The reptation model with segmental stretch

Abstract

The Doi-Edwards model with segmental stretch and a non-linear finitely extensible spring law is described and examined in simple flow situations where analytic results are derivable; namely oscillatory flow and steady state flow at high deformation rates. The model is shown to be consistent with the Bueche-Ferry hypothesis in fast large strain unidirectional flows but to violate this rule in small strain reversing flows. The discrepancy is identified with a preaveraging approximation used to describe the relative tube-chain velocity. Experimentally verifiable scaling rule for the birefringence as a universal function of a planar flow-type parameter and deformation rate are identified. Sensitivity to the extensional flow character, absent in the original tube model, manifests itself with the introduction of segmental stretch. Although the model generates a non-separable memory function kernel the deformation dependence of the memory function is quantitatively shown to have negligible impact on the predicted theological properties relative to the original Doi-Edwards model. With this simplification, relatively uncomplicated approximations to the segmental stretch model can be deduced.