Scale-dependent rotational diffusion of nanoparticles in polymer solutions†
It is shown that the rotational diffusivity of nanoparticles in polymer solutions spanning the dilute to semi-dilute regimes deviates from the predictions of the Stokes–Einstein (SE) relationship, and that this deviation can be explained by the existence of a polymer depletion layer with the viscosity of the bath solvent. The measurements of the rotational diffusion coefficient of poly(ethylene glycol) (PEG) grafted magnetic nanoparticles in PEG solutions spanning the dilute to semi-dilute regimes and a wide range of polymer molecular weights were obtained from the dynamic magnetic response of the nanoparticles to alternating magnetic fields. Experimental rotational diffusion coefficient values were compared with those predicted by the SE relation using the macroscopic viscosity of the polymer solutions and the hydrodynamic radius of the nanoparticles. Deviations between experimental and SE rotational diffusivity values were observed for nanoparticles in polymer solutions where the radius of gyration of the polymer exceeded the hydrodynamic radius of the particles. A simple model for the rotational hydrodynamic drag on a particle surrounded by a polymer depletion layer was found to describe the experimental rotational diffusivities well, suggesting that the observed phenomenon arises due to the formation of a polymer depletion layer around the nanoparticles.