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 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.