Exploring the Knowledge Attained by Machine Learning on Ion Transport across Polyamide Membranes Using Explainable Artificial Intelligence.

Recent studies have increasingly applied machine learning (ML) to aid in performance and material design associated with membrane separation. However, whether the knowledge attained by ML with a limited number of available data is enough to capture and validate the fundamental principles of membrane science remains elusive. Herein, we applied explainable artificial intelligence (XAI) to thoroughly investigate the knowledge learned by ML on the mechanisms of ion transport across polyamide reverse osmosis (RO) and nanofiltration (NF) membranes by leveraging 1,585 data from 26 membrane types. The Shapley additive explanation method based on cooperative game theory was used to unveil the influences of various ion and membrane properties on the model predictions. XAI shows that the ML can capture the important roles of size exclusion and electrostatic interaction in regulating membrane separation properly. XAI also identifies that the mechanisms governing ion transport possess different relative importance to cation and anion rejections during RO and NF filtration. Overall, we provide a framework to evaluate the knowledge underlying the ML model prediction and demonstrate that ML is able to learn fundamental mechanisms of ion transport across polyamide membranes, highlighting the importance of elucidating model interpretability for more reliable and explainable ML applications to membrane selection and design.

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.

Machine learning reveals key ion selectivity mechanisms in polymeric membranes with subnanometer pores.

Designing single-species selective membranes for high-precision separations requires a fundamental understanding of the molecular interactions governing solute transport. Here, we comprehensively assess molecular-level features that influence the separation of 18 different anions by nanoporous cellulose acetate membranes. Our analysis identifies the limitations of bulk solvation characteristics to explain ion transport, highlighted by the poor correlation between hydration energy and the measured permselectivity (R2 = 0.37). Entropy-enthalpy compensation, spanning 40 kilojoules per mole, leads to a free-energy barrier (∆G‡) variation of only ~8 kilojoules per mole across all anions. We apply machine learning to elucidate descriptors for energetic barriers from a set of 126 collected features. Notably, electrostatic features account for 75% of the overall features used to describe ∆G‡, despite the relatively uncharged state of cellulose acetate. Our work presents an approach for studying ion transport across nanoporous membranes that could enable the design of ion-selective membranes.

Selective Fluoride Transport in Subnanometer TiO2 Pores.

Synthesizing nanopores which mimic the functionality of ion-selective biological channels has been a challenging yet promising approach to advance technologies for precise ion-ion separations. Inspired by the facilitated fluoride (F-) permeation in the biological fluoride channel, we designed a highly fluoride-selective TiO2 film using the atomic layer deposition (ALD) technique. The subnanometer voids within the fabricated TiO2 film (4 Å < d < 12 Å, with two distinct peaks at 5.5 and 6.5 Å), created by the hindered diffusion of ALD precursors (d = 7 Å), resulted in more than eight times faster permeation of sodium fluoride compared to other sodium halides. We show that the specific Ti-F interactions compensate for the energy penalty of F- dehydration during the partitioning of F- ions into the pore and allow for an intrapore accumulation of F- ions. Concomitantly, the accumulation of F- ions on the pore walls also enhances the transport of sodium (Na+) cations due to electrostatic interactions. Molecular dynamics simulations probing the ion concentration and mobility within the TiO2 pore further support our proposed mechanisms for the selective F- transport and enhanced Na+ permeation in the TiO2 film. Overall, our work provides insights toward the design of ion-selective nanopores using the ALD technique.

Enthalpic and Entropic Selectivity of Water and Small Ions in Polyamide Membranes.

While polyamide reverse osmosis and nanofiltration membranes have been extensively utilized in water purification and desalination processes, the molecular details governing water and solute permeation in these membranes are not fully understood. In this study, we apply transition-state theory for transmembrane permeation to systematically break down the intrinsic permeabilities of water and small ions in loose and tight polyamide nanofiltration membranes into enthalpic and entropic components using an Eyring-type equation. We analyze trends in these components to elucidate molecular phenomena that induce water-salt, monovalent-divalent, and monovalent-monovalent selectivity at different pH values. Our results suggest that in pores that are either too small or contain an electrostatically repelling mouth, the thermal activation of ions in the form of ion dehydration is less likely, promoting entropically driven selectivity with steric exclusion of hydrated ions. Instead, larger uncharged pores enable ion dehydration, inducing enthalpic selectivity that is driven by differences in the ion hydration properties. We also demonstrate that electrostatic interactions between cations and intrapore carboxyl groups hinder salt permeability, increasing the enthalpic barrier of the transport. Last, permeation tests of monovalent cations in the loose and tight polyamide membranes expose opposite rejection trends that further support the phenomenon of ion dehydration in large subnanopores.

Intrapore energy barriers govern ion transport and selectivity of desalination membranes.

State-of-the-art desalination membranes exhibit high water-salt selectivity, but their ability to discriminate between ions is limited. Elucidating the fundamental mechanisms underlying ion transport and selectivity in subnanometer pores is therefore imperative for the development of ion-selective membranes. Here, we compare the overall energy barrier for salt transport and energy barriers for individual ion transport, showing that cations and anions traverse the membrane pore in an independent manner. Supported by density functional theory simulations, we demonstrate that electrostatic interactions between permeating counterion and fixed charges on the membrane substantially hinder intrapore diffusion. Furthermore, using quartz crystal microbalance, we break down the contributions of partitioning at the pore mouth and intrapore diffusion to the overall energy barrier for salt transport. Overall, our results indicate that intrapore diffusion governs salt transport through subnanometer pores due to ion-pore wall interactions, providing the scientific base for the design of membranes with high ion-ion selectivity.

Towards single-species selectivity of membranes with subnanometre pores.

Synthetic membranes with pores at the subnanometre scale are at the core of processes for separating solutes from water, such as water purification and desalination. While these membrane processes have achieved substantial industrial success, the capability of state-of-the-art membranes to selectively separate a single solute from a mixture of solutes is limited. Such high-precision separation would enable fit-for-purpose treatment, improving the sustainability of current water-treatment processes and opening doors for new applications of membrane technologies. Herein, we introduce the challenges of state-of-the-art membranes with subnanometre pores to achieve high selectivity between solutes. We then analyse experimental and theoretical literature to discuss the molecular-level mechanisms that contribute to energy barriers for solute transport through subnanometre pores. We conclude by providing principles and guidelines for designing next-generation single-species selective membranes that are inspired by ion-selective biological channels.

Similarities and differences between potassium and ammonium ions in liquid water: a first-principles study.

Understanding ion solvation in liquid water is critical in optimizing materials for a wide variety of emerging technologies, including water desalination and purification. In this work, we report a systematic investigation and comparison of solvated K+ and NH4+ using first-principles molecular dynamics simulations. Our simulations reveal a strong analogy in the solvation properties of the two ions, including the size of the solvation shell as well as the solvation strength. On the other hand, we find that the local water structure in the ion solvation is significantly different; specifically, NH4+ yields a smaller number of water molecules and a more ordered water structure in the first solvation shell due to the formation of hydrogen bonds between the ion and water molecules. Finally, our simulations indicate that a comparable solvation strength of the two ions is a result of an interplay between the nature of ion-water interaction and number of water molecules that can be accommodated in the ion solvation shell.

Role of Ionic Charge Density in Donnan Exclusion of Monovalent Anions by Nanofiltration.

The main objective of this study is to examine how the charge densities of four monovalent anions-fluoride (F-), chloride (Cl-), bromide (Br-), and nitrate (NO3-)-influence their Donnan (charge) exclusion by a charged nanofiltration (NF) membrane. We systematically studied the rejection behavior of ternary ion solutions containing sodium cation (Na+) and two of the monovalent anions as a function of the pH with a polyamide NF membrane. In the solutions containing F- and Cl- or F- and Br-, F- rejection was higher than Cl- or Br- rejection only when the solution pH was higher than 5.5, suggesting that F- (which has a higher charge density) was repelled more strongly by the negatively charged membrane. The order of change in the activation energy for the transport of the four anions through the polyamide membrane as a response to the increase of the membrane negative charge was the following: F- > Cl- > NO3- > Br-. This order corroborates our main hypothesis that an anion with a smaller ionic radius, and hence a higher charge density, is more affected by the Donnan (charge)-exclusion mechanism in NF. We conclude with a proposed mechanism for the role of ionic charge density in the rejection of monovalent anions in NF.

Pressurized hydrogenotrophic denitrification reactor for small water systems.

The implementation of hydrogenotrophic denitrification is limited due to safety concerns, poor H2 utilization and low solubility of H2 gas with the resulting low transfer rate. The current paper presents the main research work conducted on a pressurized hydrogenotrophic reactor for denitrification that was recently developed. The reactor is based on a new concept suggesting that a gas-liquid equilibrium is achieved in the closed headspace of denitrifying reactor, further produced N2 gas is carried out by the effluent and gas purging is not required. The feasibility of the proposed reactor was shown for two effluent concentrations of 10 and 1 mg NO3--N/L. Hydrogen gas utilization efficiencies of 92.8% and 96.9% were measured for the two effluent concentrations, respectively. Reactor modeling predicted high denitrification rates above 4 g NO3--N/(Lreactor·d) at reasonable operational conditions. Hydrogen utilization efficiency was improved up to almost 100% by combining the pressurized reactor with a following open-to-atmosphere polishing unit. Also, the potential of the reactor to remove ClO4- was shown.

Submerged bed versus unsaturated flow reactor: A pressurized hydrogenotrophic denitrification reactor as a case study.

The paper compares the main features of a submerged bed reactor (SuBR) with bubbling and recirculation of gas to those of an unsaturated flow reactor (uSFR) with liquid recirculation. A novel pressurized closed-headspace hydrogenotrophic denitrification system characterized by safe and economic utilization of H2 gas was used for the comparison. Under similar conditions, denitrification rates were lower in the SuBR as a result of a lower effective biofilm surface area and overall gas-liquid mass transfer coefficient kLa. Similar values of effluent DOC were achieved for both reactors, although effluent suspended solids concentration of the SuBR were substantially higher. On the other hand, the required cleaning frequency in the SuBR was 2.5 times lower. Moreover, the SuBR is expected to reduce the recirculation energy consumption by 0.35 kWh/m(3) treated.