Open problems in tube models for concentrated polymers

In this work we examine the Doi-Edwards (D-E) theory corrected with convective constraint release (CCR) to show that open problems still remain. One of them is incomplete fulfilment of the Cox-Merz rule. Another problem is underprediction of the normal stress ratio in shear in the limit of low stresses. The latter problem is directly linked with deformation tensor Q of D-E theory. We then show that in order to solve these problems one should account for the fact that the deformation process makes the constraining tubes elliptical in cross-section, an assumption consistent with the affine deformation of the grid of topological constraints. It is shown, however, that the affine deformation of the tube segments overpredicts the desired corrections. It so appears that, although the tube section must change during deformation to become elliptical, the constraint deformation is less than affine.