Citation: Yong-jin Ruan, Yu-yuan Lu, Li-jia An. Tube Model[J]. Acta Polymerica Sinica, ;2018, 0(12): 1493-1506. doi: 10.11777/j.issn1000-3304.2018.18172 shu

Tube Model

1.
State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022
2.
University of Chinese Academy of Sciences, Beijing 100049

Corresponding author: Yu-yuan Lu, yylu@ciac.ac.cn
Received Date: 29 July 2018
Revised Date: 25 September 2018
Available Online: 16 October 2018

Nonlinear rheology for polymers is the foundational science underlying high efficiency and energy-saving processing of polymeric materials. For chainlike polymers, complicated interchain interactions affect their dynamics and determine the structure-processing-property relationship. This interaction is often called the entanglement, and becomes the key issue in polymer rheology. To our knowledge, the rheological behavior of entangled polymers is based on the de Gennes-Doi-Edwards tube model (DE theory), which reduces the many-chain interaction into a smooth confining tube and assumes the test chain undergoes the Rouse dynamics inside the tube. Some predictions based on the DE theory are in agreement with rheological results, for instance, the time-strain separated form of the reduced relaxation modulus. To overcome some obvious disadvantages and provide reasonable results, many improvements and refinements have also been made to the DE theory. However, the tube model is only an essential single-chain mean-field theory since its intuitive molecular picture is too simple the theory cannot be derived from first principles and lacks self-consistency. In brief, the tube model does not describe how entanglement arises and cannot address the problem of when, how, and why disentanglement occurs after the external deformation. The model is inadequate in describing the chain conformation under fast and large deformations, and fails to explain a number of experimental observations in recent studies, such as the shear banding and the nonquiescent relaxation which show remarkable strain localization phenomena. Therefore, it is necessary to reexamine the single-chain mean-field assumptions and to consider the many-chain interactions explicitly. In other words, the chain entanglement may involve active localized intermolecular interactions that should be preceived as network junctions, and the critical picture of barrier-free Rouse retraction is questionable. In this article, we provide a general introduction to the original tube model and its subsequent improvements, with an emphasis on the development, basic assumptions, and key concepts. We provide derivation of some key results and explain the physical meaning of the parameters. The article ends with an outlook of the challenges and opportunities in the theory for polymer rheology, hoping to motivate researchers to working on this field.
- Non-linear rheology,
- Tube model,
- Entangled polymers,
- GLaMM theory,
- Single-chain mean-field theory
1. [1]
  Doi M, Edwards S F. The Theory of Polymer Dynamics. New York: Oxford University Press, 1986. 1 – 20, 188 – 283
2. [2]
  Dealy J M, Larson R G. Structure and Rheology of Molten Polymers: From Structure to Flow Behavior and Back Again. Munich: Hanser Publishers, 2006. 91 – 126, 193 – 229, 329 – 400, 415 – 464
3. [3]
  Rubinstein M, Colby R H, Polymer Physics. New York: Oxford University Press, 2003. 30 − 53, 197 − 252
4. [4]
5. [5]
  Kalathi J T, Kumar S K, Rubinstein M, Grest G S. Macromolecules, 2014, 47(19): 6925 − 6931 doi: 10.1021/ma500900b
6. [6]
  Casale A, Porter R S, Johnson J F. Polym Rev, 1971, 5(2): 387 − 408
7. [7]
  Berry G C, Fox T G. Adv Polym Sci, 1968, 5: 261 − 357
8. [8]
  Lodge T P. Phys Rev Lett, 1999, 83(16): 3218 − 3221 doi: 10.1103/PhysRevLett.83.3218
9. [9]
  de Gennes P G. J Chem Phys, 1971, 55(2): 572 − 579 doi: 10.1063/1.1675789
10. [10]
  Doi M, Edwards S F. J Chem Soc, Faraday Trans 2, 1978, 74: 1789 − 1801 doi: 10.1039/F29787401789
11. [11]
  Doi M, Edwards S F. J Chem Soc, Faraday Trans 2, 1978, 74: 1802 − 1817 doi: 10.1039/F29787401802
12. [12]
  Doi M, Edwards S F. J Chem Soc, Faraday Trans 2, 1978, 74: 1818 − 1832 doi: 10.1039/F29787401818
13. [13]
  Doi M, Edwards S F. J Chem Soc, Faraday Trans 2, 1979, 75: 38 − 54 doi: 10.1039/F29797500038
14. [14]
  Graham R S, Likhtman A E, McLeish T C B, Milner S T. J Rheol, 2003, 47(5): 1171 − 1200 doi: 10.1122/1.1595099
15. [15]
  Wang S-Q, Wang Y, Cheng S, Li X, Zhu X, Sun H. Macromolecules, 2013, 46(8): 3147 − 3159 doi: 10.1021/ma300398x
16. [16]
17. [17]
  Kaye A, Non-Newtonian Flow in Incompressible Fluids. Cranford: College of Aeronautics Press, 1962. 4 – 16
18. [18]
  Bernstein B, Kearsley E A, Zapas L J. Trans Soc Rheol, 1963, 7: 391 − 410 doi: 10.1122/1.548963
19. [19]
  Larson R G, Constitutive Equations for Polymer Melts and Solutions. Stoneham: Butterworth Publishers, 1988. 29 – 49
20. [20]
  Green M S, Tobolsky A V. J Chem Phys, 1946, 14(2): 80 − 92 doi: 10.1063/1.1724109
21. [21]
  Lodge A S. Rheol Acta, 1968, 7(4): 379 − 392 doi: 10.1007/BF01984856
22. [22]
  Doi M. J Polym Sci, Part B: Polym Phys, 1983, 21(5): 667 − 684 doi: 10.1002/pol.1983.180210501
23. [23]
  Milner S, McLeish T. Phys Rev Lett, 1998, 81(3): 725 − 728 doi: 10.1103/PhysRevLett.81.725
24. [24]
  Viovy J L, Rubinstein M, Colby R H. Macromolecules, 1991, 24(12): 3587 − 3596 doi: 10.1021/ma00012a020
25. [25]
  Rubinstein M, Colby R H. J Chem Phys, 1988, 89(8): 5291 − 5306 doi: 10.1063/1.455620
26. [26]
  Ianniruberto G, Marrucci G. J Non-Newton Fluid Mech, 1996, 65(2): 241 − 246
27. [27]
  Marrucci G. J Non-Newton Fluid Mech, 1996, 62(2-3): 279 − 289 doi: 10.1016/0377-0257(95)01407-1
28. [28]
  Likhtman A E, Milner S T, McLeish T C B. Phys Rev Lett, 2000, 85(21): 4550 − 4553 doi: 10.1103/PhysRevLett.85.4550
29. [29]
  Milner S T, McLeish T C B, Likhtman A E. J Rheol, 2001, 45(2): 539 − 563 doi: 10.1122/1.1349122
30. [30]
31. [31]
  Edwards S F. Proc Phys Soc, 1967, 92(575): 9 − 16
32. [32]
  Edwards S F. British Polym J, 1977, 9(2): 140 − 143 doi: 10.1002/(ISSN)1934-256X
33. [33]
  Rouse P E. J Chem Phys, 1953, 21(7): 1272 − 1280 doi: 10.1063/1.1699180
34. [34]
  Likhtman A E, Sukumaran S K, Ramirez J. Macromolecules, 2007, 40(18): 6748 − 6757 doi: 10.1021/ma070843b
35. [35]
  Onogi S, Masuda T, Kitagawa K. Macromolecules, 1970, 3(2): 109 − 116 doi: 10.1021/ma60014a001
36. [36]
  Osaki K, Kurata M. Macromolecules, 1980, 13(3): 671 − 676 doi: 10.1021/ma60075a036
37. [37]
  Osaki K, Nishizawa K, Kurata M. Macromolecules, 1982, 15(4): 1068 − 1071 doi: 10.1021/ma00232a021
38. [38]
  Archer L A. J Rheol, 1999, 43(6): 1555 − 1571 doi: 10.1122/1.551060
39. [39]
  Archer L A, Sanchez-Reyes J, Juliani. Macromolecules, 2002, 35(27): 10216 − 10224 doi: 10.1021/ma021286q
40. [40]
  Tanner R I. Trans Soc Rheol, 1973, 17(2): 365 − 373 doi: 10.1122/1.549317
41. [41]
  Gao H W, Ramachandran S, Christiansen E B. J Rheol, 1981, 25(2): 213 − 235 doi: 10.1122/1.549617
42. [42]
  Likhtman A E, McLeish T C B. Macromolecules, 2002, 35(16): 6332 − 6343 doi: 10.1021/ma0200219
43. [43]
  Graham R S, Henry E P, Olmsted P D. Macromolecules, 2013, 46(24): 9849 − 9854 doi: 10.1021/ma401183w
44. [44]
  Auhl D, Ramirez J, Likhtman A E, Chambon P, Fernyhough C. J Rheol, 2008, 52(3): 801 − 835 doi: 10.1122/1.2890780
45. [45]
  Lodge A S. Rheol Acta, 1989, 28(5): 351 − 362 doi: 10.1007/BF01336802
46. [46]
  Ravindranath S, Wang S Q. Macromolecules, 2007, 40(22): 8031 − 8039 doi: 10.1021/ma071495g
47. [47]
  Cheng S, Lu Y, Liu G, Wang S Q. Soft Matter, 2016, 12(14): 3340 − 3351 doi: 10.1039/C6SM00142D
48. [48]
  Wang S Q, Ravindranath S, Boukany P, Olechnowicz M, Quirk R P, Halasa A, Mays J. Phys Rev Lett, 2006, 97(18): 187801(1-4)
49. [49]
  Boukany P E, Wang S Q, Wang X. Macromolecules, 2009, 42(16): 6261 − 6269 doi: 10.1021/ma9004346
50. [50]
51. [51]
  Wang S Q. Nonlinear Polymer Rheology: Macroscopic Phenomenology and Molecular Foundation. Hoboken: John Wiley & Sons, 2018. 4 – 415
52. [52]
  Inoue T, Uematsu T, Yamashita Y, Osaki K. Macromolecules, 2002, 35(12): 4718 − 4724 doi: 10.1021/ma012149g
53. [53]
  Huang Q, Hengeller L, Alvarez N J, Hassager O. Macromolecules, 2015, 48(12): 4158 − 4163 doi: 10.1021/acs.macromol.5b00849
54. [54]
  Nielsen J K, Hassager O, Rasmussen H K, McKinley G H. J Rheol, 2009, 53(6): 1327 − 1346 doi: 10.1122/1.3208073
55. [55]
  Wang Z, Lam C N, Chen W R, Wang W, Liu J, Liu Y, Porcar L, Stanley C B, Zhao Z, Hong K, Wang Y. Phys Rev X, 2017, 7(3): 031003(1-16)
56. [56]
  Xu W S, Carrillo J M Y, Lam C N, Sumpter B G, Wang Y. ACS Macro Lett, 2018, 7(2): 190 − 195 doi: 10.1021/acsmacrolett.7b00900
57. [57]
  Hsu H P, Kremer K. ACS Macro Lett, 2017, 7(1): 107 − 111
58. [58]
  Kröger M, Hess S. Phys Rev Lett, 2000, 85(5): 1128 − 1131 doi: 10.1103/PhysRevLett.85.1128
59. [59]
  Kremer K, Grest G S. J Chem Phys, 1990, 92(8): 5057 − 5086 doi: 10.1063/1.458541
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