Determination of concentration-dependent transport coefficients in nanofiltration: Experimental evaluation of 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.

Evaluation of Transport Properties and Energy Conversion of Bacterial Cellulose Membrane Using Peusner Network Thermodynamics

We evaluated the transport properties of a bacterial cellulose (BC) membrane for aqueous ethanol solutions. Using the R^r version of the Kedem-Katchalsky-Peusner formalism (KKP) for the concentration polarization (CP) conditions of solutions, the osmotic and diffusion fluxes as well as the membrane transport parameters were determined, such as the hydraulic permeability (L_p), reflection (σ), and solute permeability (ω). We used these parameters and the Peusner (Rijr) coefficients resulting from the KKP equations to assess the transport properties of the membrane based on the calculated dependence of the concentration coefficients: the resistance, coupling, and energy conversion efficiency for aqueous ethanol solutions. The transport properties of the membrane depended on the hydrodynamic conditions of the osmotic diffusion transport. The resistance coefficients R11r, R22r, and Rdetr were positive and higher, and the R12r coefficient was negative and lower under CP conditions (higher in convective than nonconvective states). The energy conversion was evaluated and fluxes were calculated for the U-, F-, and S-energy. It was found that the energy conversion was greater and the S-energy and F-energy were lower under CP conditions. The convection effect was negative, which means that convection movements were directed vertically upwards. Understanding the membrane transport properties and mechanisms could help to develop and improve the membrane technologies and techniques used in medicine and in water and wastewater treatment processes.

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.

Effect of the membrane exclusion mechanism on phosphate scaling during synthetic effluent desalination

Calcium phosphate scaling is one of the main limitations in effluent desalination using membranes. This may be overcome by tailoring membranes with lower rejection of the scalant ions. In this study, we systematically examined the use of negatively and positively charged membranes, rejecting ions mainly based on Donnan exclusion, as a low-scaling alternative to dielectric-exclusion-dominated polyamide NF membranes for effluent desalination. The two charged membranes exhibited a lower calcium and especially phosphate rejection than the polyamide membrane. Consequently, the calcium phosphate supersaturation and then the propensity to scaling of the charged membranes were much lower than the polyamide membrane. This also allowed filtering at a much higher recovery ratio with the charged membranes. It was also found that, despite the fact that the charged membranes had an opposite fixed charge, their scaling behavior was similar. Apparently, although these membranes showed opposite selectivity towards scalant ions (phosphate and calcium) in single salt solutions, the rejection pattern in mixed salt solutions resulted in similar saturation indices, much lower than for polyamide membrane. The scale formed on all three membranes was identified as amorphous calcium phosphate (ACP), although its saturation index was lower than its solubility factor. This was explained by concentration polarization which increases the saturation index in the solution adjacent to the membrane surface. Tests in absence of permeate flux showed a much slower precipitation that took a few days compared with filtration conditions (few hours). In addition, under these conditions, the effect of the scaling on the membrane permeability was generally reduced and the scale contained crystalline calcium phosphate products, different from ACP. The results indicate that the ion rejection and resulting polarization next to the membrane surface plays a crucial role in scaling. Thus, tuning ion selectivity of NF membranes towards scalant ions presents a promising alternative for scaling mitigation during effluent desalination.

Modelling nanofiltration of electrolyte solutions

This review critically examines current models for nanofiltration (NF) of electrolyte solutions. We start from linear irreversible thermodynamics, we derive a basic equation set for ion transfer in terms of gradients of ion electrochemical potentials and transmembrane volume flux. These equations are extended to the case of significant differences of thermodynamic forces across the membrane (continuous version of irreversible thermodynamics) and solved in quadratures for single salts and trace ions added to single salts in the case of macroscopically-homogeneous membranes. These solutions reduce to (quasi)analytical expressions in the popular Spiegler-Kedem approximation (composition-independent phenomenological coefficients), which we extend to the case of trace ions. This enables us to identify membrane properties (e.g. ion permeances, ion reflection coefficients, electrokinetic charge density) that control its performance in NF of multi-ion solutions. Further, we specify the phenomenological coefficients of irreversible thermodynamics in terms of ion partitioning, hindrance and diffusion coefficients for the model of straight cylindrical capillaries. The corresponding expressions enable assessment of the applicability of the popular nanopore model of NF. This model (based on the use of macroscopic approaches at nanoscale) leads to a number of trends that have never been observed experimentally. We also show that the use of the Born formula (frequently employed for the description of dielectric exclusion) hardly leads to meaningful values of solvent dielectric constant in membrane pores because this formula disregards the very solvent structure whose changes are supposed to bring about the reduction of dielectric permittivity in nanopores. We conclude that the effect should better be quantified in terms of ion excess solvation energies in the membrane phase. As an alternative to the nanopore description of NF, we review recent work on the development of an advanced engineering model for NF of multi-ion solutions in terms of a solution-diffusion-electromigration mechanism. This model (taking into account spontaneously arising transmembrane electric fields) captures several trends observed experimentally, and the use of trace ions can provide model parameters (ion permeances in the membrane) from experiment. We also consider a recent model (ultrathin barrier layers with deviations from local electroneutrality) that may reproduce observed feed-salt concentration dependences of membrane performance in terms of concentration-independent properties like excess ion solvation energies. Due to its complexity, practical modelling of nanofiltration will probably be performed with advanced engineering models for the foreseeable future. Although mechanistic studies are vital for understanding transport and developing membranes, future simulations in this area will likely need to depart from typical continuum models to provide physical insight. For enhancing the quality of modelling input, it is essential to improve the control of concentration polarization in membrane test cells.

In Situ Modification of Reverse Osmosis Membrane Elements for Enhanced Removal of Multiple Micropollutants

Reverse osmosis (RO) membranes are widely used for desalination and water treatment. However, they insufficiently reject some small uncharged micropollutants, such as certain endocrine-disrupting, pharmaceutically active compounds and boric acid, increasingly present in water sources and wastewater. This study examines the feasibility of improving rejection of multiple micropollutants in commercial low-pressure RO membrane elements using concentration polarization- and surfactant-enhanced surface polymerization. Low-pressure membrane elements modified by grafting poly(glycidyl methacrylate) showed enhanced rejection of all tested solutes (model organic micropollutants, boric acid, and NaCl), with permeability somewhat reduced, but comparable with commercial brackish water RO membranes. The study demonstrates the potential and up-scalability of grafting as an in situ method for improving removal of various classes of organic and inorganic micropollutants and tuning performance in RO and other dense composite membranes for water purification.

Modeling pH variation in reverse osmosis

The transport of hydronium and hydroxide ions through reverse osmosis membranes constitutes a unique case of ionic species characterized by uncommonly high permeabilities. Combined with electromigration, this leads to complex behavior of permeate pH, e.g., negative rejection, as often observed for monovalent ions in nanofiltration of salt mixtures. In this work we employed a rigorous phenomenological approach combined with chemical equilibrium to describe the trans-membrane transport of hydronium and hydroxide ions along with salt transport and calculate the resulting permeate pH. Starting from the Nernst-Planck equation, a full non-linear transport equation was derived, for which an approximate solution was proposed based on the analytical solution previously developed for trace ions in a dominant salt. Using the developed approximate equation, transport coefficients were deduced from experimental results obtained using a spiral wound reverse osmosis module operated under varying permeate flux (2-11 μm/s), NaCl feed concentrations (0.04-0.18 M) and feed pH values (5.5-9.0). The approximate equation agreed well with the experimental results, corroborating the finding that diffusion and electromigration, rather than a priori neglected convection, were the major contributors to the transport of hydronium and hydroxide. The approach presented here has the potential to improve the predictive capacity of reverse osmosis transport models for acid-base species, thereby improving process design/control.

Predicting the Rejection of Major Seawater Ions by Spiral-Wound Nanofiltration Membranes

Seawater nanofiltration (SWNF) generates a softened permeate stream and a retentate stream in which the multivalent ions accumulate, offering opportunities for practical utilization of both streams. This study presents an approach to simulation of SWNF including all major seawater ions (Na(+), Cl(-), Ca(2+), Mg(2+), and SO4(2-)) based on the Nernst-Planck equation, and uses it for permeate and retentate streams composition prediction. The number of degrees of freedom in the system was reduced by assuming a very high ionic permeability for Na(+), which only weakly affected the other parameters in the system. Two alternatives were examined to analyze the importance of concentration dependence of ion permeabilities: The assumption of constant ion permeabilities resulted in a reasonable fit with experimental data. However, for the permeate composition the overall fit was significantly improved (P < 0.0001) when the permeabilities of Ca(2+) and Mg(2+) were allowed to depend on the ratio of their total concentration to Na(+). This type of dependence emphasizes the strong interaction of divalent ions with the membrane and its effect on the membrane fixed charge through screening or charge reversal. When this effect was included, model predictions closely matched the experimental results obtained, corroborating the phenomenological approach proposed in this study.

Fundamentals of selective ion transport through multilayer polyelectrolyte membranes

Membranes composed of multilayer poly(4-styrenesulfonate) (PSS)/protonated poly(allylamine) (PAH) films on porous alumina supports exhibit high monovalent/divalent cation selectivities. Remarkably, the diffusion dialysis K(+)/Mg(2+) selectivity is >350. However, in nanofiltration this selectivity is only 16, suggesting some convective ion transport through film imperfections. Under MgCl(2) concentration gradients across either (PSS/PAH)(4)- or (PSS/PAH)(4)PSS-coated alumina, transmembrane potentials indicate Mg(2+) transference numbers approaching 0. The low Mg(2+) transference numbers with both polycation- and polyanion-terminated films likely stem from exclusion of Mg(2+) due to its large size or hydration energy. However, these high anion/cation selectivities decrease as the solution ionic strength increases. In nanofiltration, the high asymmetry of membrane permeabilities to Mg(2+) and Cl(-) creates transmembrane diffusion potentials that lead to negative rejections (the ion concentration in the permeate is larger than in the feed) as low as -200% for trace monovalent cations such as K(+) and Cs(+). Moreover, rejection becomes more negative as the mobility of the trace cation increases. Knowledge of single-ion permeabilities is vital for predicting the performance of polyelectrolyte films in the separation and purification of mixed salts.

UV-photo graft functionalization of polyethersulfone membrane with strong polyelectrolyte hydrogel and its application for nanofiltration

A strong polyelectrolyte hydrogel was graft copolymerized on a polyethersulfone (PES) ultrafiltration (UF) membrane using vinyl sulfonic acid (VSA) as the functional monomer, and N,N'-methylenbisacrylamide (MBAA) as the cross-linker monomer. This was carried out in one simple step using the UV photoirradiation method. The effect of the polymerization conditions on the degree of grafting (DG) was investigated using the gravimetric method which measures the total hydrogel grafted on the membrane, and with ATR-FTIR spectroscopy which indicates the functional monomer fraction in the hydrogel layer. The VSA could not graft polymerize without the cross-linker as comonomer. An increase in the cross-linker fraction from 0.25 to 2.5 mol % (relative to the functional monomer VSA) resulted in a higher DG. Although the surface morphology changed upon modification, the resulting surface roughness as measured by AFM was very low. From the monitoring of DG with UV time (4.5-30 min) at constant conditions, it was deduced that during the early stages of the polymerization mainly the cross-linker was grafted, thus inducing the graft copolymerization of the functional monomer. Polymerization using a higher monomer concentration (12.5-40% VSA) at constant monomer/cross-linker ratio resulted in a higher VSA fraction in the grafted hydrogel, although the gravimetric DG was similar. Ion exchange capacity and X-ray photoelectron spectroscopy measured after modification under the different conditions supported these findings. The new membranes were tested under nanofiltration (NF) conditions. A NF membrane could be obtained when the MBAA fraction was above 0.25%. The Na2SO4 rejection was 90-99% and the permeability 10-1 L m(-2) h(-1) bar(-1) when the MBAA fraction increased from 0.75 to 2.5%. The order of rejection of single salts solution was Na2SO4 > MgSO4 ≈ NaCl > CaCl2, as expected on the basis of Donnan exclusion for negatively charged NF membranes. An increase in the salts rejection with increasing degree of cross-linking and VSA fraction was attributed to an increase in the membrane charge density and to steric exclusion that also resulted in an increase of rejection for uncharged solutes such as sucrose or glucose. The new membrane presented a high, essentially unchanged Na2SO4 rejection (>97%) in the range of salt concentrations up to 4 g/L, and only slightly reduced rejection (>92%) at a concentration of 8 g/L; this can be related to its high barrier layer charge density measured by ion exchange capacity. In addition, because poly(vinyl sulfonic acid) (PVSA) is a strong polyelectrolyte the membrane separation performance was stable in the range of pH 1.5 to pH 10.

Enhanced partitioning and transport of phenolic micropollutants within polyamide composite membranes

Aromatic phenols represent an important class of endocrine-disrupting and toxic pollutants, many of which (e.g., bisphenol A and substituted phenols) are known to be insufficiently removed by reverse osmosis (RO) and nanofiltration polyamide membranes that are widely used for water purification. In this study, the mechanism of phenol transport across the polyamide layer of RO membranes is studied using model phenolic compounds hydroquinone (HQ) and its oxidized counterpart benzoquinone (BQ). The study employs filtration experiments and two electrochemical techniques, impedance spectroscopy (EIS) and chronoamperometry (CA), to evaluate the permeability of an RO membrane SWC1 to these solutes in the concentration range 0.1-10 mM. In addition, combination of the permeability data with EIS results allows separately estimating the average diffusivity and partitioning of BQ and HQ. All methods produced permeability of the order 10(-7) to 10(-6) m s(-1) that decreased with solute concentration, even though the permeability obtained from filtration was consistently lower. The decrease of permeability with concentration could be related to the nonlinear convex partitioning isotherm, in agreement with earlier measurements by FTIR. The diffusivity of HQ and BQ was estimated to be of the order 10(-15) m(2) s(-1) and partitioning coefficient of the order 10. The high affinity of phenols toward polyamide and their high uptake may change membrane characteristics at high concentration of the solute. EIS results and hydraulic permeability indeed showed that permeability to ions and water significantly decreases with increasing concentration of organic solute.