Correlation of mass fractal dimension and asymmetry

Small-angle X-ray experiments reveal the structure and structural changes of silica embedded in a rubbery host matrix due to the deformation of the surrounding elastomer. The experiments prove that the silica is initially isotropic and becomes anisotropic due to the deformation of the matrix. Increasing the elongation ratio of the polymer results in a larger mass fractal dimension of the silica clusters. The growing mass fractal dimension can be explained simply by a rearrangement of the primary particles within the clusters. However, for the first time, mathematical reasons are presented which clearly demonstrate that self-affine clusters have to be used instead of self-similar ones in order to describe the experiments correctly.