Microscopic Picture of Constraint Release Effects in Entangled Star Polymer Melts

Abstract

The constraint release (CR) effect in entangled branched polymers is generally described by the widely accepted dynamic tube dilation (DTD) theory based on the tube model, which predicts the stress relaxation function reasonably well, but not the dielectric or arm end-to-end vector relaxation. The microscopic picture of entanglement dynamics even in the simple case of star polymers is still not fully resolved. In this work, we first perform molecular dynamics (MD) simulations of symmetric star polymer melts using the Kremer–Grest bead–spring model. The entanglement events are analyzed microscopically using the persistent close contacts between mean paths of neighboring polymer strands. The resulting survival probability function of these entanglements or close contacts shows reasonably good agreement with the stress relaxation function, which provides qualitative evidence for the binary picture of entanglements. On the basis of this understanding, we further investigate the star arm retraction and CR effects using the coarse-grained single-chain slip-spring model originally developed by Likhtman and also a simplified single-chain stochastic model. In both MD and slip-spring simulations we verified the mechanism proposed by Shanbhag et al. that constraint release events lead to the insertion of new entanglements in between the branch points and deepest entanglements so that the last remaining deepest entanglements are deleted by relatively shallow arm retractions. Our simulations further revealed that for the entanglements sitting on a target star arm, only those destroyed by the free end of the given arm dominate the arm end-to-end vector relaxation, while the broad constraint release spectrum, together with the excluded volume of entanglements and the reflecting boundary at the branch point, produces an accelerated drift of the mean positions of these specific entanglements toward the arm-end, which is an essential mechanism for understanding the relaxation of star polymers in concentrated solutions or melts. Our findings call for an examination of the microscopic foundation of conventional DTD picture and inspire the development of quantitative theories with consideration of more microscopic details.