Advertisement

The European Physical Journal E

, Volume 19, Issue 4, pp 413–422 | Cite as

The role of the amorphous fraction for the equilibrium shape of polymer single crystals

  • J. -U. SommerEmail author
Regular Article

Abstract.

The equilibrium state of polymer single crystals is considered by explicitly taking into account the amorphous fraction formed by loops and tails of the chains using a statistical model introduced by Muthukumar (Philos. Trans. R. Soc. London, Ser. A 361, 539 (2003)). We show that under realistic conditions below the equilibrium melting temperature, tight loops and close re-entries are favored, and that the amorphous fraction can be mapped into an excess surface free energy. The model is extended to many-chain crystals where it is shown that the lamellar thickness increases with the number of chains in the crystal and extended-chain conformations are thermodynamically favored if the number of chains in the crystal is sufficiently large. The number of chains necessary to form an extended-chain crystal in thermodynamic equilibrium scales with the square of the degree of polymerization of the chains. We discuss the temperature behavior of the equilibrium crystal thickness in the under-cooled state.

PACS.

05.70.Np Interface and surface thermodynamics 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling 82.60.Qr Thermodynamics of nanoparticles 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Keller, Philos. Mag. 2, 1171 (1957).Google Scholar
  2. 2.
    E.W. Fischer, Z. Naturforsch. A 12, 753 (1957).Google Scholar
  3. 3.
    P.H. Till, J. Polym. Sci. 24, 301 (1957).CrossRefGoogle Scholar
  4. 4.
    J.D. Hoffmann, G.T. Davis, J.I. Lauritzen, The Rate of Crystallization of Linear Polymers with Chain Folding, Vol. 3 (Plenum Press, 1976) pp. 497--614, treatise in solid state chemistry ed.Google Scholar
  5. 5.
    D.M. Sadler, Nature 326, 174 (1987).CrossRefADSGoogle Scholar
  6. 6.
    M. Hikosaka, K. Amano, S. Rastogi, A. Keller, Macromolecules 30, 2067 (1997).CrossRefGoogle Scholar
  7. 7.
    M. Al-Hussein, G. Strobl, Macromolecules 35, 1672 (2002).CrossRefGoogle Scholar
  8. 8.
    G. Reiter, G. Castelein, J.-U. Sommer, Phys. Rev. Lett. 86, 1918 (2001).CrossRefGoogle Scholar
  9. 9.
    J.-U. Sommer, G. Reiter, Europhys. Lett. 56, 755 (2001).CrossRefGoogle Scholar
  10. 10.
    G. Ungar, J. Stejny, A. Keller, M.C. Whiting, Science 229, 386 (1985).ADSGoogle Scholar
  11. 11.
    S. Rastogi, M. Hikosaka, H. Kawabata, A. Keller, Macromolecules 24, 6384 (1991).CrossRefGoogle Scholar
  12. 12.
    G. Strobl, The Physics of Polymers, 2nd edition (Springer, Berlin, Heidelberg, New York, 1997).Google Scholar
  13. 13.
    H. Zachmann, Kolloid Z. Z. Polym. 216-217, 180 (1967).Google Scholar
  14. 14.
    E.W. Fischer, Kolloid Z. Z. Polym. 218, 97 (1967).CrossRefGoogle Scholar
  15. 15.
    W. Hu, T. Albrecht, G. Strobl, Macromolecules 32, 7548 (1999).CrossRefGoogle Scholar
  16. 16.
    M. Muthukumar, Philos. Trans. R. Soc. London, Ser. A 361, 539 (2003).Google Scholar
  17. 17.
    L. Larini, A. Barbieri, P.A. Rolla, D. Leporini, J. Phys.: Condens. Matter 17, L199 (2005).Google Scholar
  18. 18.
    P. Welch, M. Muthukumar, Phys. Rev. Lett. 87, 218302 (2001).CrossRefADSGoogle Scholar
  19. 19.
    G. Wulff, Z. Kristallogr. Mineral. 34, 449 (1901).Google Scholar
  20. 20.
    L. Mandelkern, Crystallization of Polymers: Equilibrium Concepts (Cambridge University Press, Cambridge, UK, 2002).Google Scholar
  21. 21.
    V. Baulin, A. Johner, C. Marques, Macromolecules 38, 1434 (2005).CrossRefGoogle Scholar
  22. 22.
    D.S.M. de Silva, X.B. Zeng, G. Ungar, S.J. Spells, Macromolecules 35, 7730 (2002).CrossRefGoogle Scholar
  23. 23.
    D.S.M. de Silva, X.B. Zeng, G. Ungar, S.J. Spells, J. Macromol. Sci. B 42, 915 (2003).CrossRefGoogle Scholar
  24. 24.
    H. Čackovič, R. Hosemann, W. Wilke, Kolloid. Z. Z. Polym. 234, 1000 (1969).CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2006

Authors and Affiliations

  1. 1.Institut de Chimie des Surfaces et Interfaces (CNRS)Mulhouse CedexFrance

Personalised recommendations