Open problems in tube models for concentrated polymers

In this work we examine the Doi-Edwards (D-E) theory corrected with convect ive constraint release (CCR) to show that open problems still remain. One o f them is incomplete fulfilment of the Cox-Merz rule. Another problem is un derprediction of the normal stress ratio in shear in the limit of low stres ses. 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 acco unt for the fact that the deformation process makes the constraining tubes elliptical in cross-section, an assumption consistent with the affine defor mation of the grid of topological constraints. It is shown, however, that t he affine deformation of the tube segments overpredicts the desired correct ions. It so appears that, although the tube section must change during defo rmation to become elliptical, the constraint deformation is less than affin e. (C) 1999 Elsevier Science B.V. All rights reserved.