Polydispersity for tuning the potential of mean force between polymer grafted nanoparticles in a polymer matrix

We present an integrated theory and simulation study of polydisperse polymer grafted nanoparticles in a polymer matrix to demonstrate the effect of polydispersity in graft length on the potential of mean force between the grafted nanoparticles. In dense polymer solutions, increasing polydispersity in graft length reduces the strength of repulsion at contact and weakens the attractive well at intermediate interparticle distances, completely eliminating the latter at high polydispersity index. The reduction in contact repulsion is attributable to polydispersity relieving monomer crowding near the particle surface, especially at high grafting densities. The elimination of the midrange attractive well is attributable to the longer grafts in the polydisperse graft length distribution that introduce longer range steric repulsion and alter the wetting of the grafted layer by matrix chains. Dispersion of the grafted particles is stabilized by increased penetration or wetting of the polydisperse grafted layer by the matrix chains. This work demonstrates that at high grafting densities, polydispersity in graft length can be used to stabilize dispersions of grafted nanoparticles in a polymer matrix at conditions where monodisperse grafts would cause aggregation.