On the Mobility of Nanoparticles in Entangled Polymer Solutions

Theoretical modeling of transport through crowded heterogeneous viscous environments is important toward numerous biomedical applications, such as drug delivery. Extensive experimental evidence of enhanced transport of nanoparticles pretreated to hinder biopolymer adhesion through highly viscous gel-like media (e.g., polyethylene glycol-coated nanoparticles in mucus) still remains largely unexplained. In the present paper, we employ the two-fluid model and derive the analytical expressions for scalar frictional resistance of a rigid spherical particle translating or rotating in a semidilute entangled polymer solution. For polymers adhering to the particle, it can be shown that the frictional resistance of an arbitrary-shaped particle exhibiting rigid-body motion is Stokesian, with the apparent viscosity being equal to the bulk viscosity of the polymer solution. For nonadsorbing polymers, we consider the finite-thickness depletion layer forming at the surface of a spherical probe and derive the closed-form expressions for its frictional (translational and rotational) resistance, showing a strong dependence on the network mesh size and the depletion layer thickness, rendering it strongly non-Stokesian. The theoretical predictions of the apparent viscosity are in very good agreement with the available experimental results, while exceptionally close agreement is found for rotation. In particular, it supports the experimental findings showing that the apparent viscosities of the xanthan and poly­(ethylene oxide) solutions obtained from rotational diffusivity of surfactant-coated nanoparticles can be 1–2 orders-of-magnitude lower than the bulk viscosity of these solutions. The present study extends the previous theory that employed the two-fluid model subject to phenomenological boundary conditions at the particle surface to study its mobility. It also generalizes the earlier theories that considered the depletion layer at the particle surface but entirely disregarded heterogeneity (i.e., finite mesh size) of the entangled polymer network.