Simulation of aggregate structure and SANS-spectra in filled elastomers

We report preliminary simulations of anisotropic scattering from aggregates of small hard spherical particles embedded in an elastic polymer matrix, using simple geometrical methods. First we build several types of aggregates in three dimensions: crystalline, amorphous compact, fractals, of different numbers of particles and varying polydispersity. We then turn to the spectra of deformed samples simulated in two dimensions. We impose an affine displacement inside the matrix to the fillers, which can be isolated particles or small aggregates, and account for the collisions which arise due to lateral shrinking of the material. The two-dimensional scattering spectra are shown and discussed. They reproduce experimentally observed isointensity curves: ellipses, banana-shaped maxima and splitting of these maxima in four spots. Finally, we explore the consequences of the reduction to two dimensions via statistics of the number of collisions. It is found that even if collisions are more important in 3 dimensions, the behavior is qualitatively similar in two and three dimensions.