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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 structural scaling regime at large sizes. The hierarchical filler network is described by two crossover frequencies and associated relaxation times, τ* and τcc, and two related structural scaling regimes.

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Porous elastomeric polymers have been used in a wide range of applications due to their unique characteristics such as biocompatibility, gas permeability, thermal stability, and hydrophobic and dielectric properties. Poly(dimethyl siloxane) (PDMS), a commercially available elastomer, has also been shown to exhibit specific acoustic properties. However, the materials properties were limited due to a lack of control over the chemistry used to prepare the crosslinked PDMS elastomer. Here, the synthesis of PDMS-based polymerized medium internal phase emulsions (polyMIPEs) with tunable storage shear moduli (G') have been prepared using macromolecular thiol-ene reactions. Storage shear moduli values from ~38 to ~330 kPa were achieved by changing the stoichiometric ratio of the thiol-to ene-functionalized PDMS whereas the porosity of the polyMIPEs was controlled by the volume of aqueous phase used in the emulsion formulation. Very low sound velocities (~40 m/s) through the porous materials were recorded using acoustic characterization. Therefore, this work provides an example of the synthesis of soft polyMIPEs with possible applications as acoustic materials.

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