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Nanosized filler particles enhance the mechanical properties of polymer composites in a size-dependent fashion. This is puzzling, because classical elasticity is inherently scale-free, and models for the elasticity of composite systems never predict a filler-size dependence. Here, we study the industrially important system of silica-filled rubbers, together with a well-characterized model-filled crosslinked gel and show that at high filler content both the linear and nonlinear elastic properties of these systems exhibit a unique scaling proportional to the cube of the volume fraction divided by the particle size. This remarkable behavior makes it possible to predict the full mechanical response of particle-filled rubbers for small but finite deformations based solely on the rheology of the matrix and the size and modulus of the filler particles.

Dependence of nonlinear elasticity on filler size in composite polymer systems