Diffusion of Nanoparticles in Entangled Poly(vinyl alcohol) Solutions and Gels

Abstract

We studied the diffusion of gold nanoparticles within entangled solutions and gels formed by high molecular weight (M w = 89000 g/mol) poly­(vinyl alcohol) (PVA) in water by using fluctuation correlation spectroscopy (FCS). The nanoparticle size (2R) was varied between 5 and 30 nm, and the PVA volume fraction (ϕ) was chosen to be in the entangled regime. We found that existing hydrodynamic and obstruction models are inadequate to describe the size dependence of the particle diffusion coefficient (D). For size ratios x = 2R/a e ≈ 0.5–2.5, where a e is the entanglement tube diameter in the solution, our results suggest a functional form for D ∼ exp­(−κx), where κ ≈ 1.4. This result qualitatively agrees with the scaling theory prediction of hopping motion for particles within entangled polymer solutions. For larger particles at higher volume fractions, an additional sharp slowing down of the particle motion was observed, which also exhibited an exponential dependence on the size ratio, but with a much higher value of κ ≈ 7.5. Such a rare hopping process can be explained qualitatively by recently developed force-based nonlinear Langevin theory.

Nanoparticle Mobility within Permanently Cross-Linked Polymer Networks

“…48−53 Parrish et al 52 showed that the network confinement and heterogeneity would suppress the NP diffusion when the NP size is comparable to the gel mesh size. Senanayake et al 53 found that the presence of physical cross-linking in addition to entanglements would sharply slow down the NP mobility, which can be explained qualitatively by recently developed force-based nonlinear Langevin theory. 34 However, by experiments, polymer network quality is hard to be precisely controlled.…”

“…Though the network confinement effect has been fully considered in these theories, the impact of the permanent cross-links on the network dynamics and thereby the coupled NP mobility is missing. By use of dynamic light scattering, X-ray photon correlation spectroscopy, fluctuation correlation spectroscopy, or single particle tracking, the particle dynamics in polymer gels, consisting of either chemically or physically cross-linked networks of polymer chains immersed in solvent, has been investigated experimentally. − Parrish et al showed that the network confinement and heterogeneity would suppress the NP diffusion when the NP size is comparable to the gel mesh size. Senanayake et al found that the presence of physical cross-linking in addition to entanglements would sharply slow down the NP mobility, which can be explained qualitatively by recently developed force-based nonlinear Langevin theory .…”

The relationship between gel mesh and particle size in determining nanoparticle diffusion in hydrogel nanocomposites

“…[39][40][41][42][43][44] Not only do ligands impact NP surface chemistry, but they add an additional level of complexity to the diffusive behavior of the particles by changing the hydrodynamic diameter and introducing ligand-matrix effects. The effect of grafted polymer chains on NP surfaces has received substantial attention in the context of polymer melts and solutions, 35,[45][46][47][48][49][50][51] but these systems have important differences from networks and gels.…”

Understanding the Roles of Mesh Size,Tg, and Segmental Dynamics on Probe Diffusion in Dense Polymer Networks

“…Several prior investigations have looked at nanoparticle diffusion in polymer networks using spherical or rodlike penetrants with well-defined geometry. − Choi et al found that nanorods can exhibit diffusion coefficients orders of magnitude larger than predicted by continuum models because their anisotropic shape allows unhindered diffusion along the long axis through the network mesh . Cai et al have proposed a hopping diffusion mechanism for spherical nanoparticles in polymer networks, where the network cage conformation must extend to allow the nanoparticle to hop through .…”