Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-21T11:02:08.887Z Has data issue: false hasContentIssue false
  • English
  • Français

A Model for Relaxation in Supercooled Liquids and Polymer Melts

Published online by Cambridge University Press:  10 February 2011

T. Pakula  and
J. Teichmann
T. Pakula
Affiliation:
Max-Planck-Institut für Polymerforschung, Postfach 3148, 55021 Mainz, Germany
J. Teichmann
Affiliation:
Max-Planck-Institut für Polymerforschung, Postfach 3148, 55021 Mainz, Germany
Get access

Abstract

A new model for molecular rearrangements in liquids is proposed. The liquids are regarded as dense ensembles of vibrating molecules satisfying the excluded volume condition. A continuity condition is applied on the molecular scale of such systems and is regarded as controlling rearrangements leading to translations of molecules beyond the range of their vibration amplitude. It results in cooperative rearrangements which are considered as taking place in systems with fluctuating density. Rates of rearrangements are considered as being controlled by thermal activation with activation energy barriers dependent on local density. Various dependencies of the activation energy barriers on local density are examined. It is shown, that the model is able to reproduce the extremal cases of temperature dependencies of relaxation times represented on one edge by the Arrhenius relation and on the other edge by the Vogel-Fulcher-Tamman relation. The model can, however, provide a broad spectrum of other dependencies filling the gap between these extremes. All cases are based on the uniform microscopic picture of cooperative molecular rearrangements resulting from system continuity. The model is implemented as a simulation algorithm (Dynamic Lattice Liquid - DLL algorithm) which is used to simulate dynamic properties of liquids and polymer melts. Simulation results obtained for polymers are compared with experimental results obtained by means of the dynamic mechanical measurements on polyisobutylene samples with various molecular weights.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 455: Symposium T – Glasses and Glass Formers–Current Issues , 1996 , 211
Copyright
Copyright © Materials Research Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Brower, S., Relaxation in Viscous Liquids and Glasses, The Am. Ceramic Soc., Columbus, OH, 1985 Google Scholar
2. Götze, W. in Liquids, Freezing and Glass Transition, eds. Hansen, J. P., Levesque, D. and Zinn-Justin, J., North-Holland, Amsterdam 1991 Google Scholar
3. Donth, E., Relaxation and Thermodynamics in Polymers, Akademie Verlag, Berlin 1992 Google Scholar
4. Barker, J. A. and Henderson, D., Rev. Mod. Phys. 48, 587(1976)Google Scholar
5. Alder, B.J. and Wainwright, T.E., J. Chem. Phys. 31, 459(1969)Google Scholar
6. Widom, A., Phys. Rev. A 3, 1394(1971)Google Scholar
7. Kubo, R., Rept. Progr. Phys. 29, 255(1966)Google Scholar
8. London, R. E., J. Chem. Phys. 66, 471(1977)Google Scholar
9. Götze, W. and Sjögren, L., Rep. Prog. Phys. 55, 241(1992)Google Scholar
10. Cohen, M.H. and Grest, G.S., Phys. Rev. B, 20, 1077(1979)Google Scholar
11. Adam, G. and Gibbs, J.H., J. Chem. Phys. 43, 139(1965)Google Scholar
12. Flory, P. J., “Principles of Polymer Chemistry”, Cornell Univ. Press, Ithaca 1953 Google Scholar
13. Edwards, S.F. and Vilgis, T., in Physics of Disordered Materials, Eds.: Adler, D., Frizsche, H. and Ovshinsky, S.R., Plenum, London 1985 Google Scholar
14. Pakula, T., Macromolecules 20, 679(1987)Google Scholar
15. Glasstone, S., Laider, K.J. and Eyring, H., The Theory of Rate Processes, NcGraw-Hill, New York, 1941 Google Scholar
16. Vogel, H., Phys. Z. 22. 645(1921);Google Scholar
Fulcher, G.S., J. Am. Ceram. Soc. 8, 339(1953)Google Scholar
17. Wiliams, M.L., Landel, R.F. and Ferry, J.D., J. Am. Ceram. Soc. 8. 339(1953)Google Scholar
18. Bässler, H., Phys. Rev. Lett. 58, 767(1987)Google Scholar
19. Souletie, J. and Bertrand, D., J. Phys. France 51. 1627(1991)Google Scholar
20. Angel, C.A., Alba, C., Arzimanoglou, A., Böhmer, R., Fau, J., Lu, Q., Sanchez, E., Senapati, H. and Tatsumisaga, M., in Slow Dynamics in Condensed Matter, ed. Kawasaki, K., Tokuyama, M. and Kawakatsu, T., AIP New York 1992 Google Scholar
21. Macedo, P.B. and Litovitz, T.A., J. Chem. Phys. 42, 245(1965)Google Scholar
22. Koppelmann, J., in Proceedings of the international Congress on Rheology, 4th, ed. Lee, E.H. and Copley, A.L., Willey, New York 1965.Google Scholar
23. Hughes, B.D., Random Walks and Random Environments, Clarendon Press, Oxford, 1995 Google Scholar
24. Chow, T.S., Macromol. Theory Simul. 4, 397(1995)Google Scholar
25. Stickel, F., Fischer, E.W. and Richert, R., J. Chem. Phys. 102, 6251(1995)Google Scholar
26. Teichmann, J., PhD Thesis, Universität Mainz, 1996 Google Scholar
27. Pakula, T. and Teichmann, J. - in preparationGoogle Scholar
28. Fox, T.G. and Flory, P.J., J. Appl. Phys. 21, 581(1980)Google Scholar