Theories and simulations of polymer-based nanocomposites: From chain statistics to reinforcement

A survey of the present understanding of particle-filled polymers is presented, as obtained from either theoretical or computational approaches. We concentrate on composites in which the nanoparticles are either spherical or statistically isotropic aggregates, and the matrix is a homopolymer melt or a cross-linked elastomer. Recent progress has been prompted by the preparation and careful characterization of well-defined model systems, as well as by theoretical developments and the application of computer simulation to increasingly realistic models. After an introduction providing the main motivations (Section 1), an overview of the basic phenomenology and recent experimental results is presented (Section 2), with special emphasis on the Payne effect and related aspects. In Section 3, we discuss results of equilibrium molecular dynamics and Monte Carlo simulations of polymer chains in the presence of nanoparticles. After a concise theoretical description, these are compared with those obtained from integral equation and density functional approaches (Section 4). The molecular origins of the inter-particle-depletion interaction are discussed, as well as the phase-separation diagram of the nanoparticle/polymer system. The related issue of polymer chains and networks compressed between planar surfaces is also dealt with. In Section 5 simulations and theories of polymer dynamics at the interface are discussed, with special emphasis on the effects of surface roughness and on the vicinity of the glass transition. In Section 6 the overall viscoelastic response of polymer nanocomposites is considered, both from the point of view of molecular-level simulations and of continuum mechanics approaches. The concluding remarks (Section 7) discuss some of the open challenges in the field.