interact only by two functional units, leading to a linear structure. In the latter case, multifunctional units react, leading to a structure that is randomly branched. A very interesting aspect of this type of reaction is that as time proceeds, one eventually goes from a viscous fluid called a sol to an elastic solid called a gel. The sol-gel transition was considered first in the forties in its mean field version by Flory and by Stockmayer and Zimm. It was improved recently by noting that it is directly related to the percolation transition in Physics (de Gennes, 1976; Stauffer, 1976). More recently, the fractal aspects of these branched polymers and gels were considered both theoretically and experimentally. Although the ideas developed for these synthetic polymers are probably too simplistic for direct use in biological problems, we believe that some of them might survive even when complications such as rigidity, presence of electrical charges, and eventually others are taken into account. In what follows, we will discuss the simplest possible case of sol-gel transition.

Keywords

Fractal Dimension Scattered Intensity Single Polymer Percolation Transition Fractal Aspect 
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. Bouchaud E., Delsanti M., Adam M., Daoud M. and Durand D., J. Phys. Lett. 47 (1986) 1273.Google Scholar
  2. Cates M.E., J. Phys. Lett. 38 (1985) 2957.MathSciNetGoogle Scholar
  3. Daoud M., Family F. and Jannink G., J. Phys. Lett. 45 (1984) 119.CrossRefGoogle Scholar
  4. Daoud M. and Leibler L., Macromol. 41 (1988) 1497.ADSCrossRefGoogle Scholar
  5. Daoud M., J. Phys. A 21 (1988) L973.ADSCrossRefGoogle Scholar
  6. Durand D, Delsanti M., Adam M. and Luck J.M., Europhys. Lett. 3 (1987) 297.ADSCrossRefGoogle Scholar
  7. Devreux F., Boilot J.P., Chaput F., Malier L. and Axelos M.A.V., Phys. Rev. A 47 (1993) 2689.ADSGoogle Scholar
  8. Efros A.L. and Schklovskii B.I., Phys. Status Solidi B76 (1976) 475.ADSCrossRefGoogle Scholar
  9. Flory P.J., Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953).Google Scholar
  10. Gennes, P.G. de, J. Phys. 37 (1976) 1445.CrossRefGoogle Scholar
  11. Gennes, P.G. de, Scaling Concepts in Polymer Physics (Cornell Univ. Press, Ithaca, 1979).Google Scholar
  12. Gordon M. and Ross-Murphy S.B., Pure Appl. Chem. 43 (1975) 1.CrossRefGoogle Scholar
  13. Isaacson J. and Lubensky T.C., J. Phys. 42 (1981) 175.MathSciNetCrossRefGoogle Scholar
  14. Mandelbrot B.B., The Fractal Geometry of Nature (Freeman, San Francisco, 1977).Google Scholar
  15. Martin J.E. and Ackerson B.J., Phys. Rev. A 31 (1985) 1180.ADSCrossRefGoogle Scholar
  16. Martin J.E., In Time dependent effects in disordered systems, edited by R. Pynn and T. Riste, N.A. T. O. A.S.I. B 167 (Plenum Press, 1987) p. 425.CrossRefGoogle Scholar
  17. Munch J.P., Delsanti M. and Durand D., Europhys. Lett. 18 (1992) 557.ADSCrossRefGoogle Scholar
  18. Patton E.V., Wesson J.A., Rubinstein M., Wilson J.C. and Oppenheimer L.E., Macromol. 22 (1989) 1946.ADSCrossRefGoogle Scholar
  19. Stauffer D., J. Chem. Soc. Trans. II 72 (1976) 1354.CrossRefGoogle Scholar
  20. Stauffer D., Phys. Rep. 54 (1979) 1; Introduction to Percolation Theory (Taylor and Francis, London, 1985).ADSCrossRefGoogle Scholar
  21. Zimm B.H. and Stockmayer W.H., J. Chem. Phys. 17 (1949) 1301.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag France 1998

Authors and Affiliations

  • M. Daoud
    • 1
  1. 1.Laboratoire Léon BrillouinCE SaclayGif-sur-YvetteFrance

Personalised recommendations