High Resolution Shear Profile Measurements in Entangled Polymers

Abstract

We use confocal microscopy and particle image velocimetry to visualize motion of 250-300 nm. fluorescent tracer particles in entangled polymers subject to a rectilinear shear flow. Our results show linear velocity profiles in polymer solutions spanning a wide range of molecular weights and number of entanglements (8 Z 56), but reveal large differences between the imposed and measured shear rates. These findings disagree with recent reports that shear banding is a characteristic flow response of entangled polymers, and instead point to interfacial slip as an important source of strain loss. DOI: 10.1103/PhysRevLett.101.218301 PACS numbers: 47.57.Ng, 83.10.Kn, 83.80.Rs Flow properties of entangled polymers are important in myriad commercial processes for molding, extruding, and spinning plastic components. The Doi-Edwards (DE) theory provides the most successful molecular framework for understanding these properties. Developed around the reptation or ''tube'' model [1], this theory contends that a melt of entangled polymers responds affinely to instantaneous macroscopic deformations. The affine response is sustained by long-lived entanglements between molecules and causes the network of entanglements (tube) constraining any given molecule to orient and stretch in the same way as does the macroscopic melt. Polymer molecules trapped in the tube initially stretch and orient in synergy with their environment.DE predictions for step strain, oscillatory, and steady shear flows agree, sometimes quantitatively, with experiments [2][3][4][5][6]. A more controversial prediction is that under steady shear, the shear stress is a multivalued function of the imposed shear rate. Thus, simple shear flow is unstable to perturbations in shear rate and should produce shear banding [7,8]. Surprisingly, with the exception of entangled wormlike micellar fluids [9][10][11], banding is generally not observed in flows of entangled polymers at any shear rate. This implies that some other dynamic processes not taken into account by the theory must contribute to the fluid's response. Efforts to date have focused on understanding how convective acceleration of reptation [12][13][14][15][16][17], tube diameter shrinkage [18], and slip [19][20][21][22] near the shearing surfaces influence this prediction. All three processes eliminate or weaken the driving force for entangled polymers to shear band and, when integrated into the DE theory, lead to steady shear stress predictions that compare favorably with experiments using moderately entangled polymers.Recent velocity profile measurements using 10 m particles dispersed in entangled polybutadiene solutions show, for the first time, that entangled polymer systems do in fact appear to shear band [23][24][25]. Surprisingly, these studies find that shear banding occurs even in solutions with intermediate levels of entanglements, generally thought to be well described by DE theory with the aforementioned modifications. Parameters such as shear strain and shear rate, widely used to characterize sh...

Shear Banding of Complex Fluids

“…These arguments were shown correct in very recent simulations [152]. Since 2006, strong efforts have been made to provide a 1D picture using velocimetry techniques in various flow geometries, mostly CP [87,126] and parallel plates [17,74] and marginally TC [78] and pipe [151]. During the past decade, extensive sets of particle tracking velocimetry (PTV) experiments combined with global rheology by Wang's group [146] showed that shear banding can emerge in polymer solutions and melts (Figure 3a).…”

Constitutive equations for the flow behavior of entangled polymeric systems: Application to star polymers

“…1 On the other hand, in recent experimental work with entangled synthetic polymers shear banding was not observed, but instead interfacial slip was suggested as the origin of strain loss. 10,11 Gradient banding has also been found in glassy starlike polymers. [12][13][14] Here, depending on the functionality and arm length of the star polymers, banding may be related to entanglements and/or to excluded volume interactions.…”

Flow field visualization of entangled polybutadiene solutions under nonlinear viscoelastic flow conditions

“…A well-known failure of the DE theory lies in its inability to predict the experimentally observed monotonic steady state constitutive relationship between shear stress and shear rate [Doi and Edwards (1979)]. Specifically, if the constitutive curve indeed is non-monotonic as predicted by the DE model, shear banding should occur, meaning that bands with different shear rates could form in the sample above a critical shear stress or shear rate; however, this non-monotonicity or shear banding has not been normally observed [Hu (2010); Hayes et al (2008)]. On the other hand, in step strain tests, it was found that the DE model underestimates the strain softening behavior in some cases [Osaki and Kurata (1980); Vrentas and Graessley (1982)].…”