Mechanical reinforcement of polymer nanocomposites: theory and ultra-small angle X-ray scattering (USAXS) studies

The microstructure of polymer-grafted nanoparticles in polymer melts that are chemically identical to the brush was investigated using ultra-small angle X-ray scattering (USAXS). The dispersions were thermodynamically stable. Particle size and melt molecular weight were varied such that the particle softness, L*, or the ratio of the brush thickness to the particle radius ranged from L* = 0.02-0.29. The experimentally extracted structure factors and radial distribution functions from USAXS show stronger particle interactions in lower molecular weight melts due to brush stretching corresponding to an enhancement in bulk properties at particle concentrations above the jamming transition. Good agreement was found between the measured structure factors and those predicted using the Percus-Yevick closure. Further, enhancement in the storage modulus, previously observed with rheology, was predicted through the Zwanzig-Mountain relation and Monte Carlo simulations. Overall, the use of USAXS and rheology enables the connection between experiment and theory to predict, and ultimately control the interactions of polymer-grafted nanoparticles in polymer melts.