X-ray scattering is a structural characterization tool that has impacted diverse fields of study. It is unique in its ability to examine materials in real time and under realistic sample environments, enabling researchers to understand morphology at nanometer and angstrom length scales using complementary small and wide angle X-ray scattering (SAXS, WAXS), respectively. Herein, we focus on the use of SAXS to examine nanoscale particulate systems. We provide a theoretical foundation for X-ray scattering, considering both form factor and structure factor, as well as the use of correlation functions, which may be used to determine a particle's size, size distribution, shape, and organization into hierarchical structures. The theory is expanded upon with contemporary use cases. Both transmission and reflection (grazing incidence) geometries are addressed, as well as the combination of SAXS with other X-ray and non-X-ray characterization tools. We conclude with an examination of several key areas of research where X-ray scattering has played a pivotal role, including in situ nanoparticle synthesis, nanoparticle assembly, and operando studies of catalysts and energy storage materials. Throughout this review we highlight the unique capabilities of X-ray scattering for structural characterization of materials in their native environment.

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The implementation of membrane-based separations in the petrochemical industry has the potential to reduce energy consumption significantly relative to conventional separation processes. Achieving this goal, however, requires the development of new membrane materials with greater selectivity, permeability and stability than available at present. Here, we report composite materials consisting of nanocrystals of metal-organic frameworks dispersed within a high-performance polyimide, which can exhibit enhanced selectivity for ethylene over ethane, greater ethylene permeability and improved membrane stability. Our results suggest that framework-polymer interactions reduce chain mobility of the polymer while simultaneously boosting membrane separation performance. The increased stability, or plasticization resistance, is expected to improve membrane utility under real process conditions for petrochemical separations and natural gas purification. Furthermore, this approach can be broadly applied to numerous polymers that encounter aggressive environments, potentially making gas separations possible that were previously inaccessible to membranes.

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