Interval Sorption of Alkyl Acetates and Benzenes in Poly(methyl acrylate)

Understanding Gas Transport in Polymer-Grafted Nanoparticle Assemblies

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 = 3 R c , independent of chain chemistry and σ, i.e., at an apparently universal value of the NP volume fraction (or loading), ϕ_NP, ϕ_NP,max = [R_c/(R_c + h_max)]³ ≈ 0.049. Motivated by this conclusion, we measured CO_-2 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 ϕ_NP, with a peak in the near vicinity of the predicted ϕ_NP,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 which 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.

Location of Imbibed Solvent in Polymer-Grafted Nanoparticle Membranes

Membranes made purely from nanoparticles (NPs) grafted with polymer chains show increased gas permeability relative to the analogous neat polymer films, with this effect apparently being tunable with systematic variations in polymer graft density and molecular weight. To explore the structural origins of these unusual transport results, we use small angle scattering (neutron, X-ray) on the dry nanocomposite film and to critically examine in situ the structural effects of absorbed solvent. The relatively low diffusion coefficients of typical solvents (∼10^-12 m²/s) restricts us to thin films (≈1 μm in thickness) if solute concentration profiles are to equilibrate on the 1 s time scale. The use of such thin films, however, renders them as weak scatterers. Inspired by our nearly two decades old previous work, we address these conflicting requirements through the use of a custom designed flow cell, where stacks of 10 individual ≈1 μm thick supported films are used, while ensuring that each film is individually exposed to solvent vapor. By using isotopically labeled solvents, we study the solvent distribution within the film and show surprisingly that the solvent homogeneously swells the polymer under all conditions that we examined. These results are not anticipated by current theories, but they suggest that, at least under some conditions, the free volume increases due to the grafting of chains to nanoparticles is apparently distributed isotropically in these materials.

Decoupling energetic modifications to diffusion from free volume in polymer/nanoparticle composites

Diffusion coefficients of small molecules in a model composite of spherical nanoparticles and polymer with attractive interfacial interactions are reduced from that in the pure polymer, to a degree far below the level expected from geometric tortuosity arguments. We determine whether such dramatic reductions are due to modifications to the matrix polymer free volume near the nanoparticle surface, or alternatively are due to energetic attractions between the diffusants and nanoparticle surface. We performed ethyl acetate sorption experiments within the vicinity of the polymer glass transition (T_g ≤ T ≤ T_g + 25 K) for a model polymer/nanoparticle composite, silica-filled poly(methyl acrylate). By application of the Vrentas-Duda free volume theory of diffusion we have decoupled the energetic effects from those related to free-volume and segmental dynamics. While the latter is unaffected by addition of nanoparticles, the energy needed for the ethyl acetate diffusant to overcome neighboring attractive forces doubles after adding 40 vol% nanoparticles with a diameter of 14 nm. This is qualitatively consistent with hydrogen bonding interactions between the silica surface and ethyl acetate slowing its rate of diffusion. On the other hand for benzene, which does not hydrogen bond to the silica surface, diffusion coefficients that can be explained by tortuosity effects were obtained. This work provides quantitative evidence that the diffusant-filler energetic interactions and geometric blocking effects can be fully responsible for the substantially reduced diffusivity commonly observed in polymer/nanoparticle composite systems.