Self-Consistent Modeling of Constraint Release in a Single-Chain Mean-Field Slip-Link Model

Abstract

In slip‐link models, entanglements are discrete objects along the chain. As a result, it is not necessary to assume that constraint release is Rouse‐like motion of the primitive path. Instead, entanglements can be created or destroyed anywhere along the chain by the motion of surrounding chains. We call this motion “constraint dynamics,” since the imposition of constraints must occur, as well as their release. Also, since we deal with a stochastic model including full fluctuations, stress relaxation follows rigorously from the dynamics, and it is not necessary to assume that the relaxation modulus is a product of two simultaneous processes, as is typically done in tube models. We propose an efficient and self‐consistent method method for the implementation of constraint dynamics in a mean‐field slip‐link model. If binary interactions are assumed for entanglements, the implementation is mathematically equivalent to the algorithm employed by Takimoto and Doi. Unlike that work, however, the dynamics do not require pairing chains in the ensemble that are otherwise independent. Neither is it necessary to assume only binary interactions. We demonstrate that this implementation of constraint dynamics assuming binary chain interactions is able to capture the linear viscoelastic properties of bidisperse blends of polystyrene.