A Guide for Hydrodynamic Reinforcement Effect in Nanoparticle-filled Polymers

Despite of substantial progresses in reinforcement mechanism of nanoparticle-filled polymers (NPFPs), there are great debates about the fundamental hydrodynamics theories and the deformation localization lasting many years. In this article, we discuss the in retrospect theoretical hydrodynamic approaches used in the field of nanoparticle reinforcement for providing a critical review with the aim to identify limitations and open questions inherent to various versions of the theory. Such a discussion could serve as a guide for the formulation and modification of a model for the reinforcement in NPFPs. We look into the relationship between the highly inhomogeneous microscopic structure and the rather universal reinforcement involved in hydrodynamics of nanoparticle and their rigid fractal aggregates. Then the frequently neglected area of strain and stress amplification effects that are sometimes confused with the hydrodynamic one are discussed and highlighted. Finally, we discuss the inhomogeneously structuring characteristics of NPFPs at high filling levels, with special attention paid to the limitations of both theoretical and experimental studies. Several open challenges are remarked upon.