A Phase Diagram for Polymer-Grafted Nanoparticles in Homopolymer Matrices

We quantified the stability of polystyrene- (PS-) grafted silica nanoparticles (NPs) in PS matrices with ultrasmall angle X-ray scattering (USAXS) and transmission electron microscopy (TEM) and developed a phase diagram to predict NP dispersion based on the graft polymer density, σ, and the graft and free polymer molecular weights, or N and P, respectively. Using controlled/living polymerizations, polymer nanocomposites were formulated with silica NPs of radius, R = 9 nm where σ = 0.10–0.70 chains/nm 2 at an essentially constant N = 61–68 kg/mol. The matrix molecular weight was varied from P = 37–465 kg/mol permitting us to vary the swelling ratio, P / N = 0.6–7.7. Using USAXS and TEM, we determined whether the PS-grafted NPs were stable and dispersed uniformly, or were unstable and aggregated within the matrix. From these measurements we developed a phase diagram for NP miscibility with respect to σ, P, and N to determine the allophobic and autophobic transitions that correspond to the wetting the drying of the graft polymer brush which control NP stability in polymer matrices.