Diffusion of a sphere in a dilute solution of polymer coils

TL;DR

This paper calculates the diffusion coefficients of a spherical tracer in dilute polymer solutions, considering hydrodynamic interactions and boundary conditions, and compares results with experimental data.

Contribution

It provides a detailed theoretical analysis of tracer diffusion in polymer solutions, incorporating high-order hydrodynamic interactions and boundary conditions.

Findings

Short and long time diffusion coefficients are calculated.

Results agree qualitatively and quantitatively with experiments.

Generalized Stokes-Einstein relation holds for small polymers.

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.