Chaotic Motion of Molecular Chains

  • P. Reineker
  • R. G. Winkler
  • G. Siegert
  • G. Glatting
Part of the NATO ASI Series book series (NSSB, volume 258)


Elastic properties of metals and elastomers are rather different. In metals the maximum elastic deformation is about 0.2%, whereas in elastomers values up to 1500% are possible. While in metals in this range Hook’s law holds, this is in general not true for elastomers. The comparison of the elastic moduli shows that it is of the order of 105MPa in metals and IMPa in elastomers, it decreases with increasing temperature in metals but in contrast in elastomers an increase is observed. Metals under given strain elongate with increasing temperature whereas elastomers shorten. Beyond the limit of the elastic deformation, metals deform in a plastic manner while elastomers generally are destroyed. Finally, adiabatic extension of metals causes cooling but in elastomers the temperature raises. The basic reason for this different behaviour of metals and elastomers is the fact that in the first class of materials the elastic extension increases the internal energy whereas in the second group of materials it results in a decrease of entropy. This completely different behaviour originates from the difference in microscopic structure: the structural units in metals are atoms, while elastomers are composed of polymers, i.e. long molecular chains.


Angular Momentum Mass Point Molecular Chain Stochastic Dynamic HAMILTONIAN Dynamic 
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.


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  1. [1]
    W. Kuhn, Kolloid-Z. 68:2 (1934)CrossRefGoogle Scholar
  2. [2]
    W. Kuhn, F. Grim, Kolloid-Z. 101:248 (1942)CrossRefGoogle Scholar
  3. [3]
    L. E. G. Treloar, Trans. Faraday Soc. 42:77 (1949)CrossRefGoogle Scholar
  4. [4]
    K. H. Meyer, G. von Susich, E. Valko, Kolloid-Z. 59:208 (1932)CrossRefGoogle Scholar
  5. [5]
    F. H. Miiller, Kolloid-Z. 95:139 (1941)Google Scholar
  6. [6]
    J. H. Werner, Macromolecules 15:542 (1982)CrossRefGoogle Scholar
  7. [7]
    M. V. Volkenstein, “Configurational Statistics of Polymeric Chains”, John Wiley & Sons, New York (1963)Google Scholar
  8. [8]
    P. J. Flory, “Statistical Mechanics of Polymeric Chains”, John Wiley & Sons, New York (1969)Google Scholar
  9. [9]
    L. R. G. Treloar, “The Physics of Rubber Elasticity”, Clarendon Press, Oxford (1975)Google Scholar
  10. [10]
    P.-G. de Gennes, “Scaling Concepts in Polymer Physics”, Cornell University Press, Ithaca (1979)Google Scholar
  11. [11]
    J. II. Weiner, “Statistical Mechanics of Elasticity”, John Wiley k Sons, New York (1983)Google Scholar
  12. [12]
    M. Doi, S. F. Edwards, “The Theory of Polymer Dynamics”, Clarendon Press, Oxford (1986)Google Scholar
  13. [13]
    J. des Cloizeaux, G. Jannink, “Les Polymeres en Solution: leur Modelisation et leur Structure”, Les Edition de Physique, Les Ulis (1987)Google Scholar
  14. [14]
    K. F. Freed, “Renormalization Group Theory of Macromolecules”, John Wiley & Sons, New York (1987)Google Scholar
  15. [15]
    K. F. Freed, Adv. Chem. Phys. 22:1 (1972)CrossRefGoogle Scholar
  16. [16]
    W. Kuhn, KoHoid-Z. 76:258 (1936)CrossRefGoogle Scholar
  17. [17]
    H. M. James, E. Guth, J. Chem. Phys. 11:455 (1943)CrossRefGoogle Scholar
  18. [18]
    R. T. Deam, S. F. Edwards, Phil. Trans. Roy. Soc. Lond. A280:317 (1976)Google Scholar
  19. [19]
    M. Mooney, J. Appl. Phys. 11:582 (1940)CrossRefGoogle Scholar
  20. [20]
    R. S. Rivlin, Trans. Roy. Soc. (London) A241:379 (1948)CrossRefGoogle Scholar
  21. [21]
    M. Doi, S. F. Edwards, J. Chem. Soc. Faraday Trans. II 74:1802 (1978)CrossRefGoogle Scholar
  22. [22]
    G. Marrucci, Rheol. Acta 18:193 (1979)CrossRefGoogle Scholar
  23. [23]
    W. W. Graessley, Adv. Polym. Sci., 46:67 (1982)CrossRefGoogle Scholar
  24. [24]
    M. Gottlieb, R. J. Gaylord, Polymer, 24:1644 (1983)CrossRefGoogle Scholar
  25. [25]
    R. C. Ball, M. Doi, S. F. Edwards, M. Warner Polymer 22:1009 (1981)Google Scholar
  26. [26]
    S. F. Edwards, Th. Vilgis, Polymer 26:101 (1986)Google Scholar
  27. [27]
    P. J. Flory, B. Erman, Macromolecules 15:800 (1982)CrossRefGoogle Scholar
  28. [28]
    H. G. Kilian Polymer 22:208 (1981)CrossRefGoogle Scholar
  29. [29]
    R. G. Winkler, “Untersuchungen zum statistischen und molekulardynamischen Verhalten von Polymerketten”, Ph.D. Thesis, University of Ulm (1989)Google Scholar
  30. [30]
    G. Siegert, “Deterministisches Chaos in der Dynamik von Molekiilketten” Diplom Thesis, University of Ulm (1989)Google Scholar
  31. [31]
    R. G. Winkler, P. Reineker, M. Schreiber, Europhys. Lett 8:493 (1989)CrossRefGoogle Scholar
  32. [32]
    R. G. Winkler, P. Reineker, M. Schreiber, Entropy Elastic Forces of Chain Molecules, in: “Molecular Basis of Polymer Networks”, A. Baumgartner, C. E. Picot, eds., Springer, Berlin, Heidelberg (1989)Google Scholar
  33. [33]
    P. Reineker, R. G. Winkler, Phys. Lett. A141:264 (1989)Google Scholar
  34. [34]
    R. G. Winkler, P. Reineker, Makromol. Chem., Makromol. Symp., 30:215 (1989)CrossRefGoogle Scholar
  35. [35]
    P. Reineker, R. G. Winkler, Progr. Colloid & Polymer Sci. 80:101 (1989)CrossRefGoogle Scholar
  36. [36]
    C. D. Conte, D. de Boor, “Elementary Numerical Analysis”, Mc Graw Hill, Kogakusha, Ltd. Tokyo (1972)Google Scholar
  37. [37]
    L. Verlet, Phys. Rev. 159:98 (1967)CrossRefGoogle Scholar
  38. [38]
    A. J. Lichtenberg, M. A. Liebermann, “Regular and Stochastic Motion”, Springer, New York (1983)Google Scholar
  39. [39]
    M. Henon, Numerical exploration of Hamiltonian Systems, in: “Chaotic Behaviour of Deterministic Systems,” G. Iooss, R.H.G. Helleman, R. Stora, eds., North-Holland Publishing Company, Amsterdam (1983)Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • P. Reineker
    • 1
  • R. G. Winkler
    • 1
  • G. Siegert
    • 1
  • G. Glatting
    • 1
  1. 1.Abteilung für Theoretische PhysikUniversität UlmUlmGermany

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