Dynamics of Nanoparticles in Entangled Polymer Solutions

Abstract

The mean square displacement ⟨r⟩ of nanoparticle probes dispersed in simple isotropic liquids and in polymer solutions is interrogated using fluorescence correlation spectroscopy and single-particle tracking (SPT) experiments. Probe dynamics in different regimes of particle diameter (d), relative to characteristic polymer length scales, including the correlation length (ξ), the entanglement mesh size (a), and the radius of gyration (R), are investigated. In simple fluids and for polymer solutions in which d ≫ R, long-time particle dynamics obey random-walk statistics ⟨r⟩:t, with the bulk zero-shear viscosity of the polymer solution determining the frictional resistance to particle motion. In contrast, in polymer solutions with d < R, polymer molecules in solution exert noncontinuum resistances to particle motion and nanoparticle probes appear to interact hydrodynamically only with a local fluid medium with effective drag comparable to that of a solution of polymer chain segments with sizes similar to those of the nanoparticle probes. Under these conditions, the nanoparticles exhibit orders of magnitude faster dynamics than those expected from continuum predictions based on the Stokes-Einstein relation. SPT measurements further show that when d > a, nanoparticle dynamics transition from diffusive to subdiffusive on long timescales, reminiscent of particle transport in a field with obstructions. This last finding is in stark contrast to the nanoparticle dynamics observed in entangled polymer melts, where X-ray photon correlation spectroscopy measurements reveal faster but hyperdiffusive dynamics. We analyze these results with the help of the hopping model for particle dynamics in polymers proposed by Cai et al. and, on that basis, discuss the physical origins of the local drag experienced by the nanoparticles in entangled polymer solutions.

Bridging the spatiotemporal scales of macromolecular transport in crowded biomimetic systems

“…This size difference, which correlates to a ~6x difference in DNA coil radius, is of principal importance, as the degree of crowding-induced subdiffusion has been shown to depend directly on the ratio of particle or polymer radius to the correlation length of the crowding network. 50,51 In particular, for colloids diffusing in actin networks, subdiffusion was only apparent when the colloid radius a was comparable to the mesh size of the actin network ξ A , with α decreasing linearly with increasing ratios a:ξ A . 50 In our experiments, the DNA coil radius is ~½R coil ≈ 0.6 -0.8 μm.…”

Bridging the spatiotemporal scales of macromolecular transport in crowded biomimetic systems

“…This size difference is of principal importance as the degree of crowdinginduced subdiffusion has been shown to depend directly on the ratio of particle or polymer radius to the correlation length of the crowding network. 47,48 In particular, for colloids diffusing in actin networks, subdiffusion was only apparent when the colloid radius a was comparable to the mesh size of the actin network , with α decreasing linearly with increasing ratios a:. 47 In our experiments, the DNA coil radius is ~½Rcoil  0.6 -0.8 μm, whereas the predicted mesh sizes for the actin and microtubule networks are   0.4 μm and   0.9 μm, respectively.…”

“…The distribution of trapping times results in subdiffusion over many decades in time. 4,7,47,48 Such caging and hopping behavior should also manifest itself as large heterogeneities in transport measured for different molecules in different regions of the network. 4,47 Within this framework, more extreme subdiffusion (smaller α), resulting from more efficient caging, should be coupled with larger heterogeneities in transport.…”

Polymer Conformations, Entanglements and Dynamics in Ionic Nanocomposites: A Molecular Dynamics Study

“…As a result, an exceptional degree of dispersion of the silica in the polymer and high degree of order in both thin film and bulk forms was achieved [18]. For matrix-free model systems [34,35] it was observed that NPs diffuse similarly to a polymer solution [36][37][38], while chains diffuse faster than NPs [39]. Ionic interactions are also included in the case of ionomers in which the morphology and phase behavior depend on the electrostatic strength [40][41][42].…”