Constitutive equations for polymer mole and rubbers: Lessons from the $20^{th}$ century

  • Wagner, Manfred H. (Polymertechnik/Polymerphysik, Technische Universitat Berlin)
  • 발행 : 1999.12.01

초록

Refinements of classical theories for entangled or crosslinked polymeric systems have led to incommensurable models for rubber networks and polymer melts, contrary to experimental evidence, which suggests a great deal of similarity. Uniaxial elongation and compression data of linear and branched polymer melts as well as of crosslinked rubbers were analyzed with respect to their nonlinear strain measure. This was found to be the result of two contributions: (1) affine orientation of network strands, and (2) isotropic strand extension. Network strand extension is caused by an increasing restriction of lateral movement of polymer chains due to deformation, and is modelled by a molecular stress function which in the tube concept of Doi and Edwards is the inverse of the relative tube diameter. Up to moderate strains, $f^2$ is found to be linear in the average stretch for melts as well as for rubbers, which corresponds to a constant tube volume. At large strains, rubbers show maximum extensibility, while melts show maximum molecular tension. This maximum value of the molecular stress function governs the ultimate magnitude of the strain-hardening effect of linear and long-chain branched polymer melts in extensional flows.

키워드

참고문헌

  1. Polymer v.22 Ball, R.C.;M. Doi;S.F. Edwards;M. Warner
  2. Trans. Soc. Rheol. v.7 Bernstein, B.;E. Kearsley;L.J. Zapas
  3. Polymer v.29 Brereton, M.G.;P.G. Klein
  4. Polymer Preprints v.23 Currie, P.K.
  5. Rheol. Acta v.24 Demarmels, A.;J. Meissner
  6. Colloid and Polym. Sci. v.264 Demarmels, A.;J. Meissner
  7. Faraday Trans. Ⅱ v.74 Doi, M.;S.F. Edwards
  8. Polymer v.27 Edwards, S.F.;Th. Vilgis
  9. J. Chem. Phys. v.68 Ermann, B.;P.J. Flory
  10. J. Chem. Phys. v.66 Flory, P.J.
  11. Advances in Polym. Sci. v.47 Graessley, W.W.
  12. J. Chem. Phys. v.14 Green, M.S.;A.V. Tobolsky
  13. Disseration ETH Zurich Nr.11890 Multiaxiale Dehnung von Polymerschmelzen Hachmann, P.
  14. College of Aeronautics, Cransfield, Note No.134 Kay, A.
  15. J. Rheol. v.43 Kurzbeck, S.;F. Oster;H. Munstedt;T.Q. Nguyen;R. Gensler
  16. Constitutive equations for polymer melts and solutions Larson, R.G.
  17. Rheol. Acta v.17 Laun, H.M.
  18. Proc. Ⅷth Int. Congr. Rheol. Laun, H.M.
  19. Advances in Elastomers and Rubber Elasticity Leblans, P.J.R.;B.J.R. Scholtens;J. Lal(ed.);J.E. Mark(ed.)
  20. Trans. Faraday Soc. v.52 Lodge, A.S.
  21. Rheol. Acta v.18 Marrucci, G.
  22. Rheol. Acta v.19 Marrucci, G.;B. de Cindio
  23. Macromolecules v.13 Marrucci, G.;J.J. Hermans
  24. J. Rheol. v.27 Marrucci, G.;N. Grizzuti
  25. J. Rheol. v.42 McLeish, T.C.B.;R.G. Larson
  26. Macromolecules v.31 Mead, D.W.;R.G. Larson;M. Doi
  27. J. Appl. Polym. Sci. v.2 Mullins, L.
  28. J. Polym. Sci., Polym. Phys. Ed. v.17 Pak, H.;P.J. Flory
  29. J. Rheol. v.33 Pearson, D.S.;A.D. Kiss;L.J. Fetters;M. Doi
  30. J. Non-Newt. Fluid Mech. v.11 Raible, T.;S.E. Stephenson;J. Meissner;M.H. Wagner
  31. Phil. Trans. Royal Soc. v.A243 Rivlin, R.S.;D.W. Saunders
  32. J. Rheol. v.33 Roland, C.M.
  33. J. Non-Newt. Flurd Mech. Rubio, P.;M.H. Wagner
  34. J. Rheol. v.30 Scholtens, B.J.R.;P.J.R. Leblans
  35. Trans. Soc. Rheol. v.6 Smith, T.L.
  36. Polymer v.25 Thirion, P.;T. Weil
  37. Rub. Chem. Tech. v.51 Tsuge, K.;R.J. Arenz;R.F. Landel
  38. Rheol. Acta v.15 Wagner, M.H.
  39. J. Non-Newt. Fluid Mech. v.4 Wagner, M.H.
  40. Rheol. Acta v.18 Wagner, M.H.
  41. Proc. Ⅶth Int. Congr. on Rheol. Wagner, M.H.
  42. Rheol. Acta v.29 Wagner, M.H.
  43. J. Rheol. v.38 Wagner, M.H.
  44. J. Rheol. v.34 Wagner, M.H.;A. Demarmels
  45. J. Non-Newt. Fluid Mech. v.79 Wagner, M.H.;H. Bastian;P. Ehrecke;M. Kraft;P. Hachmann;J. Meissner
  46. sub. Rheol. Acta. Wagner, M.H.;H. Bastian;P. Hachmann;J. Meissner;S. Kurzbeck;H. Munstedt;F. Langouche
  47. Rheol. Acta v.17 Wagner, M.H.;H.M. Laun
  48. Makromol. Chem. v.181 Wagner, M.H.;J. Meissner
  49. Proc. XIth Int. Congr. on Rheol. Wagner, M.H.;J. Schaeffer
  50. J. Rheol. v.36 Wagner, M.H.;J. Schaeffer
  51. Rheol. Acta v.31 Wagner, M.H.;J. Schaeffer
  52. J. Rheol. v.37 Wagner, M.H.;J. Schaeffer
  53. J. Rheol. v.42 Wagner, M.H.;P. Ehrecke;P. Hachmann;J. Meissner
  54. J. Rheol. v.23 Wagner, M.H.;S.E. Stephenson
  55. Rub. Chem. Tec. v.63 Xu, P.;J.E. Mark
  56. J. Phys. Soc. Japan v.11 Yamamoto, M.