Nanoparticle Transport in Polymer Solutions

Conspectus

Polymer solutions are essential materials both for their uses in industries ranging from energy storage to consumer products to additive manufacturing and as model physical systems that can mimic biological tissues and hydrogels with well-controlled structures, dynamics, and properties. Nanoparticles are commonly added to these solutions to impart functionality, deliver theranostics, or manipulate mechanical properties, all of which require a fundamental understanding of nanoparticle transport through the surrounding polymer mesh. Over recent decades, nanoparticle dynamics have been analyzed using the framework of microrheology to measure the local viscoelasticity of complex fluids. In contrast to homogeneous, Newtonian fluids in which particle dynamics are described through the Stokes–Einstein-Sutherland (SES) relationship, the structural heterogeneity and viscoelasticity of polymer solutions lead to significant deviations with nanoparticles transporting up to 1,000× faster than expected from the bulk solution viscosity. These deviations dramatically alter how nanoparticles disperse and distribute through complex environments and introduce significant discrepancies between microrheological measurements and bulk mechanical properties. The vast combinatorial library of polymer chemistries, architectures, and solution formulations necessitates predictive understanding of nanoparticle transport and how it relates to the underlying physicochemical interactions.

In this Account, we describe theoretical advances and summarize experimental and simulation findings that build a comprehensive understanding of nanoparticle transport in polymer solutions. The key insight is that nanoparticle transport can be better understood by considering the local dynamics and structure of the polymer solution rather than the bulk viscoelasticity. Specifically, we show that nanoparticles violate the SES relationship because they are comparable in size to structural heterogeneities and instead exhibit a size-dependent diffusivity. Using theoretical predictions derived from polymer scaling theory, the faster dynamics are related to the ratio between nanoparticle size and the polymer correlation length ξ because the nanoparticles couple to segmental fluctuations of the polymer mesh. Despite the success of this coupling theory in describing the long-time diffusivity of nanoparticles, it does not capture the dynamics on short time scales, on which nanoparticles move subdiffusively. On these time scales, the nanoparticles not only couple to segmental fluctuations but also to the center-of-mass dynamics of the polymer coils. To expand these findings across the formulation library, we detail some impacts of nanoparticle surface interactions and polymer conformation and chemistry on this modified coupling theory. The stiffness and charge of the surrounding polymer and the softness of the particle all affect how nanoparticle dynamics couple to those of the polymers. Looking forward, we identify open questions that motivate theoretical considerations and directions for experimental and simulation thrusts toward the ultimate goal of fully describing, predicting, and tailoring nanoparticle transport in polymer solutions and other heterogeneous complex fluids for applications in medicine, energy, and advanced materials.