Nanostructure Heterogeneity and the Excess Free Volumes in Polymer-grafted Nanoparticle Membranes*

Polymer-grafted nanoparticle (PGN) membranes display significantly enhanced gas permeabilities relative to neat polymer analogs. Independent experiments have shown that the underlying cause is an increased free volume in the PGNs. However, there is no understanding of how free volume manifests in macroscale PGN properties. We use small-angle x-ray scattering with a micro-focused beam coupled with the evolving tools of artificial intelligence to measure the distribution of distances between neighboring nanoparticle centers for densely grafted poly(methyl acrylate)-grafted-silica nanoparticles (PMA-g-SiO₂) melts across macroscale areas (i.e., 4 mm x 4 mm). Based on these, we present remarkable correlated trends between the standard deviations of these nanostructure distributions and gas permeability enhancements. For the PMA graft molecular weight with the highest gas permeability enhancement, we found a broad distribution of nanostructure distances, suggesting a reduced penalty for creating such spatial heterogeneities. We posit that these results reflect the ability of these materials to tolerate density fluctuations, providing a molecular underpinning of the free volume trends.