Understanding Gas Transport in Polymer-Grafted Nanoparticle Assemblies

Abstract

We rationalize the unusual gas transport behavior of polymer-grafted nanoparticle (GNP) membranes. While gas permeabilities depend specifically on the chemistry of the polymers considered, we focus here on permeabilities relative to the corresponding pure polymer, which show interesting, “universal” behavior. For a given NP radius, R c, and for large enough areal grafting densities, σ, to be in the dense brush regime, we find that gas permeability enhancements display a maximum as a function of the graft chain molecular weight, M n. Based on a recently proposed theory for the structure of a spherical brush in a melt of GNPs, we conjecture that this peak permeability occurs when the densely grafted polymer brush has the highest, packing-induced extension free energy per chain. The corresponding brush thickness is predicted to be h max = √3R c, independent of chain chemistry and σ, i.e., at an apparently universal value of the NP volume fraction (or loading), ϕNP, ϕNP,max = [R c/(R c + h max)]3 ≈ 0.049. Motivated by this conclusion, we measured CO2 and CH4 permeability enhancements across a variety of R c, M n, and σ and find that they behave in a similar manner when considered as a function of ϕNP, with a peak in the near vicinity of the predicted ϕNP,max. Thus, the chain length-dependent extension free energy appears to be the critical variable in determining the gas permeability for these hybrid materials. The emerging picture is that these curved polymer brushes, at high enough σ, behave akin to a two-layer transport mediumthe region in the near vicinity of the NP surface is comprised of extended polymer chains that speed up gas transport relative to the unperturbed melt. The chain extension free energy increases with increasing chain length, up to a maximum, and apparently leads to an increasing gas permeability. For long enough grafts, there is an outer region of chain segments that is akin to an unperturbed melt with slow gas transport. The permeability maximum and decreasing permeability with increasing chain length then follow naturally.

Local Structure of Polymer-Grafted Nanoparticle Melts

“…18,39 In gas transport applications, for example, it has been found that increasing molecular weight for short chains increasingly enhances gas permeability in GNPs relative to the neat polymers, but beyond a critical MW g , the normalized gas permeability enhancements decrease, which is dependent on grafting density, graft chain chemistry, and core size. 18,24 We propose that this can be rationalized by postulating that the dry zone with stretched, aligned chains has a faster intrinsic diffusivity. Computational work by Bobbili and Milner has shown that stretched, aligned chains have lower monomeric friction coefficients, which support this conjecture of faster diffusivity in the dry zones.…”

“…Given these studies and the predicted presence of both a dry and an interpenetrated brush layer in all the GNPs tested in the gas permeation experiments of Bilchak et al, it is still unclear why these materials display a gas permeability enhancement relative to the neat polymer and a permeability maximum at a MW g of ∼100 kDa for a grafting density of 0.47 chains/nm 2 . , To shed light on this situation, we study GNP packing as a function of the graft chain length (at fixed grafting density) using small-angle X-ray scattering (SAXS). The data obtained on poly­(methyl acrylate)-grafted silica NP films (PMA- g -SiO 2 ) were then analyzed using the Percus–Yevick hard sphere model.…”

“…18,22,23 For a fixed grafting density (we mostly employ σ ≈ 0.47 chains/nm 2 but have systematically examined σ ≈ 0.11−0.66 chains/nm 2 ), we demonstrated a nonmonotonic gas permeability enhancement as a function of graft chain molecular weight (MW g ), with a peak in the vicinity of MW g ≈ 100 kDa for σ ≈ 0.47 chains/nm 2 (see Supporting Information, Figure S1). 18,22,24 Moreover, gas penetrants with larger kinetic diameters appear to have increased enhancements. 18 We seek to understand this unusual behavior, especially the gas transport maximum�specifically, here we explore whether the packing structure of the GNP layer (and hence of the NPs) could indirectly influence the diffusivity of light gases through GNP membranes.…”

Vesicular self-assembly of copolymer-grafted nanoparticles with anisotropic shapes

“…We presume that the limited size of vesicles of ∼80 nm AuNCs might be related to the geometric frustration due to the faceting effect, resembling the packing of viral capsids. 40 The formation of vesicles was associated with a redshift of their LSPR peak from ∼535 nm to ∼680 nm and a noticeable broadening of these peaks in the UV-visible spectra (Fig. 3f).…”

“…34 Furthermore, even for the longest polymer ligands used in our experiments, their length (∼20 nm) is not sufficient for forming a spherical corona on the surface of the NCs. 40 Thus, we presume that the interplay between cubic shape and anisotropic distribution of polymer ligands results in the different packing modes of NCs in the vesicular membranes.…”