  We investigate the role played by the bidispersity of polymer chains on the
local structure and the potential of mean force (PMF) between silica
nanoparticles (NPs) in a polystyrene melt. We use the hybrid particle-field
molecular dynamics technique which allows to efficiently relax polymer
nanocomposites even with high molecular weights.The NPs we investigate are
either bare or grafted with polystyrene chains immersed in a melt of free
polystyrene chains, whereas the grafted and the free polystyrene chains are
either monodisperse or bidisperse. The two-body PMF shows that a bidisperse
distribution of free polymer chains increases the strength of attraction
between a pair of ungrafted NPs. If the NPs are grafted by polymer chains, the
effective interaction crucially depends on bidispersity and grafting density of
the polymer chains: for low grafting densities, the bidispersity of both free
and grafted chains increases the repulsion between the NPs, whereas for high
grafting densities we observe two different effects. An increase of
bidispersity in free chains causes the rise of the repulsion between the NPs,
while an increase of bidispersity in grafted chains promotes the rise of
attraction. Additionally, a proper treatment of multi-body interactions
improves the simpler two-body PMF calculations, in both unimodal and bimodal
cases. We found that, by properly tuning the bidispersity of both free and
grafted chains, we can control the structure of the composite materials, which
can be confirmed by experimental observations. As a result, the hybrid
particle-field approach is confirmed to be a valid tool for reproducing and
predicting microscopic interactions, which determine the stability of the
microscopic structure of the composite in a wide range of conditions.
