Nonlinear flow behavior of entangled polymer solutions: Yieldlike entanglement-disentanglement transition

Macromolecules

Volumn 37, Issue 24, 2004, Pages 9083-9095

  Tapadia, Prashant ^a   Wang, Shi Qing ^a  

^a The University of Akron   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAIN RECOIL; FLOW CELLS; FLOW RESPONSES; POLYMER SOLUTIONS;

CONFORMATIONS; ELASTIC MODULI; FUNCTIONS; SHEAR FLOW; SHEAR STRESS; TORQUE;

POLYMERS;

EID: 10044290787     PISSN: 00249297     EISSN: None     Source Type: Journal    
DOI: 10.1021/ma0490855     Document Type: Article

References (47)

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22. Subsequently we choose to use the term "mode of imposing constant velocity" instead of "controlled-rate mode" to avoid any confusion about the true meaning of this conventional protocol.
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27. Hoppmann, W. H.; Miller, C. E. Trans. Soc. Rheol. 1963, 7, 181. Secondary flow is observed in this study for even a Netwonian fluid because of the unusually large cone angles employed.
28. 33 in capillary flow of highly entangled polymers, where the shear stress varies linearly with the radius and is highest at the wall. In that case the first transition to observe upon gradually increasing the applied pressure must involve the very first layer of the material. In other words, such a transition would be sharp and interfacial in nature. Because of the stress gradient, no abrupt transition would be observable at higher pressures in contrast to the present case of cone-plate geometry where the shear stress is presumably uniform and every layer undergo "chain disentanglement", leading to the bulk flow transition.
29. A related concept is coil-stretch transition. There are only two cases where the concept of coil-stretch transition (C-ST) is invoked. The first, also most extensively studied, involves subjecting a dilute polymer solution to flow, as exclusively analyzed by de Gennes (J. Chem. Phys. 1974, 60, 5030) and recently verified (Schroeder, C. M.; et al. Science 2003, 307, 1515). In the second case, the C-ST occurs to the tethered (or adsorbed) chains during a stick-slip transition. We use the word "uncoil" instead of "stretch" because the word "stretch", as used repeatedly in most of the recent theoretical publications such as refs 16 and 18, implies that the contour length exceeds its equilibrium value, and the increase of the contour length is continuous with respect to the flow condition. See footnote 29 for a more precise depiction of the uncoil state in our picture.
30. A related concept is coil-stretch transition. There are only two cases where the concept of coil-stretch transition (C-ST) is invoked. The first, also most extensively studied, involves subjecting a dilute polymer solution to flow, as exclusively analyzed by de Gennes (J. Chem. Phys. 1974, 60, 5030) and recently verified (Schroeder, C. M.; et al. Science 2003, 307, 1515). In the second case, the C-ST occurs to the tethered (or adsorbed) chains during a stick-slip transition. We use the word "uncoil" instead of "stretch" because the word "stretch", as used repeatedly in most of the recent theoretical publications such as refs 16 and 18, implies that the contour length exceeds its equilibrium value, and the increase of the contour length is continuous with respect to the flow condition. See footnote 29 for a more precise depiction of the uncoil state in our picture.
31. e, i.e., the uncoiling will involve straightening the chain backbone. Eventually at higher stresses yet, the uncoiling may look more like stretching, and coil-uncoil develops into coil-stretch.
32. Muller, R.; Pesce, J. J.; Picot, C. Macromolecules 1993, 26, 4356. In this work, a polystyrene sample between parallel plates was sheared in linear displacement at a sufficiently high stress of 0.2 MPa for a total strain of up to 4, far less than what is perhaps necessary to produce a state of high chain orientation.
33. Bent, J.; et al. Science 2003, 301, 1691. In this work, polystyrene is subjected to a channel flow, where the maximum level of shear strain is approximately 6L/H = 48, and the averaged strain is only 24, which may not be sufficient to produce chain disentanglement and uncoiling. In channel flow, only a small fraction of sample near the wall is under high shear. It is not surprising that only a small amount of averaged chain anisotropy is observed in such a flow apparatus under the specified flow condition.
34. The "hysteresis" points reported in Figure 1 of ref 27 were taken from a similar "hysteresis" experiment. In other words, those half-filled circles were similar to the data corresponding to 2.5 and 3.0 kPa. Since the 10% solution based on oBD1 is much slower, we did not shear the sample long enough at those stresses for it to make the EDT. Given longer durations of shear, we would have found those half-filled circles to be the filled circles in ref 27. In other words, there is no true hysteresis.
35. Wang, S. Q. Adv. Polym. Sci. 1999, 138, 227. The interfacial stick-slip transition exhibits hysteresis and is first order because the coil-stretch transition responsible for the wall slip involves the tethered (naturally adsorbed) chains. For these tethered chains, the shear flow is equivalent to an elongational flow.
36. Bingham, E. C. Fluidity and Plasticity; McGraw-Hill: New York, 1922; pp 215-218. The Bingham expression can be found in popular monographs such as: Bird, R. B.; Armstrong, R. C.; Hassager, O. Dynamics of Polymeric Liquids; Wiley & Sons: New York, 1987; p 228. Macosko, C. W. Rheology; VCH: New York, 1994; p 92. Unfortunately, the Bingham formula does not describe a yieldlike transition correctly because upon yield the shear rate attains a finite value instead of increasing continuously from zero as described by Bingham.
37. Bingham, E. C. Fluidity and Plasticity; McGraw-Hill: New York, 1922; pp 215-218. The Bingham expression can be found in popular monographs such as: Bird, R. B.; Armstrong, R. C.; Hassager, O. Dynamics of Polymeric Liquids; Wiley & Sons: New York, 1987; p 228. Macosko, C. W. Rheology; VCH: New York, 1994; p 92. Unfortunately, the Bingham formula does not describe a yieldlike transition correctly because upon yield the shear rate attains a finite value instead of increasing continuously from zero as described by Bingham.
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47. See Figure 5c in: Wang, S.; Wang, S. Q.; Halasa, A.; Hsu, W.-L. Macromolecules 2003, 36, 5355 for the temperature dependence of the 1,4-PBD viscosity, which shows that the viscosity of 1,4-PBD drops to half of its value as the temperature changes from 30 to 49°C.