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Within a polymer film, free-volume elements such as pores and channels typically have a wide range of sizes and topologies. This broad range of free-volume element sizes compromises a polymer's ability to perform molecular separations. We demonstrated free-volume structures in dense vitreous polymers that enable outstanding molecular and ionic transport and separation performance that surpasses the limits of conventional polymers. The unusual microstructure in these materials can be systematically tailored by thermally driven segment rearrangement. Free-volume topologies can be tailored by controlling the degree of rearrangement, flexibility of the original chain, and judicious inclusion of small templating molecules. This rational tailoring of free-volume element architecture provides a route for preparing high-performance polymers for molecular-scale separations.