Structure and Properties of Reinforcing Fractal Filler Networks in Elastomers

Abstract The effect of filler networking on mechanical and electrical properties of elastomers is discussed on the basis of percolation theory and a recently developed kinetical cluster-cluster aggregation (CCA) model, respectively. In percolation theory pure geometrical arguments are considered and the physical properties of the filler network are related to the infinite cluster that is formed at percolation threshold. In the CCA-model the particles are allowed to fluctuate around their mean position on length scales that are comparable to the polymer fluctuation length. Upon contact of neighboring particles or clusters they stick together and form larger clusters. At sufficiently large filler concentrations (above the gel point of the filler network), a fractal filler network results that corresponds to a space-filling configuration of CCA-clusters. Structure and properties of the filler network in this model are compared to the fractal characteristics of percolation networks. In particular, the influence of anomalous diffusion of charge carriers on the scaling behavior of the conductivity is demonstrated for both types of fractal networks. For the elastic modulus an universal power law behavior results that is independent of the size of the filler particles and the applied rubber in both cases.