Ion partitioning and permeation in charged low-T* membranes

Thermodynamics of Mobile Ion in Ion Exchange Membranes: Water-Swollen-Membrane Reference State and Quasi-Regular Solution Model

Thermodynamics of mobile ions in swollen ion exchange membranes (IEM) are essential for understanding their permselectivity. The theoretical modeling of the ion activity coefficient and the ion partitioning of the IEM is challenging. Based on a water-swollen membrane reference state and a quasi-regular solution model, we successfully correlated the ion activity coefficient in various IEMs. For all the studied 59 systems, the correlation coefficient r and determination coefficient R2 are 0.973 and 0.947, respectively. As expected, the water activity in the IEM and the ion partitioning between the IEM and the external salt solution are represented. In the new theory framework, the standard chemical potential of the counterion is different from that of the aqueous solution. Moreover, the ion activity coefficient in the IEM reaches unity for the infinite dilution external salt concentration for all systems. Our quasi-regular solution model only considered the short-range interactions between the co-ions and the "effective free counterion", but it showed excellent correlation ability with the activity coefficient data of extensive systems. A power-law relation between the effective concentration of the free counterion and the apparent concentration of the free counterion was suggested. This indicates that the long-range electrostatic interactions in the swollen IEM are negligible due to abundant counterion condensation shielding the charge of the polymer chain.

Unraveling the Atomistic Mechanisms Underlying Effective Reverse Osmosis Filtration by Graphene Oxide Membranes

The graphene oxide (GO) membrane displays promising potential in efficiently filtering ions from water. However, the precise mechanism behind its effectiveness remains elusive, particularly due to the lack of direct experimental evidence at the atomic scale. To shed light on this matter, state-of-the-art techniques are employed such as integrated differential phase contrast-scanning transmission electron microscopy and electron energy loss spectroscopy, combined with reverse osmosis (RO) filtration experiments using GO membranes. The atomic-scale observations after the RO experiments directly reveal the binding of various ions including Na+, K+, Ca2+, and Fe3+ to the defects, edges, and functional groups of GO. The remarkable ion-sieving capabilities of GO membranes are confirmed, which can be attributed to a synergistic interplay of size exclusion, electrostatic interactions, cation-π, and other non-covalent interactions. Moreover, GO membranes modified by external pressure and cation also demonstrated further enhanced filtration performance for filtration. This study significantly contributes by uncovering the atomic-scale mechanism responsible for ion sieving in GO membranes. These findings not only enhance the fundamental understanding but also hold substantial potential for the advancement of GO membranes in reverse osmosis (RO) filtration.

Growth of membranes formed by associating polymers at interfaces

Polymer association at liquid-liquid interfaces is a promising way to spontaneously obtain soft self-healing membranes. In the case of reversible bonding between two polymers, the macromolecules are mobile everywhere within the membrane and they can be absorbed into it at both boundaries due to binding to macromolecules of the other type. In this work, we develop the theoretical model of membrane growth based on these assumptions. The asymptotic dependence of membrane thickness on time as h ∼ t1/2, as typically observed experimentally in a stationary regime, reveals an interdiffusion-controlled process, where the polymer fluxes sustain the polymer absorption. The membrane growth rate is mainly determined by the difference in equilibrium compositions at the boundaries, the association constant, the polymer lengths and mobilities. This model is further used to describe the growth of hydrogel membranes formed via H-bonding of polymers at the interface between a solution of poly(propylene oxide) (PPO) in isopropyl myristate and an aqueous solution of poly(methacrylic acid) (PMAA). The film thickness is measured by reflectometric methods. The growth rate slows down about 25 times for 500-nm-thick films at pH = 5.1 compared to the case of pH = 3. The ionization degree of PMAA solutions is studied by potentiometric methods. Even a small change in ionization is found to influence noticeably the growth rate of the film. In the diffusion-controlled regime, the slowdown can be explained by a drop in the composition gradient in the membrane, whereas the process becomes non-stationary if the absorption of PMAA is hindered by an interfacial electrostatic barrier.

Application of the Born Model to Describe Salt Partitioning in Hydrated Polymers

The classic Born model can be used to predict salt partitioning properties observed in hydrated polymers, but there are often significant quantitative discrepancies between these predictions and the experimental data. Here, we use an updated version of the Born model, reformulated to account for the local environment and mesh size of a hydrated polymer, to describe previously published NaCl, KCl, and LiCl partitioning properties of model cross-linked poly(ethylene glycol) diacrylate polymers. This reformulated Born model describes the influence of polymer structure (i.e., network mesh size and its relationship with water content) and external salt concentration on salt partitioning in the polymers with a significant improvement relative to the classic Born model. The updated model most effectively describes NaCl partitioning properties and provides an additional fundamental understanding of salt partitioning processes, for NaCl, KCl, and LiCl, in hydrated polymers that are of interest for a variety of environmental and biological applications.

Dielectric exclusion, an éminence grise

Dielectric exclusion has long been well-established as the key mechanism in membrane desalination, critical for delivering the required levels of salt rejection, also playing important role in electro-membrane processes, nanofluidics, and biomimetics. Unfortunately, its elusive nature and many features, such as dependence on the pore size, membrane hydration, and ion size and charge, make it deceivingly similar to the other ion exclusions mechanisms, steric and Donnan, which has led to much controversy and misconceptions. Starting from the Born model and the concept of self-energy, the present paper reviews and highlights the physical basis of dielectric exclusion, its main features and the ways it may be looked at. It discusses what makes the dielectric exclusion both similar and distinctly different from the other mechanism and its synergy and intimate connection with other phenomena, such as Donnan exclusion, permeability-selectivity upper-bound, and selectivity of charged membranes towards uncharged solutes. The paper also addresses subjects that still cause much controversy at present, such as appropriate measures of ionic radii and the subtle distinction between the dielectric exclusion and primary ion hydration. It also points to gaps that need to be bridged towards more complete theory. The points addressed here are important for understanding, modeling and development of various next-generation separation technologies including water purification, resource recovery and reuse, and green energy generation and storage.

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

Significance of Co-ion Partitioning in Salt Transport through Polyamide Reverse Osmosis Membranes

Salt permeability of polyamide reverse osmosis (RO) membranes has been shown to increase with increasing feed salt concentration. The dependence of salt permeability on salt concentration has been attributed to the variation of salt partitioning with feed salt concentration. However, studies using various analytical techniques revealed that the salt (total ion) partitioning coefficient decreases with increasing salt concentration, in marked contrast to the observed increase in salt permeability. Herein, we thoroughly investigate the dependence of total ion and co-ion partitioning coefficients on salt concentration and solution pH. The salt partitioning is measured using a quartz crystal microbalance (QCM), while the co-ion partitioning is calculated from the measured salt partitioning using a modified Donnan theory. Our results demonstrate that the co-ion and total ion partitioning behave entirely differently with increasing salt concentrations. Specifically, the co-ion partitioning increased fourfold, while total ion partitioning decreased by 60% as the salt (NaCl) concentration increased from 100 to 800 mM. The increase in co-ion partitioning with increasing salt concentration is in accordance with the increasing trend of salt permeability in RO experiments. We further show that the dependence of salt and co-ion partitioning on salt concentration is much more pronounced at a higher solution pH. The good co-ion exclusion (GCE) model─derived from the solution-friction model─is used to calculate the salt permeability based on the co-ion partitioning coefficients. Our results show that the GCE model predicts the salt permeabilities in RO experiments relatively well, indicating that co-ion partitioning, not salt partitioning, governs salt transport through RO membranes. Our study provides an in-depth understanding of ion partitioning in polyamide RO membranes and its relationship with salt transport.

Unlocking the potential of polymeric desalination membranes by understanding molecular-level interactions and transport mechanisms

Polyamide reverse osmosis (PA-RO) membranes achieve remarkably high water permeability and salt rejection, making them a key technology for addressing water shortages through processes including seawater desalination and wastewater reuse. However, current state-of-the-art membranes suffer from challenges related to inadequate selectivity, fouling, and a poor ability of existing models to predict performance. In this Perspective, we assert that a molecular understanding of the mechanisms that govern selectivity and transport of PA-RO and other polymer membranes is crucial to both guide future membrane development efforts and improve the predictive capability of transport models. We summarize the current understanding of ion, water, and polymer interactions in PA-RO membranes, drawing insights from nanofiltration and ion exchange membranes. Building on this knowledge, we explore how these interactions impact the transport properties of membranes, highlighting assumptions of transport models that warrant further investigation to improve predictive capabilities and elucidate underlying transport mechanisms. We then underscore recent advances in in situ characterization techniques that allow for direct measurements of previously difficult-to-obtain information on hydrated polymer membrane properties, hydrated ion properties, and ion-water-membrane interactions as well as powerful computational and electrochemical methods that facilitate systematic studies of transport phenomena.

Polystyrene Sulfonate Particles as Building Blocks for Nanofiltration Membranes

Today the standard treatment for wastewater is secondary treatment. This procedure cannot remove salinity or some organic micropollutants from water. In the future, a tertiary cleaning step may be required. An attractive solution is membrane processes, especially nanofiltration (NF). However, currently available NF membranes strongly reject multivalent ions, mainly due to the dielectric effect. In this work, we present a new method for preparing NF membranes, which contain negatively and positively charged domains, obtained by the combination of two polyelectrolytes with opposite charge. The negatively charged polyelectrolyte is provided in the form of particles (polystyrene sulfonate (PSSA), d ~300 nm). As a positively charged polyelectrolyte, polyethyleneimine (PEI) is used. Both buildings blocks and glycerol diglycidyl ether as crosslinker for PEI are applied to an UF membrane support in a simple one-step coating process. The membrane charge (zeta potential) and salt rejection can be adjusted using the particle concentration in the coating solution/dispersion that determine the selective layer composition. The approach reported here leads to NF membranes with a selectivity that may be controlled by a different mechanism compared to state-of-the-art membranes.

Thermodynamics of Charge Regulation during Ion Transport through Silica Nanochannels

Ion-surface interactions can alter the properties of nanopores and dictate nanofluidic transport in engineered and biological systems central to the water-energy nexus. The ion adsorption process, known as "charge regulation", is ion-specific and is dependent on the extent of confinement when the electric double layers (EDLs) between two charged surfaces overlap. A fundamental understanding of the mechanisms behind charge regulation remains lacking. Herein, we study the thermodynamics of charge regulation reactions in 20 nm SiO₂ channels via conductance measurements at various concentrations and temperatures. The effective activation energies (E_a) for ion conductance at low concentrations (strong EDL overlap) are ∼2-fold higher than at high concentrations (no EDL overlap) for the electrolytes studied here: LiCl, NaCl, KCl, and CsCl. We find that E_a values measured at high concentrations result from the temperature dependence of viscosity and its influence on ion mobility, whereas E_a values measured at low concentrations result from the combined effects of ion mobility and the enthalpy of cation adsorption to the charged surface. Notably, the E_a for surface reactions increases from 7.03 kJ mol^-1 for NaCl to 16.72 ± 0.48 kJ mol^-1 for KCl, corresponding to a difference in surface charge of -8.2 to -0.8 mC m^-2, respectively. We construct a charge regulation model to rationalize the cation-specific charge regulation behavior based on an adsorption equilibrium. Our findings show that temperature- and concentration-dependent conductance measurements can help indirectly probe the ion-surface interactions that govern transport and colloidal interactions at the nanoscale─representing a critical step forward in our understanding of charge regulation and adsorption phenomena under nanoconfinement.

Putting together the puzzle of ion transfer in single-digit carbon nanotubes: mean-field meets ab initio

Nature employs channel proteins to selectively pass water across cell membranes, which inspires the search for bio-mimetic analogues. Carbon nanotube porins (CNTPs) are intriguing mimics of water channels, yet ion transport in CNTPs still poses questions. As an alternative to continuum models, here we present a molecular mean-field model that transparently describes ion coupling, yet unlike continuum models, computes ab initio all required thermodynamic quantities for the KCl salt and H⁺ and OH^- ions present in water. Starting from water transfer, the model considers the transfer of free ions, along with ion-pair formation as a proxy of non-mean-field ion-ion interactions. High affinity to hydroxide, suggested by experiments, making it a dominant charge carrier in CNTPs, is revealed as an exceptionally favorable transfer of KOH pairs. Nevertheless, free ions, coexisting with less mobile ion-pairs, apparently control ion transport. The model well explains the observed effects of salt concentration and pH on conductivity, transport numbers, anion permeation and its activation energies, and current rectification. The proposed approach is extendable to other sub-nanochannels and helps design novel osmotic materials and devices.

Salt and Water Transport in Reverse Osmosis Membranes: Beyond the Solution-Diffusion Model

Understanding the salt-water separation mechanisms of reverse osmosis (RO) membranes is critical for the further development and optimization of RO technology. The solution-diffusion (SD) model is widely used to describe water and salt transport in RO, but it does not describe the intricate transport mechanisms of water molecules and ions through the membrane. In this study, we develop an ion transport model for RO, referred to as the solution-friction model, by rigorously considering the mechanisms of partitioning and the interactions among water, salt ions, and the membrane. Ion transport through the membrane is described by the extended Nernst-Planck equation, with the consideration of frictions between the species (i.e., ion, water, and membrane matrix). Water flow through the membrane is governed by the hydraulic pressure gradient and the friction between the water and membrane matrix as well as the friction between water and ions. The model is validated using experimental measurements of salt rejection and permeate water flux in a lab-scale, cross-flow RO setup. We then investigate the effects of feed salt concentration and hydraulic pressure on salt permeability, demonstrating strong dependence of salt permeability on feed salt concentration and applied pressure, starkly disparate from the SD model. Lastly, we develop a framework to analyze the pressure drop distribution across the membrane, demonstrating that cross-membrane transport dominates the overall pressure drop in RO, in marked contrast to the SD model that assumes no pressure drop across the membrane.

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.

In Situ Characterization of Dehydration during Ion Transport in Polymeric Nanochannels

The transport of hydrated ions across nanochannels is central to biological systems and membrane-based applications, yet little is known about their hydrated structure during transport due to the absence of in situ characterization techniques. Herein, we report experimentally resolved ion dehydration during transmembrane transport using modified in situ liquid ToF-SIMS in combination with MD simulations for a mechanistic reasoning. Notably, complete dehydration was not necessary for transport to occur across membranes with sub-nanometer pores. Partial shedding of water molecules from ion solvation shells, observed as a decrease in the average hydration number, allowed the alkali-metal ions studied here (lithium, sodium, and potassium) to permeate membranes with pores smaller than their solvated size. We find that ions generally cannot hold more than two water molecules during this sterically limited transport. In nanopores larger than the size of the solvation shell, we show that ionic mobility governs the ion hydration number distribution. Viscous effects, such as interactions with carboxyl groups inside the membrane, preferentially hinder the transport of the mono- and dihydrates. Our novel technique for studying ion solvation in situ represents a significant technological leap for the nanofluidics field and may enable important advances in ion separation, biosensing, and battery applications.

Evaluation of Performance of Existing RO Drinking Water Stations in the North Central Province, Sri Lanka

Reverse osmosis (RO) drinking water stations have been introduced to provide safe drinking water for areas with prevailing chronic kidney disease with unknown (CKDu) etiology in the dry zone of Sri Lanka. In this investigation, RO drinking water stations established by community-based organizations (CBO) in the North Central Province (NCP) were examined. Water samples were collected from source, permeate, and concentrate in each station to determine water quality and performance. Furthermore, the operators of the systems were interviewed to evaluate operational and maintenance practices to identify major issues related to the RO systems. Results show that the majority (>93%) of RO systems had higher salt rejection rates (>92%), while water recovery varied from 19.4% to 64%. The removal efficiencies of hardness and alkalinity were averaged at 95.8% and 86.6%, respectively. Most dominant ions such as Ca²⁺, Mg²⁺, K⁺, Na⁺, Ba²⁺, Sr²⁺ Cl⁻, F⁻, and SO₄²⁻ showed higher rejections at averaged values of 93.5%, 97.4%, 86.6%, 90.8%, 95.4%, 96.3%, 95.7%, 96.6%, and 99.0%, respectively. Low recovery rates, lower fluoride levels in product water, and membrane fouling were the main challenges. Lack of knowledge and training were the major issues that could shorten the lifespan of RO systems.

Nanofiltration of Multi-Ion Solutions: Quantitative Control of Concentration Polarization and Interpretation by Solution-Diffusion-Electro-Migration Model

For effective use of advanced engineering models of nanofiltration quality of experimental input is crucial, especially in electrolyte mixtures where simultaneous rejections of various ions may be very different. In particular, this concerns the quantitative control of concentration polarization (CP). This work used a rotating disklike membrane test cell with equally accessible membrane surface, so the CP extent was the same over the membrane surface. This condition, which is not satisfied in the conventional membrane test cell, made possible correcting for CP easily even in multi-ion systems. Ion rejections were studied experimentally for several dominant salts (NaCl, MgCl₂, Na₂SO₄ and MgSO₄) and trace ions (Na⁺, NH₄⁺, Cl⁻ and NO₃⁻) using NF270 membrane. The solution–diffusion–electro–migration model was used to obtain ion permeances from the experimental measurements. The model could well fit the experimental data except in the case of NH₄⁺. The correlations between the ion permeances and type of dominant salt are discussed in the context of the established mechanisms of NF such as Donnan and dielectric exclusion. The obtained information contributes to the systematic transport characterization of NF membranes and may be ultimately useful for computational fluid dynamics simulations of the performance of the membranes in various applications.

Multicomponent mass transport modeling of water desalination by reverse osmosis including ion pair formation

Reverse Osmosis (RO) is one of the main membrane technologies currently used for the desalination of seawater and brackish water to produce freshwater. However, the mechanism of transport and separation of ions in RO membranes is not yet fully understood. Besides acid-base reactions (i.e., including the H⁺-ion), at high concentrations, the salt ions can associate and form ion pairs. In this study, we investigate how to include the formation of these ion pairs in the extended Donnan steric partitioning pore model. We study the desalination of a water source where three ion pairs can be formed (NaCl, MgCl⁺, and MgCl₂) and also include water self-dissociation and the carbonate system. The model assumes infinitely fast reactions, which means that the participating ions are locally at chemical equilibrium with one another. A square stoichiometric reaction matrix composed of active species, moieties, and reactions is formulated. As the final constraint equation, we use the charge balance. The model predicts profiles in concentration, flux, and reaction rates across the membrane for all species and calculates the retention per group of ions. Ion pair formation has an influence on the fluxes of individual ions and therefore influences the retention of ions.

Ionization behavior of nanoporous polyamide membranes

Escalating global water scarcity necessitates high-performance desalination membranes, for which fundamental understanding of structure-property-performance relationships is required. In this study, we comprehensively assess the ionization behavior of nanoporous polyamide selective layers in state-of-the-art nanofiltration (NF) membranes. In these films, residual carboxylic acids and amines influence permeability and selectivity by imparting hydrophilicity and ionizable moieties that can exclude coions. We utilize layered interfacial polymerization to prepare physically and chemically similar selective layers of controlled thickness. We then demonstrate location-dependent ionization of carboxyl groups in NF polyamide films. Specifically, only surface carboxyl groups ionize under neutral pH, whereas interior carboxyl ionization requires pH >9. Conversely, amine ionization behaves invariably across the film. First-principles simulations reveal that the low permittivity of nanoconfined water drives the anomalous carboxyl ionization behavior. Furthermore, we report that interior carboxyl ionization could improve the water-salt permselectivity of NF membranes over fourfold, suggesting that interior charge density could be an important tool to enhance the selectivity of polyamide membranes. Our findings highlight the influence of nanoconfinement on membrane transport properties and provide enhanced fundamental understanding of ionization that could enable novel membrane design.

Tuning the Ion-Selectivity of Thin-Film Composite Nanofiltration Membranes by Molecular Layer Deposition of Alucone

This work addresses a key challenge of tailoring the ion selectivity of a thin-film composite nanofiltration membrane to a specific application, such as water softening, without altering the water permeability. We modified the active surface of a commercial NF270 membrane by molecular layer deposition (MLD) of ethylene glycol-Al (EG-alucone). With increasing deposition cycles, we found that the MLD precursors first infiltrated and deposited in the active layer of NF270, then inflated the active layer, and finally deposited on the surface as a distinct EG-alucone layer. The deposition process changed the morphology of the membrane active layer and decreased the overall density of its fixed negative charge by embedding the positively charged EG-alucone. Filtration experiments revealed that these modifications affected the ion separation properties of the membrane without significantly hindering the water permeability. Specifically, the permeation of Na⁺ increased relative to that of Mg²⁺, as indicated by the permselectivity of Na⁺ salts over Mg²⁺ salts. The changes in permselectivities with an increasing number of MLD cycles were rationalized using the dielectric, steric, and electrostatic ion exclusion mechanisms, which are related to the membrane material, pore size, and fixed charge, respectively. These relations open a path for the rational design of nanofiltration membranes with tailored selectivity by tuning the properties of the MLD layer. Filtration results of natural brackish groundwater using the MLD modified membranes agreed with the single salt experiments. As a result, water hardness was 26% lower for the permeate obtained using the MLD-modified membranes, which were found stable even during a 24 h filtration run. These results highlight the practical potential of this approach in enhancing water softening efficiency.

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.