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

Abstract

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.

Thermodynamics of Charge Regulation during Ion Transport through Silica Nanochannels

“…From eq , the increasing conductance with respect to temperature at this high concentration (i.e., bulk-dominated transport regime) stems from the temperature dependence of the cation and anion mobilities. ,− Salt conductance can be related to salt permeability ( P S ) by where α is a temperature-independent parameter. In this form, the thermodynamics of salt transport are readily probed using the linearized form of an Arrhenius-type equation ,, where P 0 is a pre-exponential factor and E a is the activation energy for salt conductance. We fit the temperature-dependent transport data of 1 mol L –1 KCl to eq (Figure C).…”

Energy Barriers for Steroid Hormone Transport in Nanofiltration

“…Notably, J so obtained for both membranes (Figure B) further supports the dominance of size exclusion (entropic component) in the tight NF90 compared to the loose NF270. The dense structure and small pores of NF90 result in a high steric hindrance and reduced ability of steroid hormones to partition into the membrane (higher entropic barrier), giving rise to a lower J so compared to the loose NF270 membrane. ,, …”

“…While such modeling efforts might not explain the rejection trends of adsorbing MPs, the adsorption parameter and the “membrane affinity concept” were introduced to model the transport of adsorbing MPs in NF. ,, Nevertheless, the trends are typically attributed to either adsorption, diffusive, or convective components and cannot capture more fundamental factors driving MPs breakthrough in NF. In contrast, modeling solutes transport from an energy barrier perspective can elucidate important features (like the role of intrapore interactions on solute transport) promoting permeation in NF …”

“…The Arrhenius equation accounts for the influence of temperature on the specific rate of a chemical reaction, giving rise to the energy that a molecule must attain in the initial state of a process (reaction) before it can react. ,, In the case of a membrane filtration process, the reaction to be considered is the solute transport across the membrane as the solute must successively break and reform bonds with the neighboring water molecules and the polymer material (e.g., carboxyl groups) within the porous structure . Therefore, the breakage and formation of bonds can be described as elementary reactions and linked to the Arrhenius concept that can highlight the contribution of enthalpy (e.g., adsorption) and entropy (e.g., size exclusion) to solute transport in NF. , Solute confinement and freedom of motion (e.g., degree of steric constraints) are linked to the entropic component of the Arrhenius equation (e.g., J so , eq ), while the ability to overcome different hindrances and transport (see Figure ) is dictated by the enthalpy component (e.g., E p , eq ). The interpretation of the energy barriers encountered by MPs in NF provides a deeper understanding of the role of different transport mechanisms.…”

Comparison of Ion Selectivity in Electrodialysis and Capacitive Deionization

“…A potential reason for the preference for NO 3 – over Cl – is the ions’ shape, as planar-shaped NO 3 – can enter more readily into slit-shaped pores of IEMs − and porous CDI electrodes . In addition, the weaker hydration shell of NO 3 – may allow it to dehydrate and permeate the membrane or electrode pores more readily. ,,,− Other mechanisms include concentration polarization effects (nitrate is a “heavier” ion that tends to concentrate more on membrane surfaces compared to chloride) and a chemical affinity of surface groups to NO 3 – over Cl – , such as in a CDI half-cell with an anode functionalized with trimethyl quaternary amine moieties . Kesore et al demonstrated an exceptionally high value of 150 using an ED stack, an order of magnitude higher than the selectivity seen in all other studies compiled here, which was achieved at a low current density of I = 0.5 mA/cm 2 …”