The nonlinear elastic response of filled elastomers: Experiments vs. theory for the basic case of particulate fillers of micrometer size

Standard particulate fillers utilized to enhance the macroscopic elasticity of elastomers — most notably, carbon black and silica particles — are inherently of nanometer size. Because their size is comparable to the typical lengths of the polymer chain segments between crosslinks in the embedding elastomers, there is a plurality of microscopic mechanisms by which such fillers provide macroscopic enhancement. Well-known among these is the so-called hydrodynamic effect, which has long been thought to become increasingly dominant as the size of the fillers increases from nanometer to micrometer or larger length scales. This paper reports a combined experimental/theoretical investigation aimed at critically examining such a belief by isolating — that is, by excluding the presence of other enhancing mechanisms, such as interphases and occluded rubber — and quantifying the hydrodynamic effect behind the enhanced nonlinear elastic response of a prototypical class of particle-filled elastomers: polydimethylsiloxane (PDMS) featuring various cross-link densities filled with an isotropic distribution of glass spherical particles of monodisperse micrometer size. The close agreement found between the experiments for a variety of filled PDMS elastomers with the predictions based on recently developed rigorous homogenization results corroborate that the observed enhancement in the nonlinear elastic response of the PDMS elastomers upon the addition of the glass particles is indeed solely due to the hydrodynamic effect. In addition to filling a lacuna in the basic experimental knowledge of filled elastomers, the findings reported here also have direct practical implications on the modeling of a number of emerging active filled elastomers, such as for instance magnetorheological elastomers, wherein the iron filler particles — in contrast to standard fillers — are typically micrometer in size.