  We study the potential of mean force (PMF) between atomistic silica and gold
nanoparticles in the vacuum by using molecular dynamics simulations. Such an
investigation is devised in order to fully characterize the effective
interactions between atomistic nanoparticles, a crucial step to describe the
PMF in high-density coarse-grained polymer nanocomposites. In our study, we
first investigate the behavior of silica nanoparticles, considering cases
corresponding to different particle sizes and assessing results against an
analytic theory developed by Hamaker for a system of Lennard-Jones interacting
particles [H. C. Hamaker, Physica A, 1937, 4, 1058]. Once validated the
procedure, we calculate effective interactions between gold nanoparticles,
which are considered both bare and coated with polyethylene chains, in order to
investigate the effects of the grafting density \rho_g on the PMF. Upon
performing atomistic molecular dynamics simulations, it turns out that silica
nanoparticles experience similar interactions regardless of the particle size,
the most remarkable difference being a peak in the PMF due to surface
interactions, clearly apparent for the larger size. As for bare gold
nanoparticles, they are slightly interacting, the strength of the effective
force increasing for the coated cases. The profile of the resulting PMF
resembles a Lennard-Jones potentials for intermediate \rho_g , becoming
progressively more repulsive for high \rho_g and low interparticle separations.
