Influence of the Bound Polymer Layer on Nanoparticle Diffusion in Polymer Melts

Abstract

We measure the center-of-mass diffusion of silica nanoparticles (NPs) in entangled poly(2-vinylpyridine) (P2VP) melts using Rutherford backscattering spectrometry. While these NPs are well within the size regime where enhanced, nonhydrodynamic NP transport is theoretically predicted and has been observed experimentally (2R NP /d tube ≈ 3, where 2R NP is the NP diameter and d tube is the tube diameter), we find that the diffusion of these NPs in P2VP is in fact well-described by the hydrodynamic Stokes−Einstein relation. The effective NP diameter 2R eff is significantly larger than 2R NP and strongly dependent on P2VP molecular weight, consistent with the presence of a bound polymer layer on the NP surface with thickness h eff ≈ 1.1R g . Our results show that the bound polymer layer significantly augments the NP hydrodynamic size in polymer melts with attractive polymer−NP interactions and effectively transitions the mechanism of NP diffusion from the nonhydrodynamic to hydrodynamic regime, particularly at high molecular weights where NP transport is expected to be notably enhanced. Furthermore, these results provide the first experimental demonstration that hydrodynamic NP transport in polymer melts requires particles of size ≳5d tube , consistent with recent theoretical predictions.

Grafted polymer chains suppress nanoparticle diffusion in athermal polymer melts

“…This larger graft molecular weight may considerably augment the effective hydrodynamic NP size and contribute to the observed slow NP diffusion. In this regard, the current data may reflect a similar case as our recent studies of the diffusion of silica NPs in poly(2-vinyl pyridine) melts, 23 where we found unexpectedly slow NP diffusion consistent with the formation of a polymer bound layer that increases the effective NP hydrodynamic size.…”

“…22 We do not expect this assumption to hold in highly entangled polymer melts unless the particles are much larger than the tube diameter (2R/d t > 5-6). 22,23 We rewrite the Stokes-Einstein relation describing the measured NP diffusion as…”

“…Recent experiments have shown that hydrodynamic NP diffusion is indeed recovered when 2R/d t is ∼5-6 in polymer melts and in semi-dilute entangled DNA solutions. 23,24 Alternatively, Cai et al 6,25 proposed that a hopping mechanism can enhance nanoparticle mobility when 2R ∼ d t .…”

Polymer and spherical nanoparticle diffusion in nanocomposites

“…However, in polymer nanocomposites 2 there are more topological constraints due to the dispersed nanoparticles (NPs) in the polymer matrix that can influence the polymer primitive path [3][4][5][6][7] , thus the polymer dynamics. Polymer dynamics can be altered by the characteristics of nanoparticles such as size, shape, aspect ratio, surface area, volume fraction of nanoparticles and the nature of the interactions between the nanoparticle and the polymer matrix 8,9 . There are several theories that have been used to predict how the polymer diffusivity is impeded by impenetrable particles [10][11][12][13][14][15][16][17][18][19] .…”

Liquid–liquid equilibrium in polymer–fullerene mixtures; anin situneutron reflectivity study

“…In general the diffusivity of nanoparticles within polymer melts decreases with Mw, as a result of the increasing melt viscosity. 53,54 The exact nature of the behaviour (and in particular its correspondence to the predictions of the Stokes-Einstein relation) depends on a number of factors, including the relative sizes of the nanoparticles and the polymer melt tube diameter (in entangled melts), 54 and the occurrence of polymer adsorption (to larger nanoparticles). 53 However, the nature of our measurements does not allow us to resolve isothermal fullerene diffusion processes themselves, and our focus is instead on the onset temperatures for diffusion and the equilibration of the bilayer composition profiles.…”