The Physics of Temporary Polymer Networks: A Comparison of Theory and Experiment

  • E. Kröner
  • D. Chassapis
  • R. Takserman-Krozer

Abstract

Compared with permanent networks, the temporary polymer networks in solution show additional mobility in the form of viscoelasticity. This mobility results from the kinetic processes of decay and formation of junctions. The molecular-statistical theory of Takserman-Krozer and Kröner gives the viscoelastic material functions (of the velocity gradient tensor) within a generalized spring—bead model where the springs represent the network chains and the beads represent the junctions which are not conserved. The (integro-differential) diffusion equation contains the transition probabilities for junction decay and formation. The equations for these are solved in the one-junction approximation, simultaneously with the diffusion equation in the relaxation time approach. The material functions thus obtained are compared with various experiments, above all those on stationary shear flow. Adaptation of the theoretical to the experimental curves occurs only in the Newtonian range so that the non-Newtonian part of the theoretical curves represents a true prediction. Further results concern the mean number of chains per macromole cule (up to 10) and the number of decays per second of a junction (e.g. 10-2/s for the fluid at rest and 65 at a velocity gradient of 103/s).

Keywords

Diffusion Equation Velocity Gradient Contour Length Material Function Velocity Gradient Tensor 
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.
    Ziabicki, A., Molecular mechanism of non-linear rubber elasticity, in Trends in Applications of Pure Mathematics to Mechanics, Lecture Notes in Physics 249, Kröner, E. and Kirchgässner, K. (Eds), Springer-Verlag, Heidelberg, 1986, pp. 384–408.CrossRefGoogle Scholar
  2. 2.
    Rouse, R. E., A theory of the linear viscoelastic properties of dilute solutions of coiling polymers, J. Chem. Phys., 1953, 21, 1272–80.CrossRefGoogle Scholar
  3. 3.
    Zimm, B. H., Dynamics of polymer molecules in dilute solution: Viscoelasticity, flow birefringence and dielectric loss, J. Chem. Phys., 1956, 24, 269–78.CrossRefGoogle Scholar
  4. 4.
    Yamakawa, H., Modern Theory of Polymer Solutions, Harper and Row, New York, 1971.Google Scholar
  5. 5.
    Volkenstein, M. W., Configuration Statistics of Polymer Chains, Interscience, New York, 1963.Google Scholar
  6. 6.
    Flory, P. J., Statistical Mechanics of Chain Molecules, Interscience, New York, 1969.Google Scholar
  7. 7.
    Takserman-Krozer, R., Krozer, S. and Kröner, E., On the kinetics of polymer networks with temporary junctions, Colloid & Polymer Sci., 1979, 257, 1033–41.CrossRefGoogle Scholar
  8. 8.
    Takserman-Krozer, R. and Kröner, E., Statistical mechanics of temporary polymer networks I. The equilibrium theory, Rheol. Acta, 1984, 23, 1–9.CrossRefGoogle Scholar
  9. 9.
    Kröner, E. and Takserman-Krozer, R., Statistical mechanics of temporary polymer networks II. The non-equilibrium theory, Rheol. Acta, 1984, 23, 139–50.CrossRefGoogle Scholar
  10. 10.
    Chassapis, D., Zur molekular-statistischen Theorie temporärer Polymernetzwerke—Theoretische Untersuchungen und Vergleich mit Experimenten, Dissertation, Fakultät für Physik, Universität Stuttgart, 1986.Google Scholar
  11. 11.
    Flory, P. J., Thermodynamics of high polymer solutions, J. Chem. Phys., 1942, 10, 51–61.CrossRefGoogle Scholar
  12. 12.
    Flory, P. J., Statistical mechanics of swelling of network structures, J. Chem. Phys., 1950, 18, 108–11.CrossRefGoogle Scholar
  13. 13.
    Flory, P. J., Statistical mechanics of semiflexible chain molecules, Proc. Roy. Soc, 1956, A234, 60–73.Google Scholar
  14. 14.
    Flory, P. J., Hoeve, C. A. J. and Ciferri, A., Influence of bond angle restrictions on polymer elasticity, J. Polymer Sci., 1959, 34, 337–47.CrossRefGoogle Scholar
  15. 15.
    Kröner, E. and Takserman-Krozer, R., Molecular descriptions of temporary polymer networks, in Continuum Models of Discrete Systems 4, Brulin, O. and Hsieh, R. K. T. (Eds), North Holland, Amsterdam, 1981, pp. 297–310.Google Scholar
  16. 16.
    Krozer, S. and Gruber, E., Zur Temperaturabhängigkeit der viskoelastischen Eigenschaften konzentrierter Polystyrol-Lösungen in Dekalin, Rheol. Acta, 1979, 18, 86.CrossRefGoogle Scholar
  17. 17.
    Klein, J. and Kulickem, W.-M., Rheologische Untersuchungen zur Struktur hochmolekularer Polyacrylamide in wäßrigen und nichtwäßrigen Lösungen, Rheol. Acta, 1976, 15, 558–76.CrossRefGoogle Scholar
  18. 18.
    Krozer, S., Tawadjoh, M. and Gruber, E., Zur Beschreibung der rheologischen Eigenschaften konzentrierter Polystyrol-Lösungen, Rheol. Acta, 1977, 16, 438–43.CrossRefGoogle Scholar

Copyright information

© Elsevier Applied Science Publishers Ltd 1988

Authors and Affiliations

  • E. Kröner
    • 1
  • D. Chassapis
    • 1
  • R. Takserman-Krozer
    • 1
    • 2
  1. 1.Institut für Theoretische und Angewandte Physik der Universität StuttgartStuttgart 80Germany
  2. 2.Max-Planck-Institut für MetallforschungStuttgart 80Germany

Personalised recommendations