**Molecular dynamics study on nanoparticle diffusion in polymer melts: A
test of the Stokes-Einstein law**

J Liu and DP Cao and LQ Zhang, JOURNAL OF PHYSICAL CHEMISTRY C, 112, 6653-6661 (2008).

DOI: 10.1021/jp800474t

Molecular dynamics simulations are used to investigate the diffusion process of nanoparticles in polymer melts. The effects of size, concentration, and mass of the particle, chain length, and polymer- particle interaction on the diffusion of particles in polymer melts are also explored. Our simulated results indicate that the gyration radius of the polymer chain is the key factor determining the validity of the Stokes-Eintsein(SE) relation in describing the particle diffusion at infinite dilution. When the particle size is larger than the gyration radius of the polymer chain, the SE formula can predict the particle diffusion in the polymer melts correctly, and the particle diffusion does not show mass dependence. When the particle size is smaller than the gyration radius of the polymer chain, however, the SE equation becomes invalid in the prediction of particle diffusion, because particle diffusion is exactly related to the nanoviscosity rather than the macroviscosity used in the SE formula. Furthermore, it is also found that the diffusion coefficient of the particle is inversely proportional to the cube of its hydrodynamic radius. In this regime where the particle size is smaller than the gyration radius of the polymer, particle diffusion is independent of the chain length or molecular weight of the polymer, but dependent on the particle mass. In addition, we also observe the transition process of the particle experiencing macroviscosity to nanoviscosity of the polymer melts by gradually increasing the chain length. The concentration dependence of the particle diffusion is similar to the results from Heyes et al., and at high volume fractions, the negative deviations from the SE formula are found. By exploring the effect of particle-polymer interaction on the diffusion of the particle larger than the gyration radius of the polymer chain, it is found that the condition where the SE formula becomes valid in the prediction of the particle diffusion is that where different reasonably defined effective hydrodynamic radii must be used.

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