Impact of an Emergent Hierarchical Filler Network on Nanocomposite Dynamics

Aggregated polymer fillers, such as carbon black and silica, at concentrations above the percolation threshold form an emergent structure, the hierarchical filler network, in immiscible systems where dispersion is driven by accumulated strain. It is proposed that the hierarchical filler network is composed of a primary nanoscale network that locally percolates at ∼5 vol % of aggregates, associated with changes in the dynamic spectrum at low strain, and a secondary micrometer-scale network that globally percolates at ∼20 vol % associated with the Payne effect and electrical conductivity. A model is proposed with an elastomer dominated dynamic response described by Einstein–Smallwood behavior at high frequencies and small sizes and a filler network dominated response at low frequencies and large sizes. The nanoscale mesh size correlates with this transition in low strain dynamic response. The micrometer-scale network displays a gel-like dynamic response at very low frequencies and a corresponding gel-like s...