Dynamics of Dense Polymer Systems Dynamic Monte Carlo Simulation Results and Analytic Theory

  • Jeffrey Skolnick
Part of the NATO ASI Series book series (ASIC, volume 291)

Abstract

Dynamic Monte Carlo simulations of long chains confined to cubic and tetrahedral systems as a function of both volume fraction and chain length were employed to investigate the dynamics of entangled polymer melts. It is shown for a range of chain lengths there is a crossover from a much weaker degree of polymerization (n) dependence of the self-diffusion coefficient to a much stronger one, consistent with D ∼ n −2. Similarly, systems have been identified having a terminal relaxation time that varies as n3.4. Since such scaling with molecular weight signals the onset of highly constrained dynamics, an analysis of the character of chain contour motion was performed. No evidence whatsoever was found for the existence of a well defined tube required by the reptation model. Lateral motions of the chain contour are remarkably large, and the motion appears to be essentially isotropic in the local coordinates. Results from this simulation indicate that the motion of a polymer chain is essentially Rouse-like, albeit, slowed down. Motivated by the simulation results, an analytic theory for the self-diffusion coefficient and the viscoelastic properties have been derived which is in qualitative agreement with both experimental data and the simulations.

Keywords

Dynamic Entanglement Diamond Lattice Friction Constant Entangle Polymer Rouse Model 
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. 1.
    Graessley, W.W. (1982) “Entangled linear, branched, and network polymer systems — molecular theories” Adv. Poly. Sci. 47, 67–117.CrossRefGoogle Scholar
  2. 2.
    Bueche, F. (1962) Physical properties of polymers. John Wiley & Sons, Inc., New York.Google Scholar
  3. 3.
    Yu, H. (1988) “Polymer self-diffusion and tracer diffusion in condensed systems”, in M. Nagasawa (ed), Molecular Conformation and Dynamics of Macromolecules in Condensed Systems. Studies in Polymer Science, Vol. 2. Elsevier, Amsterdam (1988) 107–181.Google Scholar
  4. 4.
    Berry, G.C. and Fox T.B. (1968) “The viscosity of polymers and their concentrated solutions” Adv. Poly. Sci. 5, 261–357.CrossRefGoogle Scholar
  5. 5.
    Rouse, P.E. (1953) “A theory of the linear viscoelastic properties of dilute solutions of coiling polymers” J.Chem. Phys. 21, 1272–1280.Google Scholar
  6. 6.
    Yamakawa, H. (1968) “Modern theory of polymer solutions” Harper and Row, New York.Google Scholar
  7. 7.
    Baumgartner, A. (1984) “Simulation of polymer motion” Ann. Rev. Phys. Chem. 35, 419–435.CrossRefGoogle Scholar
  8. 8.
    De Gennes, P.G. (1971) “Reptation of a polymer chain in the presence of fixed obstacles”, J. Chem. Phys., 55, 572–578.Google Scholar
  9. 9.
    Doi, M. and Edwards, S.F. (1978) “Dynamics of concentrated polymer systems, part I. Brownian motion in the equilibrium state” J. Chem. Soc. Faraday Trans, 74, 1789–1801.CrossRefGoogle Scholar
  10. 10.
    Doi, M. and Edwards, S.F. (1978) “Dynamics of concentrated polymer systems, part II. Molecular motion under flow” J. Chem. Soc. Faraday Trans, 74, 1802–1817.CrossRefGoogle Scholar
  11. 11.
    Doi, M. and Edwards, S.F. (1978) “Dynamics of concentrated polymer systems, part III. The constitutive equation” J. Chem. Soc. Faraday Trans, 74, 1818–1832.CrossRefGoogle Scholar
  12. 12.
    Doi, M. and Edwards, S.F. (1978) “Dynamics of concentrated polymer systems, part IV. Rheological properties” J. Chem. Soc. Faraday Trans, 75, 38–54.Google Scholar
  13. 13.
    Phillies, G.D.J. (1986) “Universal scaling equation for self-diffusion by macromolecules in solution” Macromolecules, 19, 2367–2376.CrossRefGoogle Scholar
  14. 14.
    Fujita, H. and Einaga, Y. (1985) “Self diffusion and visco-elasticity in entangled systems. I. Self diffusion coefficients” Poly. J. (Tokyo) 17, 1131–1139.CrossRefGoogle Scholar
  15. 15.
    Fixman, M. (1985) “Dynamics of semidilute polymer rods: An alternative to cages” Phys Rev. Lett. 55, 2429–2432.CrossRefGoogle Scholar
  16. 16.
    Skolnick, J., Yaris, R. and Kolinski, A. (1988) “Phenomenological theory of the dynamics of polymer melts. I. Analytic treatment of self diffusion” J. Chem. Phys. 88, 1407–1417.CrossRefGoogle Scholar
  17. 17.
    Skolnick, J. and Yaris, R. (1988) “Phenomenological theory of the dynamics of polymer melts. II. Viscoelastic properties” J. Chem. Phys. 88, 1418–1442.CrossRefGoogle Scholar
  18. 18.
    Kolinski, A., Skolnick, J., and Yaris, R. (1987) “Does reptation describe the dynamics of entangled, finite length model systems? A model simulation” J.Chem. Phys. 86, 1567–1585.CrossRefGoogle Scholar
  19. 19.
    Kolinksi, A., Skolnick, J. and Yaris, R. (1987) “Monte Carlo studies on the long time dynamic properties of dense polymer systems. I. The homopolymeric melt” J. Chem.Phys. 86,7164–7173.CrossRefGoogle Scholar
  20. 20.
    Kolinksi, A., Skolnick, J. and Yaris, R. (1986) “On the short time dynamics of dense polymer systems and the origin of the glass transition. A model system” J. Chem. Phys. 84,1922–1931.CrossRefGoogle Scholar
  21. 21.
    Hilhorst, H.J. and Deutch, J.M. (1975) “Analysis of Monte Carlo results on the kinetics of lattice polymer chains with excluded volume”. J. Chem. Phys. 63, 5153–5161.CrossRefGoogle Scholar
  22. 22.
    Boots, H. and Deutch, J.M. (1977) “Analysis of the model dependence of Monte Carlo results for the relaxation of the end to end distance of polymer chains” J . Chem. Phys.., 67, 4608–4610.Google Scholar
  23. 23.
    Valeur, B.,Jarry, J.P., Geny, F. and Monnerie, L. (1975) “Dynamics of macromolecular chains. I. Theory of motions on a tetrahedral lattice” J . Poly. Sci., Poly. Phys. Ed. 13, 667–677.Google Scholar
  24. 24.
    Curler, M.T., Crabb, C.C., Dahlin, D.M. and Kovac, J. (1983) “Effect of bead movement rules on the relaxation of cubic lattice models of polymer chains” Macromolecules 36, 398–403.Google Scholar
  25. 25.
    Bishop, M., Ceperley, D., Frisch, H.L. and Kalos, M.M. (1982) “Investigations of model polymers. Dynamics of melts and statics of a long chain in a dilute melt of shorter chains”. J. Chem. Phys. 76, 1557–1563.CrossRefGoogle Scholar
  26. 26.
    Colby, R.H., Fetters, L.J. and Graessley, W.W. (1987) “Melt viscosity — molecular weight relationship for linear polymers”. Macromolecules 20, 2226–2237.Google Scholar
  27. 27.
    Fixman, M.M. (1988) “Chain entanglements. I. Theory” J. Chem. Phys. 89, 3892–3911.CrossRefGoogle Scholar
  28. 28.
    Evans, K.E. and Edwards, S.F. (1981) “Computer simulations of the dynamics of highly entangled polymers. Part 1. Equilibrium dynamics.” J . Chem. Soc. 2, 1891–1912.Google Scholar
  29. 29.
    Baumgartner, A. and Binder, K. (1981) “Dynamics of entangled polymer melts. A computer simulation” J . Chem. Phys. 75, 2994–3005.CrossRefGoogle Scholar
  30. 30.
    Hess, W. (1986) “Self diffusion and reptation in semi-dilute polymer systems” Macromolecules 19,1395–1403.CrossRefGoogle Scholar
  31. 31.
    Graessley, W.W. (1986) “Some phenomenological consequences of the Doi-Edwards theory of viscoelasticity” J. Poly. Sci., Poly. Phys. ED. 18,27–34.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Jeffrey Skolnick
    • 1
  1. 1.Institute of Macromolecular Chemistry Department of ChemistryWashington UniversitySt. LouisUSA

Personalised recommendations