Improved solute selectivity, an issue commonly approached through the development of advanced membrane materials, can be achieved through staged diafiltration processes. A mathematical model that describes the solute concentration profile within a single diafiltration module is developed and experimentally validated. For this module, where the diafiltrate is introduced uniformly over its length, a critical diafiltrate flux that results in the retentate concentration remaining constant during operations is identified. The model is then extended to examine two configurations of multistage diafiltration cascades: stripping sections and rectifying sections. The two configurations differ based on the connectivity between stages. Namely, stripping sections connect multiple modules by utilizing the retentate from one stage as the feed to the subsequent stage while the permeate is repurposed as the diafiltrate. In contrast, rectifying sections utilize the permeate from one stage as the feed to the subsequent stage and the retentate becomes the diafiltrate. For cascades that operate with a constant diafiltrate to feed flow ratio for all stages, the analysis demonstrates that stripping sections can reduce the diafiltrate consumed when separating low molar mass impurities from larger, impermeable molecules. On the other hand, cascades in a rectifying section configuration can improve the separation of two solutes with finite sieving coefficients between 0 and 1. Finally, asymmetric cascades, i.e., systems in which each stage has a unique diafiltrate to feed flow ratio, are shown to be capable of improving the recovery and purity of solutes in effluent streams relative to systems that operate at constant a diafiltrate to feed ratio. As a whole, the study highlights that the continued advancement of membrane separations will rely equally on thoughtful module and process design as well as the development of new materials.

Adsorption‐based separations have the potential to enhance the sustainability of established industrial processes and facilitate the adoption of new practices. They also provide ways to meet emerging needs in the isolation of resources from non‐traditional supplies and the remediation of hazardous environmental contaminants. In this regard, there are significant opportunities to advance both fundamental polymer science and engineering applications through next‐generation adsorbent systems. Here, after briefly reviewing the history, potential application space, and underlying physics of polymer sorbents, design considerations that connect macromolecular design with systems‐level functionality, are discussed. First, polymer processing conditions are discussed in terms of the final nano‐ and microscale structures produced. Subsequently, the macromolecular chemistry of the materials is analyzed with respect to the ability of the separations systems to have analyte‐specific binding. Finally, a similar analysis is performed regarding the desorption mechanism used to release the target solutes. In this way, the manuscript attempts to connect macromolecular architecture with polymer physics and materials processing to provide guidance on how these important interrelationships impact the ultimate performance of sorbent systems.

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Creating systems and techniques capable of reducing the time, energy, and resources needed to characterize the transport properties of polymer membranes can help to increase the rate of material and process development. Within this study, commercially available hardware and 3D-printed parts are integrated with a graphical user interface to develop an apparatus that automates the characterization of membrane transport properties. The system synchronizes the collection of the mass, concentration, and pressure data required to determine the hydraulic permeability and solute permeability coefficients. Automating the data collection and shutdown processes removes the need for a researcher to be present after the start of the experiment, effectively reducing the demand on their time by 40% per experiment. Moreover, the experiments generate more information than standard approaches by identifying the concentration dependencies of the transport coefficients. As an example, diafiltration experiments executed using the acquisition of dynamic data (ADD) device quantified MgCl 2 rejection by charge-functionalized poly[trifluoroethyl methacrylate-co-oligo(ethylene glycol) methyl ether methacrylate-co-glycidyl methacrylate] membranes over a range of retentate concentrations from 5 to 65 mM MgCl 2 . A single diafiltration experiment corroborated previously reported data, collected from a series of one-off filtration experiments, on membranes functionalized with hexamethylene diamine moieties. Membranes functionalized with ethylene diamine and trimethylolpropane tris[poly(propylene glycol), amine terminated] ether were also analyzed. High-throughput diafiltration experiments were able to elucidate the distinct concentration-dependent rejection profiles that resulted from these changes to the membrane chemistry. The versatility of the ADD device was highlighted by adapting it to characterize membrane sorbents using constant volumetric flux breakthrough experiments. Ultimately, the ability of this device to characterize functional polymer membranes will aid in the development of fundamental insights that connect macroscopic membrane properties with macromolecular design.

Membranes based on microphase-separated copolymers offer an opportunity to address the need for resilient materials that can be used in organic solvent-based filtration. Specifically, copolymer repeat unit chemistries can be chosen to impart solvent compatibility, to tailor membrane nanostructure, and to enable postsynthetic modification. In this study, a poly(trifluoroethyl methacrylate-co-oligo(ethylene glycol) methyl ether methacrylateco-glycidyl methacrylate) [P(TFEMA-OEGMA-GMA)] copolymer was synthesized and fabricated into flat sheet and hollow fiber membranes using a non-solvent-induced phase separation casting technique. The GMA repeat units possess epoxide groups that were used to cross-link the copolymer through a ring-opening reaction with diamines ranging from diaminoethane to diaminooctane. Transport experiments in water, methanol, ethanol, tetrahydrofuran, dimethylformamide, and toluene demonstrated that films reacted with longer diamines, such as diaminohexane, result in stable membranes. Conversely, the films reacted with shorter diamines degraded upon exposure to organic solvents. Because of their stability in organic solvents, transport through the diaminohexane-functionalized membranes was characterized in more detail using hydraulic permeability and neutral solute rejection experiments. The results of these experiments along with volumetric swelling and small-angle X-ray scattering (SAXS) analysis revealed that the solvent affinity for the constituent copolymer domains is critical in determining the permeation pathway. For P(TFEMA-OEGMA-GMA) membranes in protic solvents, such as ethanol, transport through the hydrophilic side chains of OEGMA was favored, while for membranes in aprotic solvents, such as toluene, transport through the hydrophobic matrix dominated. In neutral solute rejection experiments, 2000 g mol −1 polypropylene glycol molecules (solvated size ∼2 nm) permeated through the hydrophobic domain unhindered but were fully rejected when permeation occurred through the hydrophilic region. These differences highlight the need to understand the interactions between the copolymer domains and solvent when solvent-resilient membranes are developed for organic solvent filtration.