Effects of Matrix Chain Length on Miscibility of Nanoparticles

We use molecular dynamics simulations to show, for the first time, that brush collapse is observable at the single particle level, and the small magnitude of the collapse points to the subtlety of the dispersion problem for a single nanoparticle. Brush collapse or collapse of the graft chains on a polymer grafted nanoparticle (PGNP), is observed experimentally by decreasing the graft/matrix chain ratio (N/M) for PGNPs in a homopolymer matrix of free chains. This brush collapse from varying N/M has not been observed in previous simulations of a single PGNP in homopolymer matrix. Here, the free chain length was varied systematically in a series of simulations, while NP radius, grafting density, and grafted chain length were held constant. While composition profiles of the graft/matrix chains do not reveal any signs of brush collapse, brush heights calculated using a second moment of the segment density highlights a subtle indication of brush collapse. Further, by measuring free chain fluctuations and free energies via indirect umbrella sampling, we are able to suggest that interactions at the surface are significant in studying changes in miscibility of the PGNP and might be driving the morphology of the entire brush.