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Novel separation technologies are necessary to use Earth's limited resources while maintaining a high standard of living. The availability of potable water is stressed due to contamination with trace elements such as lead (Pb). The demand for lithium (Li) due to vehicle electrification will exceed its supply from primarily brine sources within a decade. Adsorption processes are promising cost-effective solutions to challenging low-concentration separations. Yet, there is a lack of quantitative modeling to assess emerging sorbents, which hinders the translation of novel materials into transformative technologies. This work proposes a generalized multiscale process targeting framework to rapidly screen candidate sorbents and set material property targets to develop adsorptive systems including Pb remediation and Li recovery applications. Langmuir isotherm and sorbent structure–property calculations explicitly link molecular properties, including affinity, saturation capacity, and pore size; device design decisions, including sorbent cross-sectional area and bed length; and system design decisions, including sorbent mass and number of parallel beds. The framework predicts that for Pb removal, there is limited scope to improve materials in isolation; instead, integration of sorbents into devices (e.g., membranes, packed beds) may be the larger barrier to realizing future technologies. Similarly, for Li recovery applications, improved materials processing techniques have the potential to accelerate the process. Moreover, the Li case study demonstrates the utility of the framework based on dimensionless formulas as an easy-to-use tool for the broader membrane science and environmental engineering communities to assess the feasibility of emerging materials to meet process demands. Finally, these dimensionless models are used to identify three distinct regions of relative performance between batch and semicontinuous processes. These results give caution to applying scale-up heuristics outside their valid region, which can lead to under- or overdesign during bottom-up studies from the bench to the process scale. The presented targeting framework bridges a crucial gap between material and technology development by identifying the potential for optimized materials processing and device design techniques to fully utilize the characteristics of emerging materials for sustainable separations of the future.

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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.

The scarcity of potable water is an imminent threat to at least half the world's population. Engineered nanomaterials (ENMs) have the potential to treat water from polluted sources to mitigate the scarcity of potable water. However, the performance demands on these materials in practical applications has not been studied in detail. This is but one of the challenges that hinder the widespread implementation of ENMs for water treatment. The emerging fit-for-purpose paradigm which encourages water treatment at the point-of-use (POU) or point-of-entry (POE) could lower the barrier for the use of ENMs in water technology by incorporating smaller, decentralized ENM-based treatment systems. This work develops a bottom-up and top-down modeling framework to facilitate the design of nanoporous membrane-based sorbents, a promising class of ENMs, for POU and POE water treatment applications. Langmuir isotherm and membrane structure-property calculations provide the multiscale link between molecular properties, including affinity, saturation capacity, and pore size, device design decisions, including membrane area and thickness, and system design decisions, including sorbent mass and number of parallel modules. The framework predicts that for lead contaminants, existing materials are near molecular and systems limitations; improvements in the properties of adsorptive materials to treat lead will yield few benefits for POU and POE treatment systems. Moreover, the framework provides dimensionless formulas that apply to all adsorptive systems that exhibit (near) equilibrium behavior as an easy-to-use tool for the broader membrane science and environmental engineering communities to assess the feasibility of emerging materials to meet process demands. A case study regarding materials for arsenic removal demonstrates how to apply the modeling framework to calculate material properties targets and predict system performance for an arbitrary single-solute adsorption process. Finally, these dimensionless models are used to identify three distinct regions of relative performance between batch and semi-continuous processes. These results give caution to applying scale-up heuristics outside their valid region, which can lead to under- or over-design during bottom-up studies. The presented modeling framework is a crucial step to fully optimize engineered nanomaterials across material, device, and system scales.