New theoretical considerations in polymer rheology: Elastic breakdown of chain entanglement network

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, 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 fiml arises and causes conformational deformation in each load-bearing strand between entanglements. The chain deformation builds up a retractive force fretract 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 lent has entropy equal to kB T, the disentanglement criterion is given by fretract > fent ∼ kB T lent in the case of interrupted deformation. This condition identifies fent 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 fiml cannot sustain the elevated fretract. 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.