Rheologica Acta

, Volume 7, Issue 4, pp 332–335 | Cite as

Evaluation of calculated entanglement spacings for undiluted linear amorphous polymers

  • R. S. Porter
  • J. F. Johnson


In reality, entanglements based on rheological measurements have been essentially defined operationally as a kinetic or time delay effect present in concentrated polymer systems. This is where intuitively molecular loops or overlap and entanglements of polymer chains are most likely to occur. The evaluation in fig. 2 suggests that the theory of rubber elasticity, even discounting the inherent imprecision of measurements, gives anM e which is not relatable to polymer composition 1and chain structure. Conversely reliable and internally consistent values ofM c can come from the molecular weight dependence of: 1.Newtonian viscosities, 2.NMR relaxation times, and 3 the shear dependence of viscosities, see fig. 1. However, entanglement spacings calculated in this way lack adequate theoretical substantiation particularly as to the mechanism of flow. Nonetheless, the correlation ofM c with composition and structure is convincing and provides a sound empirical correlation and the basis for a renaissance in theoretical interpretation of viscoelastic behavior of linear amorphous polymers. Further theory must rationalize the fact that the shear compliance, which is proportional toM e , depends on a combination of molecular weight averages involvingZ andZ+1. Yet the break in viscosity-molecular weight curves yieldingM c has been generally confirmed to depend on only weight average molecular weight. The values ofM c appear worthy of further experimental and theoretical evaluation. The values ofM e appear to be based on experimental techniques that at present do not provide sufficient precision to warrant citation of such values molekular weight distribution is thought to have an important yet ill-defined influence on calculated values of M e .


Entanglement Spacing Weight Average Molecular Weight Rubber Elasticity Sufficient Precision Newtonian Viscosity 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    Porter, R. S. andJ. F. Johnson, Chem. Rev.66, 1 (1966).CrossRefGoogle Scholar
  2. 2).
    Markovitz, H., T. G. Fox, andJ. D. Ferry, J. Phys. Chem.66, 1567 (1962).Google Scholar
  3. 3).
    Mark, H. andA. V. Tobolsky, Physical Chemistry of High Polymeric Systems (New York 1950).Google Scholar
  4. 4).
    Fox, T. G., J. Polymer Sci.9 C, 35 (1965).Google Scholar
  5. 5).
    Bueche, F., Physical Properties of Polymers (New York 1962).Google Scholar
  6. 6).
    Collins, E. A. andW. Bauer, Trans. Soc. Rheology9:1, 1 (1965).CrossRefGoogle Scholar
  7. 7).
    Schreiber, H. P., Polymer4, 365 (1963).CrossRefGoogle Scholar

Copyright information

© Dr. Dietrich Steinkopff Verlag 1968

Authors and Affiliations

  • R. S. Porter
    • 1
  • J. F. Johnson
    • 2
  1. 1.University of Massachusetts
  2. 2.Department of ChemistryUniversity of ConnecticutStorrsUSA

Personalised recommendations