Recent experimental evidence has motivated us to present a set of new theoretical considerations and to provide a rationale for interpreting the intriguing flow phenomena observed in entangled polymer solutions and melts [P. Tapadia and S. Q. Wang, Phys. Rev. Lett. 96, 016001 (2006); 96, 196001 (2006); S. Q. Wang et al., ibid. 97, 187801 (2006)]. Three forces have been recognized to play important roles in controlling the response of a strained entanglement network. During flow, an intermolecular locking force f(iml) arises and causes conformational deformation in each load-bearing strand between entanglements. The chain deformation builds up a retractive force f(retract) within each strand. Chain entanglement prevails in quiescence because a given chain prefers to stay interpenetrating into other chains within its pervaded volume so as to enjoy maximum conformational entropy. Since each strand of length l(ent) has entropy equal to k(B)T, the disentanglement criterion is given by f(retract)>f(ent) approximately k(B)Tl(ent) in the case of interrupted deformation. This condition identifies f(ent) as a cohesive force. Imbalance among these forces causes elastic breakdown of the entanglement network. For example, an entangled polymer yields during continuous deformation when the declining f(iml) cannot sustain the elevated f(retract). This opposite trend of the two forces is at the core of the physics governing a "cohesive" breakdown at the yield point (i.e., the stress overshoot) in startup flow. Identifying the yield point as the point of force imbalance, we can also rationalize the recently observed striking scaling behavior associated with the yield point in continuous deformation of both shear and extension.

We report a flow phenomenon in entangled polymer solutions that has never been described in the literature. A large-amplitude oscillatory shear was imposed on the polymer sample at a frequency higher than the overall chain relaxation rate. The resulting chain orientation led to a new environment in which the initially well-entangled chains managed to disentangle inhomogeneously in space. A layer lacking chain entanglement developed to take the load of the imposed strain. As a result of this nonlinearity, the rest of the sample avoided significant deformation and its chain entanglement remained intact.

The recent particle-tracking velocimetric (PTV) observations revealed that well-entangled polymer solutions and melts tend to either exhibit wall slip or assume an inhomogeneous state of deformation and flow during nonlinear rheological measurements in simple-shear rheometric setups. Many material parameters and external conditions have been explored since 2006, and a new phenomenological picture has emerged. In this Perspective, we not only point out the challenges to perform reliable rheometric measurements but also discuss the relation between wall slip and internal (bulk) cohesive breakdown and summarize all available findings in terms of a phase diagram. This map specifies the conditions under which shear homogeneity, interfacial slip, and bulk shear inhomogeneity would prevail. The paper is closed by enumerating a number of unresolved questions for future studies.

Large step shear experiments revealed through particle tracking velocimetry that entangled polymeric liquids display either internal macroscopic movements upon shear cessation or rupturelike behavior during shear. Visible inhomogeneous motions were detected in five samples with the number of entanglements per chain ranging from 20 to 130 at amplitudes of step strain as low as 135%.

Velocity profiles of six entangled polybutadiene solutions (PBD) have been determined during startup shear using a particle tracking velocimetric (PTV) technique, where the number Z of entanglements per chain in these solutions varies from 13 to 119, depending on the PBD molecular weight and solution concentration. Flow behavior of these solutions at various rates in the stress plateau region has been investigated in both paralleldisk and cone-plate cells. For the least entangled solution with Z ) 13, homogeneous shear was observed under all flow conditions. The solution with Z ) 27 displayed inhomogeneous shear after the stress maximum before returning to a linear velocity profile at long times. For solutions with Z g 40, shear banding was observed in both transient and steady states for a range of shear rates in the stress plateau region. At sufficiently high rates, shear homogeneity returns in steady state for these solutions (Z g 40) after initial banding.