Homogeneous shear, wall slip, and shear banding of entangled polymeric liquids in simple-shear rheometry: A roadmap of nonlinear rheology

Macromolecules

Volumn 44, Issue 2, 2011, Pages 183-190

  Wang, Shi Qing ^a   Ravindranath, S ^a,b   Boukany, P E ^a,c  

^a The University of Akron   (United States)

^b Celanese/Ticona ^*  (Hungary)

^c OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENTANGLED POLYMER SOLUTIONS; ENTANGLED POLYMERIC LIQUIDS; EXTERNAL CONDITIONS; INHOMOGENEITIES; INTERFACIAL SLIP; MATERIAL PARAMETER; NONLINEAR RHEOLOGY; RHEOLOGICAL MEASUREMENTS; RHEOMETRIC MEASUREMENTS; ROADMAP; SHEAR BANDING; SHEAR RHEOMETRY; WALL SLIP;

PHASE DIAGRAMS; POLYMER MELTS; RHEOLOGY;

WALLS (STRUCTURAL PARTITIONS);

EID: 78751490068     PISSN: 00249297     EISSN: None     Source Type: Journal    
DOI: 10.1021/ma101223q     Document Type: Review

References (121)

1. Wasserman, S. H.; Graessley, W. W. J. Rheol. 1992, 36, 543
2. Mead, D. W. J. Rheol. 1994, 38, 1797
3. Macosko, C. W. Rheology: Principles, Measurements and Applications; VCH: New York, 1994.
4. 0 exceeds a critical value (which is on the order of unity for monodisperse entangled linear polymers) and the oscillatory frequency ω is higher than 1/τ. In (c), the resulting shear stress after a step strain relaxes in a quantitatively different way (from its relaxation behavior after a small step shear) when the amplitude of the step shear is large.
5. For some recent publications invoking nonlinear rheological measurements to characterize polymer materials, see: Tezel, A. K.; Oberhauser, J. P.; Graham, R. S. J. Rheol. 2009, 53, 1193
6. Hoyle, D. M.; Harlen, O. G.; Auhl, D. J. Rheol. 2009, 53, 917
7. Kapnistos, M.; Kirkwood, K. M.; Ramirez, J. J. Rheol. 2009, 53, 1133
8. Lee, J. H.; Driva, P.; Hadjichristidis, N. Macromolecules 2009, 42, 1392
9. Lee, J. H.; Orfanou, K.; Driva, P. Macromolecules 2008, 41, 9165
10. Wang, S. Q. Macromol. Mater. Eng. 2007, 292, 15
11. Tapadia, P.; Wang, S. Q. Phys. Rev. Lett. 2006, 96, 016001
12. Boukany, P. E.; Wang, S. Q. J. Rheol. 2007, 51, 217
13. Ravindranath, S. Macromolecules 2008, 41, 2663
14. Ravindranath, S.; Wang, S. Q. J. Rheol. 2008, 52, 957
15. Ravindranath, S.; Wang, S. Q. J. Rheol. 2008, 52, 341
16. Ravindranath, S.; Wang, S. Q. Macromolecules 2007, 40, 8031. This important PTV study of step strain pointed out that only a subset of experimental data happened to agree with the tube model calculation that assumes quiescent relaxation. Actually, Osaki et al. first found the disagreement in 1980 (i.e., ref 37) before reporting the far better known agreement in ref 38 in 1982. We showed in this paper that the agreement between the stress relaxation data and the tube model prediction was completely fortuitous because the simultaneous PTV observations revealed significant macroscopic motions after shear cessation, and yet the calculation was only valid for quiescent stress relaxation
17. Boukany, P. E.; Wang, S. Q. Macromolecules 2009, 43, 6261
18. Tordella, J. P. J. Appl. Phys. 1956, 27, 454
19. Tordella, J. P. J. Appl. Polym. Sci. 1963, 7, 215
20. Bagley, E. B.; Cabott, I. M.; West, D. C. J. Appl. Phys. 1958, 29, 109
21. Rielly, F. J.; Price, W. L. SPE J. 1961, 1097
22. Benbow, J. J.; Lamb, P. SPE Trans. 1963, 3, 7
23. Blyler, L. L.; Hart, A. C. Polym. Eng. Sci. 1970, 10, 193
24. Bergem, N. Proc. Int. Congr. Rheol., 7th, Gothenburg, Sweden 1976, 50
25. Vinogradov, G. V. J. Polym. Sci., Part A-2 1972, 10, 1061
26. Vinogradov, G. V.; Malkin, A. Y. Rheology of Polymers-Viscoelasticity and Flow of Polymers; Springer-Verlag: Berlin, 1980. Apparently, the view that wall slip in spurt flow is related to the sample undergoing a "fluid-to-rubber transition" has persisted to this date
27. Malkin, A. Y.; Semakov, A. V.; Kulichikhin, V. G. Adv. Colloid Interface Sci. 2010, 157, 75
28. De Gennes, P. G. C. R. Acad. Sci. 1979, 288B, 219 Here de Gennes contemplated a case where a melt was perceived to flow by a nonadsorbing wall and rediscovered Navier's account of wall slip
29. Navier, C.-L. Mémo Acad. R. Sci. Inst. France 1823, 6, 414 This reference originates from
30. Goldstein S. Modern Developments in Fluid Mechanics; Oxford University Press: London, 1938; Vol. 2, pp 676-680.
31. Wang, S. Q. Adv. Polym. Sci. 1999, 138, 227. This review summarized the research carried out in the 1990s and mentioned key publications in the period from 1950 to 1990
32. Brochard, F.; de Gennes, P. G. Langmuir 1992, 8, 3033
33. Joshi, Y. M.; Lele, A. K.; Mashelkar, R. A. J. Non-Newton. Fluid Mech. 2000, 89, 103
34. Brochard-Wyart, F.; Gay, C.; deGennes, P. G. Macromolecules 1996, 29, 377
35. Hatzikiriakos, S. G.; Dealy, J. M. J. Rheol. 1992, 36, 703
36. Migler, K. B.; Hervet, H.; Leger, L. Phys. Rev. Lett. 1993, 70, 287
37. Archer, L. A.; Chen, Y. L.; Larson, R. G. J. Rheol. 1995, 39, 519
38. Wang, S. Q.; Drda, P. A. Macromolecules 1996, 29, 2627
39. Mhetar, V.; Archer, L. A. Macromolecules 1998, 31, 6639
40. Leger, L.; Raphael, E.; Hervet, H. Adv. Polym. Sci. 1999, 138, 185
41. Sanchez-Reyes, J.; Archer, L. A. J. Rheol. 2002, 46, 1239
42. Sanchez-Reyes, J.; Archer, L. A. Langmuir 2003, 19, 3304
43. Boukany, P. E.; Wang, S. Q. Macromolecules 2009, 42, 2222
44. Denn, M. M. Ann. Rev. Fluid Mech. 2001, 33, 265
45. Fukuda, M.; Osaki, K.; Kurata, M. J. Polym. Sci., Polym. Phys. 1975, 13, 1563
46. Osaki, K.; Kurata, M. Macromolecules 1980, 13, 671
47. Osaki, K.; Nishizawa, K.; Kurata, M. Macromolecules 1982, 15, 1068
48. Larson, R. G.; Khan, S. A.; Raju, V. R. J. Rheol. 1988, 32, 145
49. Morrison, F. A.; Larson, R. G. J. Polym. Sci., Polym. Phys. Ed. 1992, 30, 943
50. Archer, L. A.; Sanchez-Reyes, J. Macromolecules 2002, 35, 10216
51. Osaki, K. Rheol. Acta 1993, 32, 429
52. Although Osaki speculated about the possibility of wall slip, he was actually inclined toward a different explanation given by Marrucci, G. J. Rheol. 1983, 27, 433, which was prompted by the ultrastrain softening data of ref 52 on step strain of polybutadiene melts that could readily experience massive wall slip
53. Doi, M. J. Polym. Sci. 1980, 18, 1005
54. Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics, 2 nd ed.; Clarendon Press: Oxford, 1988.
55. Menezes, E. V.; Graessley, W. W. J. Polym. Sci., Polym. Phys. Ed. 1982, 20, 1817
56. Mhetar, V.; Archer, L. A. Macromolecules 1998, 31, 6639
57. Plucktaveesak, N.; Wang, S. Q.; Halasa, A. Macromolecules 1999, 32, 3045
58. Ravindranath, S.; Wang, S. Q. Rheol. Acta 2010, in press.
59. Wang, S. F.; Wang, S. Q.; Halasa, A.; Hsu, W.-L. Macromolecules 2003, 36, 5355 The conclusion of this paper disagrees with: Struglinksi, M. J.; Graessley, W. W. Macromolecules 1985, 18, 2630
60. Boukany, P. E.; Wang, S. Q. Soft Matter 2009, 5, 780
61. Boukany, P. E.; Wang, S. Q. J. Rheol. 2006, 50, 641
62. Vrentas; Graessley, W. W. J. Rheol. 1982, 26, 359
63. Li, X.; Wang, S. Q.; Wang, X. R. J. Rheol. 2009, 57, 1255
64. Li, X.; Wang, S. Q. Rheol. Acta 2010, 49, 985
65. Tordella, J. P. J. Rheol. 1957, 1, 203
66. Galt, J. C.; Maxwell, B. Mod. Plast. 1964, 42, 115
67. White, J. L. US-Japan Seminar on Polymer Processing and Rheology Appl. Polym. Symp. 1973, 20, 155
68. Rodriguez-Gonzalez, F.; Perez-Gonzalez, J.; Marin-Santibanez, B. M. Chem. Eng. Sci. 2009, 64, 4675
69. Ramamurthy, A. V. Trans. Soc. Rheol. 1974, 18, 431
70. Munstedt, H.; Schmidt, M.; Wassner, E. J. Rheol. 2000, 44, 413
71. Schwetz, M.; Munstedt, H.; Heindl, M. J. Rheol. 2002, 46, 797
72. Adrian, R. J. Annu. Rev. Fluid Mech. 1991, 23, 261
73. Maas, H. G.; Gruen, A.; Papantoniou, D. Exp. Fluids 1993, 15, 133
74. Cowen, E. A.; Monismith, S. G. Exp. Fluids 1997, 22, 199
75. Melling, A. Meas. Sci. Technol. 1997, 8, 1406
76. Adrian, R. J. Exp. Fluids 2005, 39, 159
77. Archer, L. A.; Larson, R. G.; Chen, Y. L. J. Fluid Mech. 1995, 301, 133
78. Hu, Y. T. J. Rheol. 2007, 51, 275. This rheometric setup is a circular Couette that has a finite shear stress gradient across the sample thickness. Sharp shear banding may not survive in presence of such a stress gradient for the moderately entangled polymer solutions under study
79. Boukany, P. E.; Wang, S. Q. J. Rheol. 2009, 53, 73
80. Boukany, P. E.; Wang, S. Q. Macromolecules 2010, 43, 6950
81. Cheng, S. W.; Ravindranath, S.; Chavan, V. S.; Quirk, R. P. To be submitted.
82. Boukany, P. E.; Hu, Y. T.; Wang, S. Q. Macromolecules 2008, 41, 2644
83. Hayes, K. A. Macromolecules 2010, 43, 4412
84. We omit here the only other available data from ref 68 because we do not have the explicit information on the extrapolation lengths.
85. Boukany, P. E.; Ravindranath, S.; Wang, S. Q.; Lee, L. J. To be submitted.
86. Hayes, K. A. Phys. Rev. Lett. 2008, 101, 218301
87. Schweizer, T.; van Meerveld, J.; Öttinger, H. C. J. Rheol. 2004, 48, 1345
88. Auhl, D. J. Rheol. 2008, 52, 801
89. Wang, H.; Tapadia, P.; Wang, S. Q. Unpublished, 2005.
90. "In engineering, the transition from elastic behavior to plastic behavior is yield" according to Wikipedia http://en.wikipedia.org/wiki/ Plasticity-%28physics%29. The flow is possible only after the underlying structure has yielded. This yielding concept is not very different from "yield" in the concept of yield-stress that describes mechanical response to external stress of materials such as ketchup and yogurt. In such yield-stress materials, the viscosity is very high and abruptly drops greatly over a narrow range of shear stress due to some stress-induced structure rearrangements; i.e., the structure that survives at low stresses yields to a new state of flow beyond a particular stress level. Yield-stress materials are usually amorphous and noncrystalline. Evans (Evans, I. D. J. Rheol. 1992, 36, 1313) settled the controversy brought up by Barnes and Walters
91. Barnes; Walters Rheol. Acta 1985, 24, 323)
92. Ravindranath, S.; Wang, S. Q. J. Rheol. 2008, 52, 681
93. Boukany, P. E.; Wang, S. Q. J. Rheol. 2009, 53, 617
94. Wang, S. Q.; Ravindranath, S.; Wang., Y. Y.; Boukany, P. E. J. Chem. Phys. 2007, 127, 064903
95. Wang, Y. Y.; Wang, S. Q. J. Rheol. 2009, 53, 1389
96. Fetters Macromolecules 1994, 27, 4639
97. Wang, S. Q. Macromolecules 2007, 40, 8684
98. Colby, R. H.; Rubinstein, M. Macromolecules 1990, 23, 2753
99. The physics of the stress overshoot is rich and has to do with yielding of the entanglement network and cannot be readily captured by the tube model calculation where the shear stress is calculated from the intrachain force of a single chain.
100. Doi, M.; Edwards, S. F. J. Chem. Soc., Faraday Trans. 2 1979, 75, 38
101. McLeish, T. C. B.; Ball, R. C. J. Polym. Sci., Polym. Phys. 1986, 24, 1735
102. Cates, M. E.; McLeish, T. C. B.; Marrucci, G. Europhys. Lett. 1993, 21, 451
103. Callaghan, P. T. J. Phys. II 1996, 6, 375
104. Mair, R. W.; Callaghan, P. T. Europhys. Lett. 1996, 36, 719
105. Britton, M. M.; Callaghan, P. T. Phys. Rev. Lett. 1997, 30, 4930
106. Britton, M. M.; Mair, R. W.; Lambert, R. K.; Callaghan, P. T. J. Rheol. 1999, 43, 897
107. Fischer, E.; Callaghan, P. T. Europhys. Lett. 2000, 50, 803
108. Salmon, J. B.; Colin, A.; Manneville, S.; Molino, F. Phys. Rev. Lett. 2003, 90, 228303
109. Salmon, J. B.; Manneville, S.; Colin, A. Phys. Rev. E 2003, 68, 051503
110. Becu, L.; Manneville, S.; Colin, A. Phys. Rev. Lett. 2004, 93, 018301
111. Hu, Y. T.; Lips, A. J. Rheol. 2005, 49, 1001
112. Lopez-Gonzalez, M. R.; Holmes, W. M.; Callaghan, P. T. Soft Matter 2006, 2, 855
113. Boukany, P. E.; Wang, S. Q. Macromolecules 2008, 41, 1455
114. Ballesta, P.; Manneville, S. J. Non-Newtonian Fluid Mech. 2007, 147, 23
115. Britton, M. M.; Callaghan, P. T. J. Rheol. 1997, 41, 1365
116. Callaghan, P. T.; Gil, A. M. Macromolecules 2000, 33, 4116 It was concluded that "the origin of shear banding in (relatively polydisperse) polyacrylamide solutions is associated with hydrogen bond breakage above a critical shear rate". Such a conclusion was reached because other polymer (PS and PEO) solutions and poly(dimethylsiloxane) melt were found to display no shear banding: private communication with Paul T. Callaghan. PDMS is naturally polydisperse and consequently does not show shear banding
117. see: Li, X.; Wang, S. Q. Rheol. Acta 2010, 49, 89 We can indeed find a more recent example where hydrogen bonding seems to play a dominant role
118. See: van der Gucht, J. Phys. Rev. Lett. 2006, 97, 108301
119. Mead, D. W.; Larson, R. G.; Doi, M. Macromolecules 1998, 31, 7895
120. Graham, R. S.; Likhtman, A. E.; McLeish, T. C. B.; Milner, S. T. J. Rheol. 2003, 47, 1171
121. Marrucci, G. J. Non-Newtonian Fluid Mech. 1996, 62, 279