Colloid and Polymer Science

, Volume 269, Issue 11, pp 1090–1098 | Cite as

Force-length relation for a short freely jointed chain: mass and volume dependence

  • P. Reineker
  • G. R. Siegert
  • R. G. Winkler
Original Contributions
  • 51 Downloads

Abstract

We evaluate the force-length relation for short model chains. It is shown that this relation is markedly different when evaluated for static and dynamic model chains with rigid segments. The relation also differs for chains with rigid segments when they are isolated and coupled to a canonical heatbath, respectively. Furthermore, it is derived that the variation of the masses along the chain only has a small influence on the force-length relation. On the other hand, restricting the motion of the chain by walls perpendicular to the chain extension has a pronounced effect. We especially find that in this situation the chain has a finite equilibrium length.

Key words

Elastomer force-lengthrelation masseffect finitevolumeeffect dynamictreatment 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kuhn W (1934) Kolloid Z 68:2Google Scholar
  2. 2.
    Volkenstein MV (1963) Configurational statistics of polymeric chains. John Wiley Sons, New YorkGoogle Scholar
  3. 3.
    Flory PJ (1969) Statistical mechanics of chain molecules. John Wiley Sons, New YorkGoogle Scholar
  4. 4.
    Treloar LRG (1975) The physics of rubber elasticity, 3rd ed. Clarendon Press, OxfordGoogle Scholar
  5. 5.
    De Gennes P-G (1979) Scaling concepts in polymer physics. Cornell University Press, IthacaGoogle Scholar
  6. 6.
    Weiner JH (1983) Statistical mechanics of elasticity. John Wiley Sons, New YorkGoogle Scholar
  7. 7.
    Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon Press, OxfordGoogle Scholar
  8. 8.
    Des Cloizeaux J, Jannink G (1987) Les polymères en solution: leur modélisation et leur structure. Les Edition de Physique, Les UlisGoogle Scholar
  9. 9.
    Ryckaert JP (1985) Mol Phys 54:587Google Scholar
  10. 10.
    Winkler RG, Reineker P (1989) Makromol Chem Macromol Symp 30:215Google Scholar
  11. 11.
    Winkler RG, Reineker P, Schreiber M (1989) In: Baumgärtner A, Picot CE (eds) Molecular basis of polymer networks. Springer, Berlin, HeidelbergGoogle Scholar
  12. 12.
    Winkler RG, Reineker P, Schreiber M (1989) Europhys Lett 8:493Google Scholar
  13. 13.
    Reineker P, Winkler RG (1989) Phys Lett A 141:264Google Scholar
  14. 14.
    Reineker P, Winkler RG (1989) Progr Colloid Polym Sci 80:101Google Scholar
  15. 15.
    Winkler RG, Reineker P (1990) In: Hernandez ES (ed) Nonequilibrium statistical mechanics. World Scientific, Singapore, New Jersey, London, Hong KongGoogle Scholar
  16. 16.
    Reineker P, Winkler RG, Siegert G, Glatting G (1991) In: Gans W, Blumen A, Amann A (eds) Large scale molecular systems: quantum and stochastic aspects. Plenum, New YorkGoogle Scholar
  17. 17.
    Kilian HG (1981) Polymer 22:208Google Scholar
  18. 18.
    Mooney M (1940) J Appl Phys 11:582Google Scholar
  19. 19.
    Rivlin RS (1948) Trans R Soc (Lond) A240:459, 491, 509Google Scholar
  20. 20.
    Perchak D, Weiner JH (1982) Macromolecules 15:545Google Scholar
  21. 21.
    Winkler RG (1989) PhD Thesis, University of UlmGoogle Scholar
  22. 22.
    Siegert G (1989) Diplom Thesis, University of UlmGoogle Scholar
  23. 23.
    Schwarz H (1988) Numerische Mathematik. Teubner, StuttgartGoogle Scholar
  24. 24.
    Verlet L (1987) Phys Rev 159:98Google Scholar
  25. 25.
    Ciccotti G, Ryckaert JP (1986) Comp Phys Rep 4:345Google Scholar
  26. 26.
    Siegert G, Winkler RG, Reineker P (to be published)Google Scholar

Copyright information

© Steinkopff-Verlag 1991

Authors and Affiliations

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

Personalised recommendations