Understanding Gas Transport in Polymer-Grafted Nanoparticle Assemblies

We measure and rationalize the unusual gas transport behavior of polymer-grafted nanoparticle (GNP) membranes, in particular focusing on their enhanced permeabilities relative to the corresponding pure polymer. For a given NP radius and grafting density in the dense brush regime we find that gas permeabilities display a maximum as a function of the graft chain molecular weight. Based on a newly proposed theory for the structure of a spherical brush, we postulate that the peak permeability for these brush constructs occurs when the densely grafted polymer brush has the highest, packing-induced extension free energy per chain. The brush thickness corresponding to this maximum extension free energy is predicted to be independent of chain chemistry and at an apparently universal value of the NP loading. Motivated by this conjecture, we measured carbon dioxide and methane permeability enhancements across a variety of NP core sizes, graft density and graft chain length, and find that they behave in a similar manner when considered as a function of NP core volume fraction, with a peak in the near vicinity of the predicted value when the chain extension free energy is maximized. Thus, the chain 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 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, and apparently leads to an increasing gas permeability. For long enough grafts, there is an outer region of chain segments that that is akin to an unperturbed melt with slow gas transport.