Polymers of intrinsic microporosity (PIMs) have shown promise in pushing the limits of gas separation membranes, recently redefining upper bounds for a variety of gas pair separations. However, many of these membranes still suffer from reductions in permeability over time, removing the primary advantage of this class of polymer. In this work, a series of pentiptycene-based PIMs incorporated into copolymers with PIM-1 are examined to identify fundamental structure–property relationships between the configuration of the pentiptycene backbone and its accompanying linear or branched substituent group. The incorporation of pentiptycene provides a route to instill a more permanent, configuration-based free volume, resistant to physical aging via traditional collapse of conformation-based free volume. PPIM-ip-C and PPIM-np-S, copolymers with C- and S-shape backbones and branched isopropoxy and linear n-propoxy substituent groups, respectively, each exhibited initial separation performance enhancements relative to PIM-1. Additionally, aging-enhanced gas permeabilities were observed, a stark departure from the typical permeability losses pure PIM-1 experiences with aging. Mixed-gas separation data showed enhanced CO2/CH4 selectivity relative to the pure-gas permeation results, with only ∼20% decreases in selectivity when moving from a CO2 partial pressure of ∼2.4 to ∼7.1 atm (atmospheric pressure) when utilizing a mixed-gas CO2/CH4 feed stream. These results highlight the potential of pentiptycene’s intrinsic, configurational free volume for simultaneously delivering size-sieving above the 2008 upper bound, along with exceptional resistance to physical aging that often plagues high free volume PIMs.

Novel processes are urgently needed to recycle critical materials (e.g., cobalt, lithium, nickel, and manganese) from spent lithium-ion batteries (LIBs). These separations are vital both to meet growing global demand and to mitigate a looming e-waste crisis. Currently, to recover cobalt and lithium from spent LIBs, high temperatures and organic solvents are used to separate Co2+ and Li+ in complex leaching and extraction processes. In contrast to using expensive designer ligands or harmful organic solvents, this work reveals that continuous membrane cascades are a promising aqueous-based alternative to recover these critical materials and facilitate their reuse. A superstructure optimization model that designs diafiltration cascades to maximize material recovery and purity as a function of membrane material performance and feed specifications is developed. This approach enables the comparison of candidate membrane materials by rapidly predicting the Pareto optimal trade-offs between the recovery and purity of lithium and cobalt for bespoke cascade designs. For example, the model predicts that, when deployed in an optimized two-stage cascade configuration, a nanofiltration membrane with a modest selectivity of 32 can be used to recover 95% Li+ and 99% Co2+ at 93 and 99.5 wt % purity, respectively. On the basis of analysis of over 1000 Pareto optimal designs, six design heuristics for executing binary separations using staged diafiltration cascades are proposed. Moreover, by evaluating membrane materials in the context of optimized diafiltration processes, this work quantifies the benefits of materials improvements and shows that the greatest research opportunities for membrane-based LIB recycling are at the device and systems scales. More broadly, the optimization models represent a robust framework for identifying the most effective way to deploy emerging materials in integrated process systems. This transformative capability is widely applicable to many of the separations needed to support sustainable global development.