title: Mobility of Nonsticky Nanoparticles in Polymer Liquids.
abstract: We use scaling theory to derive the time dependence of the mean-square displacement 〈Δr2〉 of a spherical probe particle of sizedexperiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (〈Δr2(t)〉 ~t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ <d<a), whereais the tube diameter for entangled polymer liquids, is sub-diffusive (〈Δr2(t)〉 ~t1/2) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameterd. The motion of particles larger than the tube diameteraat time scales shorter than the relaxation time τeof an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t> τe) large particles (d>a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τrep. At longer timest> τrep, the motion of such large particles (d>a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.
authors: Curriculum in Applied Sciences and Engineering, University of North Carolina, Chapel Hill, North Carolina 27599-3287.
authors: Li-Heng
authors: LH
authors: Cai
authors: P. N. Lebedev Physics Institute, Russian Academy of Sciences, Moscow 117924, Russia.
authors: Sergey
authors: S
authors: Panyukov
authors: Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290; Curriculum in Applied Sciences and Engineering, University of North Carolina, Chapel Hill, North Carolina 27599-3287.
authors: Michael
authors: M
authors: Rubinstein