Summary
An entangled network such as a polymer melt or a concentrated solution is here described by a set of two simultaneous equations. One of them is a balance of entanglements, the other gives the stress in the classical form of aMaxwell equation.
The balance of entanglements contains both an entanglement generation term which depends on the “distance” from equilibrium and an entanglement destruction term which depends on the stress level. The parameters appearing in theMaxwell and the balance equations are made to depend in a specified way on the existing number of entanglements.
The model is here tested by comparison with existing data of steady-state elongational and shear viscosity of polymer melts.
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References
Green, M. S. andA. V. Tobolsky, J. Chem. Phys.14, 80 (1946).
Lodge, A. S., Trans. Faraday Soc.52, 120 (1956).
Yamamoto, M., J. Phys. Soc. Japan11, 413 (1956).
Yamamoto, M., ibidem12, 1148 (1957).
Yamamoto, M., ibidem13, 1200 (1958).
Kaye, A., Brit. J. Appl. Phys.17, 803 (1966).
Lodge, A. S., Rheol. Acta7, 379 (1968).
Lodge, A. S., Elastic Liquids (London 1964).
Graessley, W. W., J. Chem. Phys.43, 2696 (1965).
Graessley, W. W., ibidem47, 1942 (1967).
Ziabicki, A. andR. Takserman-Krozer, J. Polymer Sci. A-2,7, 2005 (1969);Takserman-Krozer, R. andA. Ziabicki, J. Polymer Sci. A-2,8, 321 (1970);Ziabicki, A., J. Polymer Sci. A-2,
Oldroyd, J. G., Proc. Roy. Soc.\( > \) 200, 523 (London 1950).
White, J. L. andA. B. Metzner, J. Polymer Sci.7, 1867 (1963).
Lodge, A. S., Proc. 5th Int. Congr. Rheology, Vol. 4 (Baltimore 1970).
Marrucci, G., Trans. Soc. Rheol.16, 321 (1972).
Bogue, D. C. andJ. O. Doughty, Ind. Eng. Chem. Fund.5, 243 (1966);Doughty, J. O. andD. C. Bogue, ibidem6, 388 (1967).
Bird, R. B. andP. J. Carreau, Chem. Eng. Sci.23, 427 (1968).
Tanner, R. I. andJ. M. Simmons, Chem. Eng. Sci.22, 1803 (1967).
Ferry, J. D., Viscoelastic properties of polymers, p. 542 (New York 1970).
Nakayasu, H. andT. G. Fox, Abstracts 137th Meeting American Chem. Soc., p. 11-I (1960).
Shultz, A. R., W. R. Shultz, andT. G. Fox, unpublished experiments.
Ninomiya, K., J. R. Richards, andJ. D. Ferry, J. Phys. Chem.67, 327 (1963).
Oyanagi, Y. andJ. D. Ferry, J. Colloid Sci.21, 547 (1966).
Berry, G. C., J. Phys. Chem.70, 1194 (1966).
Ballman, R. L., Rheol. Acta4, 137 (1965).
Meissner, J., Rheol. Acta8, 78 (1969).
Vinogradov, G. V., B. D. Radushkevich, andV. D. Fikhman, J. Polymer Sci. A-2,8, 1 (1970).
Vinogradov, G. V., A. I. Leonov, andA. N. Prokunin, Rheol. Acta8, 482 (1969).
Vinogradov, G. V., V. D. Fikhman, B. D. Radushkevich, andA. Ya. Malkin, J. Polymer Sci. A-2,8, 657 (1970).
Cogswell, F. N., Plastics & Polymers36, 109 (1968).
Cogswell, F. N., Rheol. Acta8, 187 (1969).
Cogswell, F. N., Measuring the extensional rheology of polymer melts, presented at American Soc. Rheol. Conference Knoxville 1971, to be published in Trans. Soc. Rheol.
Chen, I-Jen andD. C. Bogue, Trans. Soc. Rheol.16, 59 (1972).
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Marrucci, G., Titomanlio, G. & Sarti, G.C. Testing of a constitutive equation for entangled networks by elongational and shear data of polymer melts. Rheol Acta 12, 269–275 (1973). https://doi.org/10.1007/BF01635115
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DOI: https://doi.org/10.1007/BF01635115