Hopping Diffusion of Nanoparticles in Polymer Matrices

Abstract

We propose a hopping mechanism for diffusion of large nonsticky nanoparticles subjected to topological constraints in both unentangled and entangled polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size ax of unentangled polymer networks or tube diameter ae of entangled polymer liquids are trapped by the network or entanglement cells. At long time scales, however, these particles can diffuse by overcoming free energy barrier between neighboring confinement cells. The terminal particle diffusion coefficient dominated by this hopping diffusion is appreciable for particles with size moderately larger than the network mesh size ax or tube diameter ae. Much larger particles in polymer solids will be permanently trapped by local network cells, whereas they can still move in polymer liquids by waiting for entanglement cells to rearrange on the relaxation time scales of these liquids. Hopping diffusion in entangled polymer liquids and networks has a weaker dependence on particle size than that in unentangled networks as entanglements can slide along chains under polymer deformation. The proposed novel hopping model enables understanding the motion of large nanoparticles in polymeric nanocomposites and the transport of nano drug carriers in complex biological gels such as mucus.

Perspective: Outstanding theoretical questions in polymer-nanoparticle hybrids

“…107,[222][223][224][225] For systems where there is no specific interaction between the NPs and the matrix, theory predicts that NP diffusion will be controlled by a constraint release mechanism, which opens up the network locally, enabling NP motion. 223,226 Although simulations have provided a microscopic picture of the distribution of entanglements around grafted spherical NPs, many basic questions remain. For example, how do the entanglement distributions change as the grafted layer transitions from a state that is wet by the matrix to a dry brush, and how does this subsequently affect the diffusion of grafted NPs?…”

Probing Non-Gaussianity in Confined Diffusion of Nanoparticles

“…This result also explains the effect of MW on the non-Gaussian parameter shown in Figure 2d. We propose that the influence of MW can be considered under the theory given by Cai et al 38 They suggest that there is a MW-dependent threshold size below which the hopping diffusion becomes easy. When larger MW PEO is used, it becomes easier for the NP whose size is smaller or comparable to the threshold size to hop through the polymer networks.…”

Size-Dependent Dynamics of Nanoparticles in Unentangled Polyelectrolyte Solutions

“…Hydrodynamic models treat the polymer solution as a homogeneous medium in which hydrodynamic interactions are screened over the correlation length between polymer chains ξ. 10,15,16 Scaling models describe the particle mobility in terms of the polymer dynamics, 13,17,18 which are set by the characteristic length scales ξ and the polymer radius of gyration R g . Identifying the relevant physics requires model systems that are compatible with a wide range of particle sizes and span the transition from dilute to semidilute regimes in unentangled solutions.…”