Structure and relaxation of end-linked polymer networks

Abstract

The kinetics of end crosslinking a linear polymer melt and the dynamics of the resulting network is studied using molecular dynamics (MD) simulations. Starting from equilibrated melts of linear chains of length ranging from 1/3Ne to 3Ne, where Ne is the entanglement length, tetrafunctional crosslinkers are attached to a fraction x of the chain ends. When a free end comes within a short capture distance rx from an unsaturated crosslinker, the chain ends are attached. With a stoichmetric number x of crosslinkers, the long time kinetics for the number of free ends and the number of unsaturated crosslinkers decays as a power law in time t−a, with a≊0.5 for the present range of chain lengths. The resulting networks are then used to study the effect of entanglements on the motion of the crosslinks and the modulus of the network. Using a cluster search algorithm, the microscopic characteristics of the networks are determined. This allows us to compare our simulated networks to theoretical models of rubber elasticity without any adjustable parameters. While our results for the modulus are close to the phantom network model for the shortest chains, for the longer chains our results clearly support the Edwards tube model. Already for the presently employed largest chains the modulus is about 1.9 times larger than predicted from the affine model. Asymptotically, within an affine network model, about 2.2 entanglement lengths are needed to contribute to the modulus in the same way as one elastically active chemical crosslink. The data agree very well with recent experiments.