Internal viscosity was introduced in the model of randomly coiled macromolecule by Kuhn and Kuhn (1) in order to explain the gradient dependence of intrinsic viscosity. In laminar flow with transverse gradient the molecule rotates with an angular velocity equal to half the gradient and during each rotation gets twice extended and twice compressed. Hence the amplitude and the frequency of shape change are increasing almost linearly, the rate of deformation quadratically with the gradient. The resistance of the macro-molecular chain to rapid change of shape reduces the coil deformation below the value expected for a completely flexible elastic dumbbell or necklace model. As a consequence, the increase of end-to-end distance cannot compensate the decrease of viscosity contribution caused by chain orientation so that with increasing gradient the intrinsic viscosity drops below the initial value at zero gradient. The effect is extreme for perfectly rigid molecule and disappears for ideally flexible coil.


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  1. 1).
    Kuhn, W. and H. Kuhn, Helv. Chim. Acta 29, 609, 830 (1946).CrossRefGoogle Scholar
  2. 2).
    Čopič, M., J. Chim. Phys. 54, 348 (1956).Google Scholar
  3. 3).
    Peterlin, A. and M. Čopič, J. Appl. Phys. 27, 434 (1956).ADSCrossRefGoogle Scholar
  4. 4).
    Ikeda, E., Phys. Soc. Japan 12, 378 (1957).ADSCrossRefGoogle Scholar
  5. 5).
    Zimm, B. Z., J. Chem. Phys. 24, 269 (1956).ADSCrossRefMathSciNetGoogle Scholar
  6. 6).
    Peterlin, A., J. Chem. Phys. 33, 1799 (1960).ADSCrossRefGoogle Scholar
  7. 7).
    Fixmann, M., J. Chem. Phys. 5, 793 (1966).ADSCrossRefGoogle Scholar
  8. 8).
    Leray, J., Compt. Rend. Acad. Sci. (Paris) 241, 1741 (1955).Google Scholar
  9. Leray, J., J. Polymer Sci. 23, 167 (1957).CrossRefGoogle Scholar
  10. 9).
    Cerf, R., Compt. Rend. Acad. Sci. (Paris) 230, 81 (1950).Google Scholar
  11. Cerf, R., J. Chim. Phys. 48, 85 (1951).Google Scholar
  12. 10).
    Tsvetkov, V. N. and V. P. Budtov, Vysokomol. Soedin 6, 1209 (1964).Google Scholar
  13. 11).
    Cerf, R., J. Phys. & Radium 19, 122 (1958).CrossRefzbMATHGoogle Scholar
  14. 12).
    Cerf, R., Adv. Polymer Sci. 1, 382 (1959).CrossRefGoogle Scholar
  15. 13).
    Chaffey, C., J. Chem. Phys. 63, 1385 (1966).Google Scholar
  16. 14).
    Janeschitz-Kriegl, H., Adv. Polymer Sci. 6, 170 (1969).CrossRefGoogle Scholar
  17. 15).
    Philippoff, W., Trans. Soc. Rheol. 8, 117 (1964).CrossRefGoogle Scholar
  18. 16).
    Ferry, J. D., L. A. Holmes, J. Lamb, and A. J. Matheson, J. Chem. Phys. 70, 1685 (1966).CrossRefGoogle Scholar
  19. 17).
    Massa, D. J., J. L. Schrag, and J. D. Ferry, Macromol. 4, 210 (1961).ADSCrossRefGoogle Scholar
  20. 18).
    Osaki, K. and J. L. Schräg, Polymer J. Japan 2, 541 (1971).CrossRefGoogle Scholar
  21. 19).
    Peterlin, A., Kolloid-Z. u. Z. Polymere 209, 181 (1966).CrossRefGoogle Scholar
  22. 20).
    Peterlin, A., J. Polymer Sci. A-2, 5, 179 (1967).CrossRefGoogle Scholar
  23. 21).
    Peterlin, A. and C. Reinhold, Trans. Soc. Rheol. 11:1,15(1967).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • A. Peterlin
    • 1
  1. 1.Camille Dreyfus LaboratoryResearch Triangle InstituteResearch Triangle ParkUSA

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