In our previous publication, we presented a molecular model to describe the dynamics of the interfacial layer between a flowing polymer melt and a die wall. We showed that the ensemble-averaged behavior of polymer molecules adsorbed on the wall could be successfully described in terms of the so-called bond vector probability distribution function (BVPDF). The BVPDF couples the chain orientation and chain stretch on the level of single segment, and thus is an extension of the orientation distribution function of Doi and Edwards introduced for inextensible chains. In this paper, the developed formalism is extended to molecules in the polymer bulk. We show how the well-known Doi and Edwards theory (DE) for inextensible chains based on the orientation distribution function can be naturally extended to include chain stretch and (convective) constraint release (CCR). The final constitutive equation accounts for such mechanisms on polymer chains as reptation, retraction, convection, contour length fluctuations, and (convective) constraint release. It is valid for both linear and non-linear flow regimes. The proposed theory is quantitative, and contains the same input parameters as the original DE model. As an application of the full theory, a simple equation of motion for the stress tensor is derived. Despite the simplicity, its predictions are found to be in good agreement with available experimental data over a wide range of flow regimes and histories.
Tchesnokov, M. A., Molenaar, J., Slot, J. J. M., & Stepanyan, R. (2004). A constitutive model with moderate chain stretch for linear polymer melts. Journal of Non-Newtonian Fluid Mechanics, 123(2-3), 185-199. https://doi.org/10.1016/j.jnnfm.2004.08.007