Network model for the viscoelastic behavior of polymer nanocomposites

A theoretical network model reproducing some significant features of the viscoelastic behavior of unentangled polymer melts reinforced with well dispersed non-agglomerated nanoparticles is presented. Nanocomposites with low filler volume fraction (∼10%) and strong polymer–filler interactions are considered. The model is calibrated based on results obtained from discrete simulations of the equilibrium molecular structure of the material. This analysis provides the statistics of the network of chains connecting fillers, of dangling strands having one end adsorbed onto fillers, and that of the population of loops surrounding each nanoparticle. The network kinetics depends on the attachment–detachment dynamics of grafted chains of various types and is modeled by using a set of convection equations for the probability distribution functions. The overall viscoelastic response depends strongly on the lifetime of the polymer–filler junctions. The largest reinforcement is observed at low strain rates and low frequency oscillations. A solid like behavior is predicted for systems in which the polymer molecules interact strongly with the nanoparticles, effect which is associated with the behavior of the network of bridging segments.