Since their discovery over a decade ago, thermally rearranged polymers have become established as a new class of glassy polymer membrane with superior permeability-selectivity combinations for mixed gas transport compared to conventional glassy polymers. Permeability-selectivity combinations surpassing Robeson’s upper bound have been attributed to the porosity that is developed during thermal rearrangement resulting in nanospace reminiscent of bottlenecks connecting adjacent chambers, such as those found in nature in the form of ion channels and aquaporins. Applications of these polymer membranes for clean energy include CO2 separation to make existing power generation industries cleaner. In research designed to understand and optimize the performance of these membranes we have measured the development of free volume in thermally rearranged polymers using positron annihilation lifetime spectroscopy and small angle X-ray scattering. In addition, we have performed a theoretical study, based on the free volume elements, in order to explain why these membranes perform so well. The hour-glass shaped pores are shown to provide a series of size-selective necks connected with larger flux-assisting cavities. Remarkably, with the correct neck and cavity size, the upper bound can be exceeded for many different gas mixtures. The ability to measure and tailor free volume at the Angstrom scale is shown to be critical for prediction of membrane performance.