(92c) Rotational Dynamics of Nanoparticles in Polymer Solutions and Melts

The dynamics of nanoparticles in complex fluids are of interest for a wide range of applications, such as high performance materials, where nanoparticles are used to tune mechanical properties or add functionality, and biomedical applications, where nanoparticles must navigate a complex, crowded, and confined environment. Polymer solutions and melts are good examples of complex fluids where improved understanding of nanoparticle dynamics could impact applications while improving our fundamental understanding of nanoparticle behavior. Prior studies have explored the translational diffusion of nanoparticles in polymer melts and polymer solutions, demonstrating so-called breakdown of the Stokes-Einstein equation for the diffusivity under certain conditions. However, the rotational diffusion of nanoparticles in such systems has remained largely unexplored.

Here we report on studies of the rotational diffusivity of inorganic nanoparticles coated with a polymer brush and dispersed in polymer solutions and melts. The nanoparticles consist of cobalt ferrite cores with narrow size distribution coated with poly(ethylene glycol) covalently grafted to the particles through a silane coupling agent. The counterpart polymer used in the solutions and melts was also poly(ethylene glycol). The rotational diffusivity of the nanoparticles was determined by measuring their response to alternating magnetic fields of low amplitude and variable frequency, in what we call Dynamic Magnetic Susceptibility (DMS) measurements. In the case of polymer solutions we explored the effects of ratio of particle radius to polymer radius of gyration and of polymer crowding by varying the molecular weight and concentration of the solution polymer. Our results suggest breakdown of the Stokes-Einstein relation for the rotational diffusivity of the nanoparticles when the radius of gyration of the polymer in solution is much greater than the particle’s hydrodynamic radius. A simple model for rotational diffusion of a nanoparticle surrounded by a polymer depletion layer and embedded in a polymer solution was obtained and appears to explain the measurements well. In the case of polymer melts, the nanoparticles were dispersed in poly(ethylene glycol) melts of varying molecular weights and their rotational diffusivity was measured also by DMS measurements. The predictions of the Stokes-Einstein relation were found to be valid when the contour length of the polymer was shorter than the nanoparticle’s hydrodynamic diameter. For larger polymer chains in the melt it appears as if the rotational hydrodynamic drag on the nanoparticles is no longer a function of melt polymer molecular weight. These observations suggest that rotational hydrodynamic drag on the nanoparticle is determined by the melt polymer segments in the immediate vicinity of the nanoparticles, and not by the motion of the melt chains as a whole.