Diffusion of Particles in Polymer Solutions

We use scaling theory to derive the time dependence of the mean-square-displacement $\langle\Delta r^2\rangle$ of a probe particle of size $d$ in an entangled semidilute polymer solution. Particles with size smaller than solution correlation length $\xi$ undergo ordinary diffusion ($\langle\Delta r^2 (t)\rangle \sim t$) with diffusion coefficient determined by the solvent viscosity. The motion of particles with intermediate sizes ($\xia$) at time scales shorter than the relaxation time of an entanglement strand $\tau_e$ is similar to the motion of particles with intermediate sizes. At longer time scales ($t>\tau_e$) large particles ($d>a$) are trapped by entanglement mesh and cannot move until the surrounding chains relax at the reptation time scale $\tau_{rep}$. At longer times $t>\tau_{rep}$, the motion of large particles becomes diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer solution.