Contour length fluctuations and constraint release in entangled polymers: Slip-spring simulations and their implications for binary blend rheology

We study the interaction between constraint release and contour length fluctuations in well entangled polymers, by means of a set of slip-spring simulations in which the rate of constraint release is precisely controlled. In the present simulations, a fraction f = 0.9 of the slip-springs undergo constraint release, whilst the remaining slip-springs do not, as an idealised model to mimic the constraint release environment of a bidisperse polymer melt. Both populations of slip-springs allow reptation of the chain. Our analysis of the data indicates time and parameter regions in which contour length fluctuations occur effectively along a thin tube, or along a diluted fat tube. We predict the parameters for which case each is observed and the rate of relaxation due to contour length fluctuations in each region. Finally, we draw the implications of the simulations for bidisperse blend rheology, by revisiting the classic “Viovy diagram” for such melts. We relocate some of the lines on the original diagram, and identify new regimes, based on the physics and quantitative information supplied by the simulation data. In particular, we identify a new region in the diagram in which along-tube motion of the long chains is predominantly along the contour of the thin tube, yet contour length fluctuations occur in the fat tube, resulting in an acceleration of the terminal relaxation. We successfully and quantitatively locate a wide range of literature data on our redrawn diagram.