Elastic Moduli of Polymer Nanocomposites Derived from the Molecular Structure

Abstract

Polymer based nanocomposites are a novel class of materials in which the polymer matrix is filled with nanoscale fillers, nanoparticles or nanotubes. These materials exhibit interesting mechanical, optical and transport properties and are currently under intense scrutiny. In this work we focus on a model polymeric material filled with spherical nanoparticles, with the goal of identifying the relationship between the molecular structure and the elastic properties of the composite. The effect of the confinement imposed by fillers on chain conformations in the vicinity of the interface is investigated using an atomistic model for the polymeric material. The polymer structure is determined by lattice Monte Carlo simulations. Realistic energetics, including excluded volume and cohesive interactions in the bulk polymer, as well as filler-polymer interactions are considered. The elastic constants of the polymer structure are derived from the free energy of the system of chains, and based on the determined structure. Four contributions to the matrix polymer stiffness are identified: due to bonded and non-bonded interactions, due to the energetic interaction between polymer and fillers, and due to the entropie component of the free energy. The resulting continuum model for the matrix is in the form of a material with graded elasticity in a spherical layer surrounding each filler. The filler is considered rigid. The overall composite moduli are obtained by homogenization of this graded structure. The scaling of the overall composite moduli with filler radius at constant filler volume fraction is determined.