We employ all-atom
molecular dynamics simulations up to microsecond
time scales to study diffusion of fullerene nanoparticles (C60 and its derivative PCBM) in a polyimide matrix above its glass transition
temperature. A detailed examination of the fullerene mobility in the
embedding polymer system reveals the presence of different diffusion
regimes (ballistic, subdiffusive, and normal diffusive). The microscopic
origin of the observed subdiffusive regime is discussed by comparing
the behavior to the one displayed by different anomalous diffusion
processes, namely, continuous time random walk (CTRW), random walk
on a fractal (RWF), and fractional Langevin equation (FLE). A series
of statistical tests suggests that the FLE framework is the more appropriate
one to describe subdiffusion of fullerenes in our system. Furthermore,
a comprehensive analysis of the self-part of the van Hove function
shows that the normal diffusion regime observed at long times displays
a nonclassical behavior characterized by the simultaneous presence
of several Gaussian peaks. We ascribe this behavior to a mechanism
of diffusion by hopping. Until recently, it was commonly believed
that hopping of tracer particles in polymer systems is only relevant
for particle sizes that are of the order of the reptation tube diameter
(d
T), while smaller particles are considered
to slip through the entanglement mesh. However, our results provide
direct evidence for hopping as a relevant mechanism for diffusion
of particles whose sizes are commensurate with the correlation length
(ξ) of the polymer system. These results emphasize the importance
of local interactions at the atomic level for the understanding of
nanoparticle dynamics in polymer melts.
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