Prediction of the elastic response of polymer based nanocomposites: A mean field approach and a discrete simulation

The aim of this paper is to better understand mechanisms of reinforcement in particular nanocomposites, by studying the effects of filler ratio (varying from 0 to 45%) and strength of filler-filler interactions (either slightly or strongly bonded) on the viscoelastic behavior. Nanocomposites materials consisting, at room temperature, of submicronic rigid polysytrene (PS) particles randomly dispersed in a soft polybutylacrylate (PBA) polymeric matrix were obtained from mixtures of a film-forming PBA latex and a PS latex. Their viscoelastic behaviors have been characterized (i) after the film formation at room temperature and (ii) after an annealing treatment performed to enhance the interactions between neighboring PS particles (coalescence). The observed increase of elastic modulus and its evolution with temperature depend both on the filler ratio and on the strength of filler-filler interactions. Two micro-mechanical models have been then proposed to account for the short range interactions between filler particles: a self consistent scheme introducing a third rigidifying phase of matrix immobilized on the surface of filler particles, and a discrete model of sphere assembly taking into account the local contacts between filler/filler and matrix/filler. In addition to the good agreement with the experimental results, the discrete model highlighted the importance of filler-filler interactions on the reinforcement above the percolation threshold.