Size-dependent reinforcement of composite rubbers

Particulate fillers are often used to enhance the properties of soft materials; polymer composites often contain nanometer-sized particles to improve reinforcement, for example. The rationale for using nanometer-sized particles remains unclear, however, and classical micromechanical models cannot account for a scale dependent reinforcement. The systems studied here reveal that the reinforcement increases with decreasing filler size. A new relation is proposed, based only on the particle size, volume fraction, and relative moduli of filler and matrix, that describes the experimental results for reinforcement of both filled rubbers and a model system.