A coarse-grained thermodynamic model for the predictive engineering of valence-selective membranes
Membrane-based filtration has shown promise in the treatment of municipal and industrial water supplies. Most existing filtration membranes rely on size-selective rejection mechanisms and do not offer a systematic means to tune the chemistry of the membrane and, in turn, the rejection of solutes based on chemical factors. Technological advancements in copolymer self-assembly have permitted the creation of highly porous membranes through arrested microphase separation. The resulting structures exhibit nanoscale pores whose size and chemistry are controlled by the macromolecular architecture of the copolymer precursors. Here, we examine in detail how the structure and chemistry of charge-functionalized copolymers affect their performance as nanofiltration membranes through experiments and coarse-grained molecular simulation of membranes formed from poly(acrylonitrile-r-oligo(ethylene glycol) methyl ether methacrylate-r-glycidyl methacrylate) (P(AN-r-OEGMA-r-GMA)). Charge-selective moieties were introduced into the membranes through reactions with diamine salts of varying length, enabling these membranes to offer preferential rejection of multivalent ionic species. Using a minimal model, we explore the essential thermodynamics features of salt rejection in these membranes, and develop a model capable of linking the performance of the membranes to their molecular character through measurement of the underlying free energy profile. Our key result is an effective membrane porosity which quantitatively describes experiments for a wide variety of situations after calibrating a single parameter. These results demonstrate that at moderate ion concentrations and flow rates, the selection of ions is driven predominantly by equilibrium thermodynamics. Going forward, the ability of the model to capture the rejection of dissolved solutes can be leveraged to design optimized membranes for targeted performance profiles in silico before undertaking time consuming batteries of Edisonian experiments.