Effect of diameter distribution on two-dimensional scattering patterns of a rubber model filled with carbon black and silica NPs

Abstract

Coarse-grained molecular dynamics (CGMD) simulations of a polymer network filled with explicitly polydisperse nanoparticles (NPs) were performed to evaluate the changes in two-dimensional small-angle scattering (2D-SAS) patterns under elongation. The effect of a contrast between fillers and polymers was examined and the 2D-SAS patterns corresponding to X-ray scattering experiments with carbon black and silica NPs and neutron scattering experiments with deuterated polymers were tested. In the case of carbon black, a contrast between fillers and polymers is important because both contribute to the 2D-SAS patterns. By considering explicit polydisperse NPs, the 2D-SAS patterns of structure factor at an elongation ratio λ = 200% show four spot patterns which are similar to the patterns observed in experiments by Zhang et al., Macromolecules45, 1529 (2012). When the polydispersity of the filler diameters is small, a ring pattern originating from the uniform spheres became clear. However, this was not observed in our experiments because a larger polydispersity was used. It is concluded that an explicit diameter distribution in CGMD simulations is essential for comparison of 2D-SAS patterns between real experiments and virtual simulations.