Partition–diffusion–reaction bounds for thin-film membrane formation kinetics

Abstract

New membrane chemistries and structures have rapidly developed over the last ten years, driven by applications ranging from critical metals separations and carbon capture to highly chlorine-resistant reverse-osmosis membranes. The thin selective layer at the heart of reverse osmosis and nanofiltration membranes is typically fabricated using interfacial synthesis, with multifunctional aqueous-phase monomers and organicphase monomers. Here, we develop a physics-based model of partition, diffusion, and reaction dynamics during the early stages of interfacial synthesis. These processes critically impact membrane structure and performance. By solving the resulting partial differential equations numerically and with analytical approximations, we demonstrate that the planar reaction rate is initially limited by the partitioning and diffusion of the aqueous-phase reactant into the organic phase. Later, finite reactant availability and aqueous-phase diffusion become limiting. Through a combination of nondimensionalization, parameter mapping, and property prediction, we develop a framework that spans a wide parameter space in reactant chemistry, solvent and support layer choice, and initial reactant concentrations. We demonstrate that the planar reaction rate and dynamics are strongly affected by the partition coefficient of the aqueous reactant, which varies rapidly with changes in reactant and solvent chemistry. The influence of diffusion variations is more limited. This tractable, physics-based model enables the rapid quantification of monomer and solvent impact on interfacial synthesis, which is essential for the rational development of new high-performance thin-film composite membranes.