Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Extensional and Fractural Properties of Concentrated Solutions of Monodisperse Polystyrene at Elevated Temperatures


The extensional and fractural properties were measured for concentrated solutions of polystyrene over wide ranges of extension rate and temperature. From stress—strain curves failure parameters such as failure stress σf and failure strain γf fractural parameters such as breaking stress σb and breaking strain γb, and extensional parameters such as time dependent maximum extensibility n(t)1/2 and extensional modulus E(t) were evaluated and compared with those of bulk polystyrenes. The dependence of these parameters on the concentration was also discussed. The height of the rubbery plateau, EeN°, in the time curves of the elongational modulus is proportional to (ρsw)−2, where ρs is the density of solution and w is the weight fraction of polymer in solution. This result is consistent with the previous results of our dynamic viscoelastic measurements for polystyrene solutions. The master curves of n(t)1/2 show a concentration dependence in the plateau region and are similar in shape to the master curves of the draw ratio at the breaking point, λb, in the short time scale region below the maximum λb. This result indicates that the master curve of λb on the short time scale side below the maximum point may obey the stored energy constant criterion for fracture. The variation of the γb with time depends upon polymer concentration and also shows a much sharper maximum compared with that for the bulk polystyrenes in the intermediate rate region. Such a very sharp maximum is characteristic of solutions.The concentration dependence of the failure envelope, the average molecular weight Me and the chain length Ze between entanglement loci were also discussed.


  1. S. Onogi, T. Matsumoto, and E. Kamei, Polym. J., 3, 531 (1972).

  2. E. Kamei and S. Onogi, Applied Polymer Symposia, No. 27, 19 (1975).

  3. L. R. G. Treloar, “The Physics of Rubber Elasticity”, Oxford University Press, London, 1958.

    Google Scholar 

  4. W. W. Graessley, J. Chem. Phys., 43, 2696 (1965).

  5. W. W. Graessley, J. Chem. Phys., 47, 1942 (1967).

  6. T. Masuda, N. Toda, Y. Aoto, and S. Onogi, Polym. J., 3, 315 (1972).

  7. T. Masuda, Ph. D. Thesis, Kyoto University, Kyoto, 1973.

    Google Scholar 

  8. T. Masuda, Y. Ohota, M. Minamide, and S. Onogi, J. Soc. Mater. Sci., Jpn. 21, 436 (1972).

  9. W. W. Graessley, R. L. Hazleton, and L. R. Lindeman, Trans. Soc. Rheol., 11, 267 (1967).

  10. W. W. Graessley and L. Segal, Macromolecules, 2, 49 (1969).

  11. L. A. Holmes and J. D. Ferry, J. Polym. Sci., Part C, 23, 291 (1968).

  12. S. Kusamizu, L. A. Holmes, A. A. Moore, and J. D. Ferry, Trans. Soc. Rheol., 12, 559 (1968).

  13. Y. Einaga, K. Osaki, M. Kurata, and M. Tamura, Macromolecules, 4, 87 (1971).

  14. R. I. Wolkowicz and W. C. Forsman, Macromolecules, 4, 184 (1971).

  15. N. Nemoto, T. Ogawa, H. Odani, and M. Kurata, Macromolecules, 5, 641 (1972).

  16. T. Masuda, K. Kitagawa, T. Inoue, and S. Onogi, Macromolecules, 3, 116 (1970).

  17. D. C. Bogue, T. Masuda, Y. Einaga, and S. Onogi, Polym. J., 1, 563 (1970).

  18. J. D. Ferry, “Viscoelastic Properties of Polymers”, 2nd ed., John Wiley, New York, N.Y., 1970.

    Google Scholar 

  19. T. L. Smith and J. E. Frederic, J. Appl. Phys., 36, 2996 (1965).

  20. T. L. Smith and R. A. Dickie, J. Polym. Sci., Part A-2, 7, 635 (1969).

  21. J. C. Halpin, J. Appl. Phys., 36, 2975 (1965).

  22. J. C. Halpin, J. Polym. Sci., Part C, 16, 1073 (1967).

  23. F. Bueche, J. Appl. Phys., 29, 1231 (1958).

  24. F. Bueche, “Physical Properties of Polymers”, Interscience, New York, N.Y., 1962.

    Google Scholar 

  25. G. C. Berry and T. G Fox, Adv. Polym. Sci., 5, 261 (1968).

  26. S. Onogi, T. Masuda, and K. Kitagawa, Macromolecules, 3, 109 (1970).

  27. M. L. Williams, R. F. Landel, and J. D. Ferry, J. Am. Chem. Soc., 77, 3701 (1955).

  28. J. D. Ferry, R. F. Landel, and M. L. Williams, J. Appl. Phys., 26, 359 (1955).

  29. T. Yokobori, “Strength, Fracture, and Fatigue of Materials”, Gihodo, Tokyo, 1955.

    Google Scholar 

  30. K. Osaki, M. Tamura, T. Kotaka, and M. Kurata, J. Phys. Chem., 69, 3642 (1965).

  31. H. C. Booij, Rheol. Acta, 5, 215 (1966).

  32. J. M. Simmons, J. Sci. Instr., 43, 887 (1966).

  33. R. I. Tanner and J. M. Simmons, Chem. Eng. Sci., 22, 1803 (1967).

  34. P. J. Carreau, Trans. Soc. Rheol., 16, 99 (1972).

  35. D. C. Bogue, Ind. Eng. Chem. Fund., 5, 253 (1966).

  36. M. Yamamoto, Trans. Soc. Rheol., 15, 331 (1971).

  37. T. W. Spriggs, J. D. Huppler, and R. B. Bird, Trans. Soc. Rheol., 10, 191 (1966).

  38. W. W. Graessley, J. Chem. Phys., 54, 5143 (1971).

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kamei, E., Onogi, S. Extensional and Fractural Properties of Concentrated Solutions of Monodisperse Polystyrene at Elevated Temperatures. Polym J 8, 347–362 (1976).

Download citation

  • Issue Date:

  • DOI:


  • Extension
  • Fracture
  • Concentrated Solution
  • Monodisperse Polystyrene
  • Stress—Strain Curve

Further reading


Quick links