A CONSTANT-CONTOUR-LENGTH REPTATION MODEL WITHOUT INDEPENDENT ALIGNMENT OR CONSISTENT AVERAGING APPROXIMATIONS FOR CHAIN RETRACTION

A reptation model for the primitive chain that does not assume indepen dent alignment or consistent-averaging for the retraction process, or equilibrium relaxation for the reptation process is proposed and compa red to the analytical expressions of Doi and Edwards in single-step, d ouble-step strains and steady-state shear flow. The Doi and Edwards mo del with independent alignment approximation underpredicts the magnitu de of the relaxation modulus by 25%, and consistently overpredicts the magnitude of the damping function; for steady shear flow, it predicts the correct shape for the steady-state viscosity and the first normal stress difference coefficient, although the magnitude is incorrect. T he analytical expressions of Doi and Edwards without independent align ment approximation are excellent approximations to the damping functio n. In double-step strains, the expressions of Doi assuming consistent averaging, but no independent alignment, predict well the stress decay following the second strain. Linear response theory is found to be in valid for describing the stress relaxation following single-step strai n for the models considered. Similar to the Doi and Edwards model, no overshoot for the first normal stress difference is observed for the s imulation model. Unlike the Doi equation derived without the independe nt alignment approximation but restricted to double-step strains, the simulation model proposed here can be easily generalized to complex fl ow fields. No contour length fluctuation or constraint release is cons idered in this model, and chain retraction is assumed to be instantane ous.