Breakdown of the Stokes–Einstein Relation for the Rotational Diffusivity of Polymer Grafted Nanoparticles in Polymer Melts

Abstract

We report observations of breakdown of the Stokes-Einstein relation for the rotational diffusivity of polymer-grafted spherical nanoparticles in polymer melts. The rotational diffusivity of magnetic nanoparticles coated with poly(ethylene glycol) dispersed in poly(ethylene glycol) melts was determined through dynamic magnetic susceptibility measurements of the collective rotation of the magnetic nanoparticles due to imposed time-varying magnetic torques. These measurements clearly demonstrate the existence of a critical molecular weight for the melt polymer, below which the Stokes-Einstein relation accurately describes the rotational diffusivity of the polymer-grafted nanoparticles and above which the Stokes-Einstein relation ceases to apply. This critical molecular weight was found to correspond to a chain contour length that approximates the hydrodynamic diameter of the nanoparticles.

Coupling of Nanoparticle Dynamics to Polymer Center-of-Mass Motion in Semidilute Polymer Solutions

“…When this continuum approximation is broken by a particle that is comparably sized to a characteristic length scale of the material, however, the particle dynamics deviates from these expressions and a description based solely on the zero-shear viscosity of the material becomes insufficient. [3][4][5][6][7][8][9][10] Semidilute polymer solutions are non-Newtonian fluids used commonly during polymer composite processing, 11 as sweep fluids in enhanced oil recovery methods, 12 and to produce hydrogels. 13 They serve as ideal models for complex heterogeneous materials because their characteristic length scales, such as the polymer radius of gyration R g and the correlation length ξ, are well-defined and easily tuned by changing the molecular weight and concentration of the polymer.…”

Diffusion and flow in complex liquids

“…Combination of the Stokes' law for rotational motion (13) with the inverse Stokes' law for translation (9)…”

“…6,7 However, when a probe becomes small this formula has known shortcomings. 8,9 For example, Gisler and Weitz noticed that for 3 mm tracer particles in a suspension of 20 mm long F-actin filaments, the frequencydependent Stokes-Einstein relation is no longer valid. 10 In this article we focus on the zero-frequency limit, which is equivalent to the observation of the mean square displacement for long times, but for probe sizes that sample the microstuctural length scales.…”

Size effects on rotational particle diffusion in complex fluids as probed by Magnetic Particle Nanorheology

“…Stringent deviations from the rheological performance, as obtained by conventional methods, are expected and experimentally observed. 21,22 In particular, in polymer-based fluids and soft solids (e.g. gels, melts or solutions), specific characteristic length scales (e.g.…”