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arXiv · 0908.1661

Diffusion of a sphere in a dilute solution of polymer coils

Matthias Krüger·Markus Rauscher
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Abstract

We calculate the short time and the long time diffusion coefficient of a spherical tracer particle in a polymer solution in the low density limit by solving the Smoluchowski equation for a two-particle system and applying a generalized Einstein relation (fluctuation dissipation theorem). The tracer particle as well as the polymer coils are idealized as hard spheres with a no-slip boundary condition for the solvent but the hydrodynamic radius of the polymer coils is allowed to be smaller than the direct-interaction radius. We take hydrodynamic interactions up to 11th order in the particle distance into account. For the limit of small polymers, the expected generalized Stokes-Einstein relation is found. The long time diffusion coefficient also roughly obeys the generalized Stokes-Einstein relation for larger polymers whereas the short time coefficient does not. We find good qualitative and quantitative agreement to experiments.

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Matthias Krüger, Markus Rauscher. 2009-08-12. Diffusion of a sphere in a dilute solution of polymer coils. https://doi.org/10.1063/1.3216108

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