Concepts and conflicts in nanoparticles reinforcement to polymers beyond hydrodynamics

With substantial progresses in reinforcement mechanism of nanoparticle filled polymers (NPFPs) beyond the hydrodynamic limit, now is the time to reconsider this topic characterized by emergence of a universal solid-like rheology at nanoparticle contents above a critical value in relation to the heterogeneously retarded polymer dynamics and structured filler network. A comprehensive survey is presented herein to report the cluster-cluster aggregation model, and jamming, percolation and soft colloidal dynamics theories and their applications in NPFPs in relation to nanoparticle reinforcement of polymers beyond hydrodynamics. Methods for separating the filler contribution to the reinforcement within the frame work of two-phase models are highlighted and three main kinds of theoretical models (cluster-cluster aggregation model, jamming theory, and rigidity percolation theory) are discussed for addressing the conflicts of concepts in experiments. Many years research practice shows that there is still lack of a credible relation describing the reinforcement with respect to the network structure (nanoparticle dispersity) mediated by microscopic interaction and sample preparation. Furthermore, viscoelasticity of the filler phase is discussed according to two-phase models and beyond. Finally several open challenges are remarked.