Applying Transition-State Theory to Explore Transport and Selectivity in Salt-Rejecting Membranes: A Critical Review

Membrane technologies using reverse osmosis (RO) and nanofiltration (NF) have been widely implemented in water purification and desalination processes. Separation between species at the molecular level is achievable in RO and NF membranes due to a complex and poorly understood combination of transport mechanisms that have attracted the attention of researchers within and beyond the membrane community for many years. Minimizing existing knowledge gaps in transport through these membranes can improve the sustainability of current water-treatment processes and expand the use of RO and NF membranes to other applications that require high selectivity between species. Since its establishment in 1949, and with growing popularity in recent years, Eyring's transition-state theory (TST) for transmembrane permeation has been applied in numerous studies to mechanistically explore molecular transport in membranes including RO and NF. In this review, we critically assess TST applied to transmembrane permeation in salt-rejecting membranes, focusing on mechanistic insights into transport under confinement that can be gained from this framework and the key limitations associated with the method. We first demonstrate and discuss the limited ability of the commonly used solution-diffusion model to mechanistically explain transport and selectivity trends observed in RO and NF membranes. Next, we review important milestones in the development of TST, introduce its underlying principles and equations, and establish the connection to transmembrane permeation with a focus on molecular-level enthalpic and entropic barriers that govern water and solute transport under confinement. We then critically review the application of TST to explore transport in RO and NF membranes, analyzing trends in measured enthalpic and entropic barriers and synthesizing new data to highlight important phenomena associated with the temperature-dependent measurement of the activation parameters. We also discuss major limitations of the experimental application of TST and propose specific solutions to minimize the uncertainties surrounding the current approach. We conclude with identifying future research needs to enhance the implementation and maximize the benefit of TST application to transmembrane permeation.