Entanglement-induced reinforcement in polymer nanocomposites

Abstract

We propose a coarse-grained model able to describe filled entangled polymer melts. Our purpose is to study the reinforcement caused by the effect of fillers on the entanglement network, as speculated in previous experimental work, and also observed in molecular dynamics studies. In this work, the filler volume fraction effect, the distribution of the fillers (cubic lattice, randomly dispersed, and small clusters randomly dispersed) and the presence or absence of grafted chains on the fillers are investigated. Our model is based on a “slip-link” model initially developed to study the entanglements in pure polymer melts and offers a less costly computational method than molecular dynamics simulations for the study of entangled polymer melts. The polymer chains are described as Rouse chains of Brownian particles connected by Hookean springs, and are subject to friction and random forces. Entanglements are artificially imposed by objects (slip-links) exhibiting statistical fluctuations that do not modify the equilibrium statistics of the melt. In addition we introduced excluded volume interactions between chain segments, to take into account the incompressibility of the melt. These excluded volume interactions do not perturb the dynamics of the chains in the homogeneous limit as expected from theoretical considerations on short range interactions. Finally, the fillers are modeled by immobile spherical objects, with or without grafted chains, which interact with a repulsive potential with the chain monomers. The chains grafted onto the fillers are represented by “additional slip links” confined in the vicinity of each filler. We first present the effect of the filler distribution and filler volume fraction, considering only bare fillers. Then, the effect of grafted chains via the additional slip-links is also shown as a function of the same parameters. Our results show that the presence of grafted chains induces an important change in the viscosity, calculated by integrating the stress autocorrelation function. Both the plateau value and the terminal relaxation time depend on the density of fillers and on the number of grafted chains. Moreover, we find that a disordered filler configuration induces confinement effects that amplify reinforcement compared to the case of a perfectly ordered configuration.