Modelling nanofiltration of electrolyte solutions

Evaluation of enhanced nanofiltration membranes for improving magnesium recovery schemes from seawater/brine: Integrating experimental performing data with a techno-economic assessment

The global demand for valuable metals and minerals necessitates the exploration of alternative, sustainable approaches to mineral recovery. Seawater mining has emerged as a promising option, offering a vast reserve of minerals and an environmentally friendly alternative to land-based mining. Among the various techniques, Nanofiltration (NF) has gained significant attention as a preliminary treatment step in Minimum Liquid Discharge (MLD) and Zero Liquid Discharge (ZLD) schemes. This study focused on the potential of two underexplored commercial polyamide based NF membranes, Synder NFX and Vontron VNF1, with enhanced divalent over monovalent separation factors, in optimizing the extraction of magnesium hydroxide (Mg(OH)2) from seawater and seawater reverse osmosis (SWRO) brines. The research encompassed a thorough characterization of the membranes utilizing advanced physic-chemical analytical techniques, followed by rigorous experimental assessments using synthetic seawater and SWRO brine in concentration configuration. The findings highlighted the superior selectivity of NFX for magnesium recovery from SWRO brine and the promising concentration factors of VNF1 for seawater treatment. Cross-validation of experimental data with a mathematical model demonstrated the model's reliability as a process design tool in predicting membrane performance. A comprehensive techno-economic evaluation demonstrates the potential of NFX, operating optimally at 23 bar pressure and 70% permeate recovery rate, to yield an estimated annual revenue of 5.683 M€/yr through Mg(OH)2 production from SWRO brine for a plant with a nominal capacity of 0.8 Mm3/y. This research shed light on the promising role of NF membranes in enhancing mineral recovery taking benefit of their separation factors and emphasizes the economic viability of leveraging NF technology for maximizing magnesium recovery from seawater and SWRO brines.

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.

Interplay of the forces governing steroid hormone micropollutant adsorption in vertically-aligned carbon nanotube membrane nanopores

Vertically-aligned carbon nanotube (VaCNT) membranes allow water to conduct rapidly at low pressures and open up the possibility for water purification and desalination, although the ultralow viscous stress in hydrophobic and low-tortuosity nanopores prevents surface interactions with contaminants. In this experimental investigation, steroid hormone micropollutant adsorption by VaCNT membranes is quantified and explained via the interplay of the hydrodynamic drag and friction forces acting on the hormone, and the adhesive and repulsive forces between the hormone and the inner carbon nanotube wall. It is concluded that a drag force above 2.2 × 10-3 pN overcomes the friction force resulting in insignificant adsorption, whereas lowering the drag force from 2.2 × 10-3 to 4.3 × 10-4 pN increases the adsorbed mass of hormones from zero to 0.4 ng cm-2. At a low drag force of 1.6 × 10-3 pN, the adsorbed mass of four hormones is correlated with the hormone-wall adhesive (van der Waals) force. These findings explain micropollutant adsorption in nanopores via the forces acting on the micropollutant along and perpendicular to the flow, which can be exploited for selectivity.

Self-assembled dendrimer polyamide nanofilms with enhanced effective pore area for ion separation

Membrane technology using well-defined pore structure can achieve high ion purity and recovery. However, fine-tuning the inner pore structure of the separation nanofilm to be uniform and enhance the effective pore area is still challenging. Here, we report dendrimers with different peripheral groups that preferentially self-assemble in aqueous-phase amine solution to facilitate the formation of polyamide nanofilms with a well-defined effective pore range and uniform pore structure. The high permeabilities are maintained by forming asymmetric hollow nanostripe nanofilms, and their well-designed ion effective separation pore ranges show an enhancement, rationalized by molecular simulation. The self-assembled dendrimer polyamide membrane provides Cl-/SO42- selectivity more than 17 times that of its pristine polyamide counterparts, increasing from 167.9 to 2883.0. Furthermore, the designed membranes achieve higher Li purity and Li recovery compared to current state-of-the-art membranes. Such an approach provides a scalable strategy to fine-tune subnanometre structures in ion separation nanofilms.

Multipass Nanofiltration for Lithium Separation with High Selectivity and Recovery

Nanofiltration (NF) is a promising and sustainable process to extract Li+ from brine lakes with high Mg2+/Li+ mass ratios. However, a trade-off between Li/Mg selectivity and Li recovery exists at the process scale, and the Li/Mg selectivity of commercially and lab-made NF membranes in a single-pass NF process is insufficient to achieve the industrially required Li purity. To overcome this challenge, we propose a multipass NF process with brine recirculation to achieve high selectivity without sacrificing Li recovery. We experimentally demonstrate that Li/Mg selectivity of a three-pass NF process with a commercial NF membrane can exceed 1000, despite the compromised Li recovery as a result of co-existing cations. Our theoretical analysis further predicts that a four-pass NF process with brine recirculation can simultaneously achieve an ultrahigh Li/Mg selectivity of over 4500 and a Li recovery of over 95%. This proposed process could potentially facilitate efficient NF-based solute-solute separations of all kinds and contribute to the development of novel membrane-based separation technologies.

Quantifying uncertainty in nanofiltration transport models for enhanced metals recovery

To decarbonize our global energy system, sustainably harvesting metals from diverse sourcewaters is essential. Membrane-based processes have recently shown great promise in meeting these needs by achieving high metal ion selectivities with relatively low water and energy use. An example is nanofiltration, which harnesses steric, dielectric, and Donnan exclusion mechanisms to perform size- and charge-based fractionation of metal ions. To further optimize nanofiltration systems, multicomponent models are needed; however, conventional methods necessitate large amounts of data for model calibration, introduce substantial uncertainty into the characterization process, and often yield poor results when extrapolated. In this work, we develop a new computational architecture to alleviate these concerns. Specifically, we develop a framework that: (1) reduces the data requirement for model calibration to only charged species measurements; (2) eliminates uncertainty propagation problems present in conventional characterization processes; (3) enables exploration of pH optimization for enhancing metal ion selectivities; and (4) enables uncertainty quantification to assess the sensitivity of partition coefficients and ion driving forces to learned pore size distributions. Our framework captures eight independent datasets comprising over 500 measurements to within ±15%. Our studies also suggest that the expectation-maximization algorithm can effectively learn pore size distributions and that optimizing pH can improve metal ion selectivities by a factor of 3-10×. Our findings also reveal that image charges appear to play a less pronounced role in dielectric exclusion under the studied conditions and that ion driving forces are more sensitive to pore size distributions than partition coefficients.

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.

Electrochemical Characterization of Charged Membranes from Different Materials and Structures via Membrane Potential Analysis

Electrochemical characterization of positively and negatively charged membranes is performed by analyzing membrane potential values on the basis of the Teorell-Meyer-Sievers (TMS) model. This analysis allows the separate estimation of Donnan (interfacial effects) and diffusion (differences in ions transport through the membrane) contributions, and it permits the evaluation of the membrane's effective fixed charge concentration and the transport number of the ions in the membrane. Typical ion-exchange commercial membranes (AMX, Ionics or Nafion) are analyzed, though other experimental and commercial membranes, which are derived from different materials and have diverse structures (dense, swollen or nanoporous structures), are also considered. Moreover, for some membranes, changes associated with different modifications and other effects (concentration gradient or level, solution stirring, etc.) are also analyzed.

Experimental and Modeling Study of the Nanofiltration of Alcohol-Based Molecules and Amino Acids by Commercial Membranes

The nanofiltration performance of three commercial membranes was analyzed by the Steric Pore Model (SPM) and the extended Nernst-Planck diffusion equation inside membrane pores. The model was completed with the equation to predict the concentration polarization, and the mass transfer coefficient was determined by considering the presence of a feed spacer. The model parameters that characterized the performance of the membrane were the hydrodynamic coefficient, which accounts for the possible variations in solute size and membrane pore radius, the effective membrane thickness, and the water permeability coefficient. All experiments were conducted at fixed feed pH of 6. The rejections of uncharged solutes (glucose for membranes with a high molecular weight cut-off (MWCO) and glycerol and ethylene glycol for membranes with a low MWCO) allowed the model parameters to be determined. We found that glycerol and ethylene glycol overestimate the membrane pore radius due to their ability to interact with the membrane matrix. Therefore, the rejection of glycine as a small amino acid was explored to characterize the membranes with low MWCO since these molecules do not interact with the membrane matrix and have an almost zero charge at pH values between 4.5 and 6.5. Based on the experimental rejections, it was stated that glucose and glycine could be separated by these membranes operating in continuous diafiltration mode.

Modelling the Performance of Electrically Conductive Nanofiltration Membranes

Electrically conductive membranes are a class of stimuli-responsive materials, which allow the adjustment of selectivity for and the rejection of charged species by varying the surface potential. The electrical assistance provides a powerful tool for overcoming the selectivity-permeability trade-off due to its interaction with charged solutes, allowing the passage of neutral solvent molecules. In this work, a mathematical model for the nanofiltration of binary aqueous electrolytes by an electrically conductive membrane is proposed. The model takes into account the steric as well as Donnan exclusion of charged species due to the simultaneous presence of chemical and electronic surface charges. It is shown that the rejection reaches its minimum at the potential of zero charge (PZC), where the electronic and chemical charges compensate for each other. The rejection increases when the surface potential varies in positive and negative directions with respect to the PZC. The proposed model is successfully applied to a description of experimental data on the rejection of salts and anionic dyes by PANi-PSS/CNT and MXene/CNT nanofiltration membranes. The results provide new insights into the selectivity mechanisms of conductive membranes and can be employed to describe electrically enhanced nanofiltration processes.

Lithium Concentration from Salt-Lake Brine by Donnan-Enhanced Nanofiltration

Membranes offer a scalable and cost-effective approach to ion separations for lithium recovery. In the case of salt-lake brines, however, the high feed salinity and low pH of the post-treated feed have an uncertain impact on nanofiltration's selectivity. Here, we adopt experimental and computational approaches to analyze the effect of pH and feed salinity and elucidate key selectivity mechanisms. Our data set comprises over 750 original ion rejection measurements, spanning five salinities and two pH levels, collected using brine solutions that model three salt-lake compositions. Our results demonstrate that the Li⁺/Mg²⁺ selectivity of polyamide membranes can be enhanced by 13 times with acid-pretreated feed solutions. This selectivity enhancement is attributed to the amplified Donnan potential from the ionization of carboxyl and amino moieties under low solution pH. As feed salinities increase from 10 to 250 g L^-1, the Li⁺/Mg²⁺ selectivity decreases by ∼43%, a consequence of weakening exclusion mechanisms. Further, our analysis accentuates the importance of measuring separation factors using representative solution compositions to replicate the ion-transport behaviors with salt-lake brine. Consequently, our results reveal that predictions of ion rejection and Li⁺/Mg²⁺ separation factors can be improved by up to 80% when feed solutions with the appropriate Cl^-/SO₄^2- molar ratios are used.

Water transport in reverse osmosis membranes is governed by pore flow, not a solution-diffusion mechanism

We performed nonequilibrium molecular dynamics (NEMD) simulations and solvent permeation experiments to unravel the mechanism of water transport in reverse osmosis (RO) membranes. The NEMD simulations reveal that water transport is driven by a pressure gradient within the membranes, not by a water concentration gradient, in marked contrast to the classic solution-diffusion model. We further show that water molecules travel as clusters through a network of pores that are transiently connected. Permeation experiments with water and organic solvents using polyamide and cellulose triacetate RO membranes showed that solvent permeance depends on the membrane pore size, kinetic diameter of solvent molecules, and solvent viscosity. This observation is not consistent with the solution-diffusion model, where permeance depends on the solvent solubility. Motivated by these observations, we demonstrate that the solution-friction model, in which transport is driven by a pressure gradient, can describe water and solvent transport in RO membranes.

Nanopores: synergy from DNA sequencing to industrial filtration - small holes with big impact

Nanopores in thin membranes play important roles in science and industry. Single nanopores have provided a step-change in portable DNA sequencing and understanding nanoscale transport while multipore membranes facilitate food processing and purification of water and medicine. Despite the unifying use of nanopores, the fields of single nanopores and multipore membranes differ - to varying degrees - in terms of materials, fabrication, analysis, and applications. Such a partial disconnect hinders scientific progress as important challenges are best resolved together. This Viewpoint suggests how synergistic crosstalk between the two fields can provide considerable mutual benefits in fundamental understanding and the development of advanced membranes. We first describe the main differences including the atomistic definition of single pores compared to the less defined conduits in multipore membranes. We then outline steps to improve communication between the two fields such as harmonizing measurements and modelling of transport and selectivity. The resulting insight is expected to improve the rational design of porous membranes. The Viewpoint concludes with an outlook of other developments that can be best achieved by collaboration across the two fields to advance the understanding of transport in nanopores and create next-generation porous membranes tailored for sensing, filtration, and other applications.

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.

Kinematic and volumetric analysis of coupled transmembrane fluxes of binary electrolyte solution components

The paper deals with relationships between the individual transmembrane fluxes of binary electrolyte solution components and the experimentally measurable quantities describing rates of transfer processes, namely, the electric current, the transmembrane volume flow and the rates of concentration changes in the solutions adjacent to the membrane. Also, we collected and rigorously defined the kinetic coefficients describing the membrane selective and electrokinetic properties. A set of useful relationships between these coefficients is derived. An important specificity of the proposed analysis is that it does not use the Irreversible Thermodynamic approach by analyzing no thermodynamic forces that generate the fluxes under consideration. Instead, all the regularities are derived on the basis of conservation and linearity reasons. The terminology "Kinematics of Fluxes" is proposed for such an analysis on the basis of the analogy with Mechanics where Kinematics deals with regularities of motion by considering no mechanic forces. The only thermodynamic steps of the analysis relate to the discussion on the partial molar volumes of electrolyte and ions that are the equilibrium thermodynamic parameters of the adjacent solutions. These parameters are important for interrelating the transmembrane fluxes of the solution components and the transmembrane volume flow. The paper contains short literature reviews concerned with the partial molar volumes of electrolyte and ions: the methods of measurement, the obtained results and their theoretical interpretations. It is concluded from the reviews that the classical theories should be corrected to make them applicable for sufficiently concentrated solutions, 1 M or higher. The proposed correction is taken into account in the kinematic analysis.

Ion and Water Transport in Ion-Exchange Membranes for Power Generation Systems: Guidelines for Modeling

Artificial ion-exchange and other charged membranes, such as biomembranes, are self-organizing nanomaterials built from macromolecules. The interactions of fragments of macromolecules results in phase separation and the formation of ion-conducting channels. The properties conditioned by the structure of charged membranes determine their application in separation processes (water treatment, electrolyte concentration, food industry and others), energy (reverse electrodialysis, fuel cells and others), and chlore-alkali production and others. The purpose of this review is to provide guidelines for modeling the transport of ions and water in charged membranes, as well as to describe the latest advances in this field with a focus on power generation systems. We briefly describe the main structural elements of charged membranes which determine their ion and water transport characteristics. The main governing equations and the most commonly used theories and assumptions are presented and analyzed. The known models are classified and then described based on the information about the equations and the assumptions they are based on. Most attention is paid to the models which have the greatest impact and are most frequently used in the literature. Among them, we focus on recent models developed for proton-exchange membranes used in fuel cells and for membranes applied in reverse electrodialysis.

Nanofiltration Treatment of Industrial Wastewater Doped with Organic Dye: A Study of Hydrodynamics and Specific Energy

This study was conducted to eliminate the ions and molecules present in the industrial wastewater received by the municipal wastewater treatment plant (WWTP) of Reghaia, which is located east of Algiers, Algeria. The process was developed for two different study matrices: (a) the wastewater from WWTP and (b) wastewater mixed with Brilliant Blue FCF (BBF) dye to show the influence of the strength of the ionic solution on the treatment. The most effective operating parameters were determined by assessing the residence time distribution applied to the reactor flow regime. Energy analysis showed the viability of a nanofiltration membrane, improving the permeate flux. The nanofiltration process consumed 1.94 kWh/m3 to reduce the chemical oxygen demand (COD) of 63.58% and 48.35% for raw wastewater and doped BBF wastewater, respectively. The results demonstrated that nanofiltration performance with a volume dilution ratio of 1/2 showed the reduction of the COD of 87.2% after 15 min for undoped wastewater, whereas the retention rate decreases to 64% with an increase of dilution ratio to 4/5 for the same water matrix. The influence of a pH of 5 has a significant influence on the composition of the wastewater matrix by the reduction of COD of 49.8% and 59.68% for doped wastewater and raw wastewater, respectively. This could be explained by the isolated points of the membrane in the order of 4.5.

Modeling micropollutant removal by nanofiltration and reverse osmosis membranes: considerations and challenges

Organic micropollutants (OMPs) in drinking water constitute a potential risk to human health; therefore, effective removal of these pollutants is required. Nanofiltration (NF) and reverse osmosis (RO) are promising membrane-based technologies to remove OMPs. In NF and RO, the rejection of OMPs depends on the properties and characteristics of the membrane, the solute, and the solution. In this review, we discuss how these properties can be included in models to study and predict the rejection of OMPs. Initially, an OMP classification is proposed to capture the relevant properties of 58 OMPs. Following the methodology described in this study, more and new OMPs can be easily included in this classification. The classification aims to increase the comprehension and mechanistic understanding of OMP removal. Based on the physicochemical principles used to classify the 58 OMPs, it is expected that other OMPs in the same groups will be similarly rejected. From this classification, we present an overview of the rejection mechanisms involved in the removal of specific OMP groups. For instance, we discuss the removal of OMPs classified as perfluoroalkyl substances (e.g., perfluorooctanoic acid, PFOA). These substances are highly relevant due to their human toxicity at extremely low concentration as well as their persistence and omnipresence in the environment. Finally, we discuss how the rejection of OMPs can be predicted by describing both the membrane-solution interface and calculating the transport of solutes inside the membrane. We illustrate the importance and impact of different rejection mechanisms and interfacial phenomena on OMP removal and propose an extended Nernst-Plank equation to calculate the transport of solutes across the membrane due to convection, diffusion, and electromigration. Finally, we show how the theory discussed in this review leads to improved predictions of OMP rejection by the membranes.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

Selenium species removal by nanofiltration: Determination of retention mechanisms

Selenium (Se) is a dissolved oxyanion drinking water contaminant requiring appropriate removal technologies. The removal of selenite (Se^IV) and selenite (Se^VI) with nanofiltration (NF) was investigated with an emphasis on the role of Se speciation and membrane charge screening on the retention mechanisms. The pH (2 to 12) showed strong pH dependence of Se retention, which was due to the speciation. No significant impact of salinity was observed by increasing NaCl concentration from 0.58 to 20 g/L. Application of the Donnan steric pore partitioning model with dielectric exclusion (DSPM-DE) showed that Donnan exclusion was the dominant retention mechanism for the oxyanions Se species. Nine different organic matter (OM) types were investigated at 10 mgC/L to determine if OM affects Se retention. Only OM characterised by negatively charged fractions, such as humic acid (HA), enhanced Se retention with NF270 of up to 20% for Se^IV and 10% for Se^VI. This was explained by enhanced Donnan exclusion. NF270 was effective in removing Se from real water (Gahard groundwater, Ille et Vilaine, France). The EU guideline (20 μg/L) of Se in drinking water was achieved with comparable performance to OM-free experiments using synthetic waters.

Understanding Selectivity in Solute-Solute Separation: Definitions, Measurements, and Comparability

The development of membranes capable of precise solute-solute separation is still in its burgeoning stage without a standardized protocol for evaluating selectivity. Three types of membrane processes with different driving forces, including pressure-driven filtration, concentration difference-driven diffusion, and electric field-driven ion migration, have been applied in this study to characterize solute-solute selectivity of a commercial nanofiltration membrane. Our results demonstrated that selectivity values measured using different methods, or even different conditions with the same method, are generally not comparable. The cross-method incomparability is true for both apparent selectivity, defined as the ratio between concentration-normalized fluxes, and the more intrinsic selectivity, defined as the ratio between the permeabilities of solutes through the active separation layer. The difference in selectivity measured using different methods possibly stems from the fundamental differences in the driving force of ion transport, the effect of water transport, and the interaction between cations and anions. We further demonstrated the difference in selectivity measured using feed solutions containing single-salt species and that containing mixed salts. A consistent protocol with standardized testing conditions to facilitate fair performance comparison between studies is proposed.

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.

Osmotic Pressure and Diffusion of Ions in Charged Nanopores

The transport of ions and water in nanopores is of interest for a number of natural and technological processes. Due to their practically identical long straight cylindrical pores, nanoporous track-etched membranes are suitable materials for investigation of its mechanisms. This communication reports on simultaneous measurements of osmotic pressure and salt diffusion with a 24 nm pore track-etched membrane. Due to the use of dilute electrolyte solutions (1-4 mM KCl and LiCl), this pore size was commensurate with the Debye screening length. Advanced interpretation of experimental results using a full version of the space-charge model has revealed that osmotic pressure and salt diffusion can be quantitatively correlated with electrostatic interactions of ions with charged nanopore walls. The surface-charge density is shown to increase with electrolyte concentration in agreement with the mechanism of deprotonation of weakly acidic surface groups. Moreover, a lack of significant surface-charge dependence on the kind of cation (K+ or Li+) demonstrates that binding of salt counterions does not play a major role in this system.

Advances and Applications of Hollow Fiber Nanofiltration Membranes: A Review

Hollow fiber nanofiltration (NF) membranes have gained increased attention in recent years, partly driven by the availability of alternatives to polyamide-based dense separation layers. Moreover, the global market for NF has been growing steadily in recent years and is expected to grow even faster. Compared to the traditional spiral-wound configuration, the hollow fiber geometry provides advantages such as low fouling tendencies and effective hydraulic cleaning possibilities. The alternatives to polyamide layers are typically chemically more stable and thus allow operation and cleaning at more extreme conditions. Therefore, these new NF membranes are of interest for use in a variety of applications. In this review, we provide an overview of the applications and emerging opportunities for these membranes. Next to municipal wastewater and drinking water processes, we have put special focus on industrial applications where hollow fiber NF membranes are employed under more strenuous conditions or used to recover specific resources or solutes.

Aminophosphonates in Nanofiltration and Reverse Osmosis Permeates

Aminophosphonates such as aminotris(methylenephosphonic acid) (ATMP) are common constituents of antiscalants. In nanofiltration (NF) and reverse osmosis (RO) processes, ATMP prevents inorganic scaling leading to more stable membrane performance. So far, little attention has been paid to the possible permeation of aminophosphonates through NF and RO membranes. We have investigated the permeability of these membrane types for ATMP and its potential metabolites iminodi(methylenephosphonic acid) (IDMP) and amino(methylenephosphonic acid) (AMPA) with two different NF membranes (TS40 and TS80) and one RO membrane (ACM2) and three different water compositions (ultra-pure water, synthetic tap water and local tap water). We found traces of phosphonates in all investigated permeates. The highest phosphonate rejection occurred with local tap water for all three membranes investigated. Filtration experiments with a technical antiscalant formulation containing ATMP indicated similar trends of phosphonate permeability through all three membranes. We assume that the separation mechanisms of the membranes are the results of a very complex relationship between physico-chemical properties such as Donnan exclusion, feed pH, feed ionic strength and feed concentration, as well as solute-solute interactions.

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.

Fluorescence Microscopic Investigations of Molecular Dynamics in Self-Assembled Nanostructures

Many analytical methods employ self-assembled nanostructured materials as chemical recognition media. Molecular permeation through these materials exhibits unique selectivity owing to nanoconfinement-induced enhancement of permeant-nanostructure interactions. This Personal Account introduces our efforts to investigate the detailed dynamics of single or a small number of molecules in nanostructured materials. We developed new experimental and analysis approaches built upon laser-based fluorescence microscopy to measure the detailed translational and orientational dynamics of molecules diffusing in horizontally-oriented, cylindrical nanostructures, including surfactant micelles, silica mesopores, block copolymer microdomains, and bolaamphiphile-based organic nanotubes. Our studies clarified nanoscale details on the structural/chemical heterogeneity of the nanostructures, and their impacts on molecular mass transport dynamics.

Removal of Sulfadiazine by Polyamide Nanofiltration Membranes: Measurement, Modeling, and Mechanisms

In this study, a complete steric, electrostatic, and dielectric mass transfer model is applied to investigate the separation mechanism of typical antibiotic sulfadiazine by NF90, NF270, VNF-8040 and TMN20H-400 nanofiltration membranes. FTIR and XPS analysis clearly indicate that the membranes we used possess skin layers containing both amine and carboxylic acid groups that can be distributed in an inhomogeneous fashion, leading to a bipolar fixed charge distribution. We compare the theoretical and experimental rejection rate of the sulfadiazine as a function of the pressure difference across the nanopore for the four polyamide membranes of inhomogeneously charged nanopores. It is shown that the rejection rate of sulfadiazine obtained by the solute transport model has similar qualitative results with that of experiments and follows the sequence: RNF90>RVNF2−8040>RNF270>RTMN20H−400. The physical explanation can be attributed to the influence of the inhomogeneous charge distribution on the electric field that arises spontaneously so as to maintain the electroneutrality within the nanopore.

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.

Ion partitioning and permeation in charged low-T* membranes

Understanding ion transport in membrane materials is key to engineering and development of desalination and water purification technologies as well as electro-membrane applications. To date, modeling of ion transport has mainly relied on mean-field approaches, originally intended for weak inter-ionic interactions, i.e., high reduced temperature T*. This condition is violated in many membranes, which could explain disagreement between predicted trends and experiments. The paper highlights observed discrepancies and develops a new approach based on the concept of ion association, more adequate in the low-T^⁎ limit. The new model addresses ion binding and mobility consistently within the same physical picture, applied to different types of single and mixed salts. The resulting relations show a significantly weaker connection between ion partitioning and permeability than the standard ones. Estimates using primitive model (PM) of ions in a homogeneous dielectric suggest that non-PM mechanisms, originating from the molecular structure of the ion-solvating environment, might enhance ion association in membranes. PM analysis also predicts that ion solvation and association must be rigidly related, yet non-PM effects may decouple these phenomena and allow a crossover to non-trivial regimes consistent with experiments and simulations. Despite the crude nature of the presented approach and some questions remaining open, it appears to explain most available experimental data and presents a step towards predictive modeling of ion-selective membrane separations in water-, environment- and energy-related applications.

Investigation of dielectric constants of water in a nano-confined pore

We report the dielectric properties of pure water confined in a silica hydrophilic nanopore determined from the computation of the density of liquid in the confined phase by the grand canonical Monte Carlo (GCMC) simulations. The silica cylindrical nanopore is divided into n concentric radial shells to get a better insight into the dielectric properties of nanoconfined water. We find that the average values of the dielectric constants are very close and almost independent of the number of concentric radial shells. The decrease in the dielectric constant of confined pure water is due to the strong orientation of water dipoles in the vicinity of the surface while water dipoles do not exhibit any preferential orientation in bulk phase.

Investigation of dielectric properties in a silica hydrophilic pore with two water reservoirs.

A Review on Reverse Osmosis and Nanofiltration Membranes for Water Purification

Sustainable and affordable supply of clean, safe, and adequate water is one of the most challenging issues facing the world. Membrane separation technology is one of the most cost-effective and widely applied technologies for water purification. Polymeric membranes such as cellulose-based (CA) membranes and thin-film composite (TFC) membranes have dominated the industry since 1980. Although further development of polymeric membranes for better performance is laborious, the research findings and sustained progress in inorganic membrane development have grown fast and solve some remaining problems. In addition to conventional ceramic metal oxide membranes, membranes prepared by graphene oxide (GO), carbon nanotubes (CNTs), and mixed matrix materials (MMMs) have attracted enormous attention due to their desirable properties such as tunable pore structure, excellent chemical, mechanical, and thermal tolerance, good salt rejection and/or high water permeability. This review provides insight into synthesis approaches and structural properties of recent reverse osmosis (RO) and nanofiltration (NF) membranes which are used to retain dissolved species such as heavy metals, electrolytes, and inorganic salts in various aqueous solutions. A specific focus has been placed on introducing and comparing water purification performance of different classes of polymeric and ceramic membranes in related water treatment industries. Furthermore, the development challenges and research opportunities of organic and inorganic membranes are discussed and the further perspectives are analyzed.