Interaction between polydisperse polymer-grafted nanoparticles in polymer nanocomposites

In this research, we develop a new numerical scheme of self-consistent field theory (SCFT) to quantify interaction properties between two spherical nanoparticles (NPs) coated with polydisperse homopolymer grafts in chemically identical homopolymer melts. In our numerical SCFT calculation, two-dimensional finite volume method (FVM) which efficiently conserves the amount of material in curvilinear coordinate is adopted, and the differential equation for partition function is solved in real space with Multicoordinate-system (MCS) scheme which makes use of the mirror symmetry between the two particles. In this research, we investigate how distribution of polydisperse chain lengths affects grafted chain conformation and enhances stabilization mechanism for dispersion by calculating interaction potentials between two polymer-coated NPs as functions of grafting density, polydispersity index (PDI) and distance between the two particles. Our results reveal that polydisperse distribution stabilizes dispersions more efficiently than bidisperse or monodisperse counterpart