Dependence of nonlinear elasticity on filler size in composite polymer systems

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.