Structural modelling and stiffness of filled elastomers

A realistic model of spatial arrangement of fillers in the rubber matrix is developed. The structural parameters of the model such as the distribution of filler sizes, the fractal characteristics of clusters (agglomerates) and the presence of large dense particles (micropellets) are taken from the AFM-images of carbon black filled styrene–butadiene vulcanizates. A descriptor of filler distribution in the matrix, namely an index of heterogeneity, is proposed. The analysis of stiffness of synthesized 3D-structures allows us to determine the minimal representative size of the constructed systems and to judge the validity of various model simplifications (e.g., fillers of equal size or random arrangement, lack of micropellets, etc.).