Membrane Charge Density Research Articles

Beta-Cyclodextrin-Modified Covalent Organic Framework Nanochannel for Electrochemical Chiral Recognition of Amino Acids.

The chiral recognition and separation of enantiomers are of great importance for biological research and the pharmaceutical industry. Preparing homochiral materials with adjustable size and chiral binding sites is beneficial for achieving an efficient chiral recognition performance. Here, a homochiral covalent organic framework membrane modified with β-cyclodextrin (CD-COF) was constructed, which was subsequently utilized as an electrochemical sensor for the enantioselective sensing of tryptophan (Trp) molecules. The preferential adsorption of l-Trp over d-Trp at the β-CD sites can enhance the surface charge density and hydrophilicity of the CD-COF membrane, resulting in an increased transmembrane ionic current. Trp enantiomers with concentrations down to 0.28 nM can be effectively discriminated. The l-/d-Trp recognition selectivity increases with the Trp concentration and reaches a value of 19.2 at 1 mM. The selective adsorption of l-Trp to the CD-COF membrane will also hinder its transport, resulting in a l-/d-Trp permeation selectivity of 15.3. This study offers a new strategy to construct homochiral porous membranes and achieve efficient chiral sensing and separation.

Techno-economic analysis of arsenic (III) removal using spiral wound polyethersulfone nanofiltration membrane at pilot scale

In this work, the influence of initial solution pH on membrane performance was carried out for arsenic (III) removal using spiral wound polyethersulfone (HFN300) Nanofiltration membrane at pilot scale. The rejection percentage was found to increase from 49 % to 96 % while increasing initial solution pH from 4 to 10. Speciation of arsenic, solute-membrane affinity, electric-migration effect along with convection and diffusion were found to be dominant mechanisms for arsenic removal. Donnan Steric Pore Model was selected to estimate the membrane parameters including pore radius (0.313 nm), membrane thickness (2.17 μm), and membrane charge density (−3.56 mol/m3).Excellent agreements were found between the experimental and simulated values for all the studied pH range. Selected model works satisfactorily within 10 % of error for both rejection percentage and permeate flow. Economic feasibility study was carried out for the rural population (India) and total annualized cost was found to be USD 0.90/m3 that seems both reasonable and affordable for arsenic free drinking water. It can be concluded that annualized production cost was dependent on membrane lifespan, electricity tariff, per capita, population size, arsenic feed concentration, etc. The result obtained in the study suggests the feasibility of using the NF process in removing arsenic from contaminated water. Overall, the study provides valuable insights into the mechanisms governing arsenic (III) removal through nanofiltration process using spiral wound polyethersulfone nanofiltration membrane at pilot scale, demonstrating the effectiveness of pH optimization and membrane modelling in improving removal efficiency, which can contribute to the development of cost-effective solutions for safe drinking water in arsenic-affected rural areas.

High-performance and ultra-robust triboelectric nanogenerator based on hBN nanosheets/PVDF composite membranes for wind energy harvesting

Triboelectric nanogenerator (TENG) is a novel energy technology that converts high-entropy mechanical energy from the environment into electrical energy using triboelectrification and electrostatic induction effects. However, the low surface charge density and easy wear of traditional triboelectric materials are bottlenecks for their practical applications. Here, a remarkable triboelectric properties, superior mechanical properties, exceptional wear resistance, and high thermal conductivity hexagonal boron nitride nanosheets (hBNNS)/ polyvinylidene difluoride (PVDF) composite negative triboelectric material is developed. The inclusion of hBNNS as an electron acceptor and nucleating agent not only effectively boosted the surface charge density (711 μC/m2) and mechanical characteristics of the composite membrane, but also the friction coefficient (COF) and thermal conductivity of the 2 wt% hBNNS/PVDF composite membrane decreased by 28.6 % and increased by 22.2 % compared to the PVDF matrix, respectively. The optimized TENG delivers a peak voltage of 434 V, a current of 53 μA, and a power of 4.84 mW. Furthermore, it exhibits exceptional ultra-robust, enabling continuous operation for 72 h at a wind speed of 17.5 m/s while maintaining performance above 90.6 %. Additionally, the TENG is capable of effectively powering a smart hygrothermograph and realizing wireless real-time monitoring, or directly lit up 102 white LEDs in a serial connection. This work addresses the challenges of low output performance and limited lifespan in TENG from a material perspective, providing a valuable reference method for the design of negative triboelectric materials with high surface charge density, good mechanical properties, low COF, and high thermal conductivity.

HIV-1 Gag Polyprotein Affinity to the Lipid Membrane Is Independent of Its Surface Charge.

The binding of the HIV-1 Gag polyprotein to the plasma membrane is a critical step in viral replication. The association with membranes depends on the lipid composition, but its mechanisms remain unclear. Here, we report the binding of non-myristoylated Gag to lipid membranes of different lipid compositions to dissect the influence of each component. We tested the contribution of phosphatidylserine, PI(4,5)P2, and cholesterol to membrane charge density and Gag affinity to membranes. Taking into account the influence of the membrane surface potential, we quantitatively characterized the adsorption of the protein onto model lipid membranes. The obtained Gag binding constants appeared to be the same regardless of the membrane charge. Furthermore, Gag adsorbed on uncharged membranes, suggesting a contribution of hydrophobic forces to the protein-lipid interaction. Charge-charge interactions resulted in an increase in protein concentration near the membrane surface. Lipid-specific interactions were observed in the presence of cholesterol, resulting in a two-fold increase in binding constants. The combination of cholesterol with PI(4,5)P2 showed cooperative effects on protein adsorption. Thus, we suggest that the affinity of Gag to lipid membranes results from a combination of electrostatic attraction to acidic lipids, providing different protein concentrations near the membrane surface, and specific hydrophobic interactions.

The influence of divalent ions on the osmotic energy conversion performance of 2D cation exchange membrane in reverse electrodialysis process

As reverse electrodialysis (RED) technology evolves, achieving high-performance osmotic energy conversion (OEC) necessitates porous membranes with exceptional ion selectivity and permeability. Two-dimensional membranes crafted from graphene oxide (GO) or MXene stand out for their immensely high surface charges, which facilitate superb ion selectivity during transport. Their unique layered stacking structure further yields ultra-small nanochannel radii, bolstering ion selectivity while maintaining high permeability. This makes them prime candidates for osmotic energy conversion. However, the presence of divalent ions in natural seawater readily alters the surface charge density and interlayer spacing of these 2D membranes, significantly impacting their OEC performance, resulting in a power density reduction of about 6 % -10 %. Prior research focused on the ionic properties of divalent ions but overlooked their impact on the nanochannel structure, including changes in interlayer spacing and surface charge density. This study thus delves into the OEC performance variations of GO and MXene 2D layered membranes under varying divalent ion concentrations and salt ratios. Starting from the ion properties of divalent ions and their impact on the nanochannel structure, combined with simulation research, explain their mechanism of action. This research offers theoretical foundations for the future design and application of 2D layered membranes, providing novel solutions and insights to tackle critical challenges like enhancing power density and adapting to real seawater conditions.

Engineering polyvinylidene fluoride membranes using charge tunable dendrimer polyamidoamine to enable microporous membranes for protein separation

Dendrimers are structurally precise molecules, whose peripheral layer provides ample sites for anchoring functional groups of different charges and charge densities. This characteristic renders them capability of providing numerous target functional groups on the surface of filtration membranes when modified by dendrimers. Consequently, there has been a growing interest in dendrimer-modified membranes. In this study, we investigated the engineering of polyvinylidene fluoride (PVDF) membranes using polyamidoamine (PAMAM) dendrimers anchoring different functional groups to tune the charges and charge density of membranes to enable microporous membranes for separation of charged macromolecules. PVDF membranes were functionalized by grafting PAMAM-G3.0 (generation 3) dendrimers with amine groups onto their surfaces and internal surfaces of membrane pores. Subsequently, the peripheral functional groups of dendrimers on the membranes were replaced by carboxyl groups, quaternary ammonium groups, or sulfonic acid groups for charges of different nature and densities. Surface chemical properties, electrical properties, and morphology were characterized using various techniques, including attenuated total reflectance Fourier-transform infrared (ATR-FTIR) spectroscopy, X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), and surface zeta potential measurement. The filtration performance of both PVDF and modified membranes was evaluated using polyethylene oxide (PEO), polyacrylic acid (PAA), and whey protein filtration. Among the modified membranes, the G3PA membranes, with carboxyl functional groups, exhibited the most effective whey protein separation performance. The whey protein rejection and permeate flux of the G3PA membranes were 79 % and 30.3 LMH, respectively. As a comparison, the whey protein rejection and permeate flux of the pristine PVDF membranes were 58.9 % and 15.3 LMH, respectively.

Polyamide Membranes with Tunable Surface Charge Induced by Dipole-Dipole Interaction for Selective Ion Separation.

Nanofiltration (NF) has the potential to achieve precise ion-ion separation at the subnanometer scale, which is necessary for resource recovery and a circular water economy. Fabricating NF membranes for selective ion separation is highly desirable but represents a substantial technical challenge. Dipole-dipole interaction is a mechanism of intermolecular attractions between polar molecules with a dipole moment due to uneven charge distribution, but such an interaction has not been leveraged to tune membrane structure and selectivity. Herein, we propose a novel strategy to achieve tunable surface charge of polyamide membrane by introducing polar solvent with a large dipole moment during interfacial polymerization, in which the dipole-dipole interaction with acyl chloride groups of trimesoyl chloride (TMC) can successfully intervene in the amidation reaction to alter the density of surface carboxyl groups in the polyamide selective layer. As a result, the prepared positively charged (PEI-TMC)-NH2 and negatively charged (PEI-TMC)-COOH composite membranes, which show similarly high water permeance, demonstrate highly selective separations of cations and anions in engineering applications, respectively. Our findings, for the first time, confirm that solvent-induced dipole-dipole interactions are able to alter the charge type and density of polyamide membranes and achieve tunable surface charge for selective and efficient ion separation.

On the discrepancy between nominal and effective charge density of polyamide reverse osmosis membranes

Quantitative and reliable information on the ionization of functional groups in polyamide (PA) active layers of thin film composite membranes is of vital importance for understanding and modeling of ion transport. Independent measurements using Ag+ ion-probing with RBS, XPS, or ICP-MS, indicate a nominal charge density in the order of 0.5 M. Conversely, model fitting to salt rejection experiments suggests an effective membrane charge at least three orders of magnitude lower for brackish water (BWRO) and seawater (SWRO) membranes. In this study we show that the original interpretation of the ion-probe experiments is inconsistent with the principles of ion partitioning used in ion transport models. We provide an alternative interpretation of ion-probe experiments in the literature, explaining the results through binding of silver ions to the carboxylic groups. By using this interpretation, the discrepancy between nominal and effective charge can be resolved: the Ag measured in the ion-probe experiments is mostly bound to the membrane (-COOAg, not –COO−/Ag+), while the membrane is virtually uncharged. Consequently, the ion-probe experiments can quantify the concentration of functional groups, but not theirpKa. We propose that confinement affecting membrane ionization, should be explicitly included in ion-transport modeling.

A Novel Circuit-Based Model of Electrodialysis Avoiding the Use of Empirical Parameters

Electrodialysis (ED) is an emerging membrane-based electroseparation technology for desalination, water treatment, and ionic pollutant removal. Compared to conventional separation methods such as reverse osmosis, ED offers several advantages including lower energy consumption, higher selectivity, and lower fouling propensity. Further, coupling ED with renewable electricity sources enables it to be far more sustainable than competing technologies (reverse osmosis and evaporation) across a wide range of scales. However, the design and operation of ED systems are still challenging due to the complex interactions between the membrane, the electrolytes, and the applied electric field. To address this issue, advanced process models are required to provide accurate predictions of ED performance and to guide system optimisation. Existing ED models tend to be highly dependent on empirical parameters and thus are only applicable to a narrow range of process conditions and require several data sets to validate. Therefore, in this work we aimed to develop a glabal model of ED without reliance on experimental training data.Herein, we present a novel circuit-based model for ED. The model considers the membrane stack as a series of resistors, where the membranes and electrolytes are represented as separate resistive elements. Crucially, the membrane resistance is calculated directly from the electrostatic interaction between ions and fixed charge groups, rather than from manufacturer data or empirical sub-model. This allows for consideration of the ion identity and electrolyte concentration when determining the membrane resistance. Ohm's law is used to relate the applied voltage and stack electrical resistance to a current density, which is then converted to a flux using Faraday's law and current efficiency model. Historically, current efficiencies are calculated from transport numbers provided from membrane manufactures and assumed constant. A novel model for the current efficiency has been developed by us in which the current efficiency is a function of the trans-membrane concentration difference. A space-wise material balance is employed to determine the concentration profile along the stack, while a time-wise material balance tracks the changes in reservoir concentration for recirculating batch experiments.To validate the model, desalination experiments were conducted on a PC BED 1-4 recirculating batch system and compared the model predictions with experimental data. The model demonstrated excellent matching on a range of variables across a range of conditions, including current density, current efficiency, and ion concentration.The proposed model has various applications in ED process modelling, optimisation, and economic analysis. It can be used to evaluate the impact of different design parameters such as membrane thickness, membrane charge density, and flow rate on system performance as well as to optimise these.In summary, the circuit-based model presented in this work offers a robust and versatile tool for ED process simulation and optimisation, which can be used for effective and efficiency desalination and water treatment. Two major advancements presented include models for the membrane electrical resistance and current efficiency, which have historically been considered constant. Figure 1

The potential of electrodialysis as a cost-effective alternative to reverse osmosis for brackish water desalination

While electrodialysis (ED) demonstrates lower energy consumption than reverse osmosis (RO) in the desalination of low salinity waters, RO continues to be the predominant technology for brackish water desalination. In this study, we probe this skewed market share and project the potential for future disruption by ED through systematic assessment of the levelized cost of water (LCOW). Using rigorous process- and economic-models, we minimize the LCOW of RO and ED systems, highlighting important tradeoffs between capital and operating expenditure for each technology. With optimized current state-of-the-art systems, we find that ED is more economical than RO for feed salinities ≤ 3 g L−1, albeit to a minor extent. Considering that RO is a highly mature technology, we focus on predicting the future potential of ED by evaluating plausible avenues for capital and operating cost reduction. Specifically, we find that reduction in the price of ion-exchange membranes (i.e., < 60 USD m−2) can ensure competitiveness with RO for feed salinities up to 5 g L−1. For higher feed salinities (≥ 5 g L−1) we reveal that the LCOW of ED may effectively be reduced by decreasing ion-exchange membrane resistance, while preserving high current efficiency. Through extensive assessment of structure-property-performance relationships, we precisely identify target membrane charge densities and diffusion coefficients which optimize the LCOW of ED, thus providing novel guidance for future membrane material development. Overall, we emphasize that with a unified approach — whereby ion-exchange membrane price is reduced and performance is enhanced — ED can become the economically preferable technology compared to RO across the entire brackish water salinity range.

Imaging Structural and Electrical Changes of Aging Cells Using Scanning Ion Conductance Microscopy.

The local charge density and distribution of extracellular membranes play a crucial role in the various cellular processes, such as regulation and localization of membrane proteins, electrophysiological signal transduction, transcriptional control, cell growth, and cell death. In this study, a novel scanning ion conductance microscopy-based method is employed to extracellular membrane mapping. This method allows to not only visualize the dynamic topography and surface charge distribution around individual cells, but also distinguish the charge difference. To validate the accuracy and effectiveness of this method, the charge density on model sample surfaces are initially manipulated and the charge sensing mechanism using finite element modeling (FEM) is explored subsequently. By applying this method, both the extracellular charge distributions and topography structures of normal and senescent human dental pulp stem cells (hDPSCs) are able to monitor. Interestingly, it is observed that the surface charge became significantly more negative after cellular senescence. This innovative approach enables us to gain valuable insights into surface charge changes during cellular senescence, which can contribute to a better understanding of the underlying mechanisms and potential therapeutic strategies for age-related diseases.

The density of anionic lipids modulates the adsorption of α-Synuclein onto lipid membranes

α-Synuclein is an intrinsically disordered presynaptic protein associated with Parkinson's disease. The physiological role of α-Synuclein is not fully understood, but the protein is known to interact with lipid membranes. We here study how membrane charge affects the adsorption of α-Synuclein to (i) supported lipid bilayers and (ii) small unilamellar vesicles with varying amounts of anionic lipids. The results showed that α-Synuclein adsorbs onto membranes containing ≥5% anionic phosphatidylserine (DOPS) lipids, but not to membranes containing ≤1% DOPS. The density of adsorbed α-Synuclein increased steadily with the DOPS content up to 20% DOPS, after which it leveled off. The vesicles were saturated with α-Synuclein at a 3–5 times higher protein density compared to the supported bilayers, which suggests that a more deformable membrane binds more α-Synuclein. Altogether, the results show that both membrane charge density and flexibility influence the association of α-Synuclein to lipid membranes.

Quantification of overcompensated cations in layer-by-layer membrane by Orange yellow II

The charge density of the nanofiltration (NF) membrane separation layer is critical for ion separation because the charge-based Donnan exclusion plays a critical role. To quantified the charge density has been an important but difficult task. We recently discovered the excellent performance of poly(styrene sulfonate) (PSS)/ poly (allylamine hydrochloride) (PAH) layer-by-layer (LBL) NF membranes for Mg2+/Li+ separation. The overcompensated amine groups (R-NH3+) in PAH were assumed to be the main contribution, but lacked a quantification of the charge density for further proof. Here, a simple quantitative experimental method by Orange yellow II staining was reported for the first time to measure the overcompensated amine groups in the separation layer. The sulfonic acid group (R-SO3-) in Orange yellow II stoichiometrically adsorbed to the excessive R-NH3+ at pH = 3 by electrostatic interaction, and desorbed at pH = 12. Thermodynamics and kinetics analysis of the sorption process demonstrated a Langmuir monolayer sorption and the sorption was controlled by sorption reaction not diffusion. The pore size distribution and rejection measurement confirmed that Orange yellow II sorption did not disrupt the original PSS/PAH layer. A linear relationship was observed between the charge density and the coating bi-layers or PAH layers. The accurate, easy assessment of charge density of LBL NF membrane provides future possibility for understanding overcompensation during LBL assembly and a bottom-up understanding of the charges to the NF performance in separation.

Impact of Ionic Strength and Charge Density on Donnan Potential in the NaCl-Cation Exchange Membrane System

This work aims to theoretically investigate the effect of both the fixed charge density of ion exchange membranes and the ionic strength of the treated aqueous NaCl solution on the generated Donnan potential at thermodynamic equilibrium conditions. The direct objective of our work is to calculate the equilibrium concentration of the Cl− co-ion inside a swelled cation-exchange membrane equilibrated with a water/NaCl system. Two activity coefficient models are employed, i.e., the Debye–Huckel (DH) model (as a reference model) and the Meissner model, which is known for its applicability in treating concentrated solutions. Experimental data available in the literature for Donnan potential are used to verify model predictions. Our study confirms that a high fixed charge density is required to counterbalance the deterioration in membrane selectivity encountered in high-salinity systems. The DH model can be safely used to predict the Donnan potential for feed compositions up to 0.1 M. At higher compositions, the DH model significantly overestimates the predicted (absolute) Donnan potential compared to the Meissner model. The osmotic pressure resulting from the difference in ionic concentration between the membrane phase and the feed phase is found to have insignificant effects on the Donnan potential. The equilibrium computations and methodology are presented in a general way that enables handling multivalent electrolyte systems such as CaCl2.

Novel insight into prior induced crystallization on brackish water nanofiltration

An ultrafiltration/nanofiltration system enhanced by induced crystallization was constructed. The aim of this study was to assess the feasibility and contribution of fouling mitigation during brackish water nanofiltration by prior induced crystallization at ultrafiltration stage. Induced crystallization and increased negative charge density caused by alkalization probably have a synergistic effect on nanofiltration (NF) scaling and fouling mitigation. The electron acceptor surface tension and water contact angle indicated that the NF membrane became more hydrophilic during the alkalization. And thus the influence of acid-base polar interactions on membrane fouling behavior was strengthened to increase the energy barrier, improved the anti-fouling capacity. The total cost of moderate alkalization was reduced to $ 0.18 per ton, indicated a great potential for practical application. Furthermore, the functional model between irreversible resistance with hydrogen ion concentration and membrane charge density was also created. This study developed a sustainable and economy approach for brackish water treatment.

An interlayer-based positive charge compensation strategy for the preparation of highly selective Mg2+/Li+ separation nanofiltration membranes

The Mg2+/Li+ screening selectivity determines the practical application of nanofiltration technology in lithium extraction from salt-lake brines and industrial lithium production. In this work, a membrane structure design strategy based on the interlayers was developed to prepare nanofiltration (NF) membranes with high Mg2+/Li+ separation selectivity and high permeability. Through investigating the influence of the interlayer charge on the structure and performance of the NF membrane, the interlayer for the preparation of the NF membrane with high Mg2+/Li + separation selectivity was screened. Relevant characterizations indicate that the positively charged interlayer can endow the NF membrane with appropriate pore size and surface charge density to achieve high Mg2+/Li+ separation selectivity through the synergistic effect of size sieving and Donnan exclusion. Moreover, the pore size of the NF membrane is controlled by the release rate of the piperazine (PIP) from the interlayer, while the surface charge density of the NF membrane is jointly determined by the charge of the interlayer and PA layer. The performance evaluation suggests that the NF membrane prepared with the best screened interlayer has a Mg2+/Li+ separation factor up to 88.6 while maintaining a high permeability (22.5 L m−2 h−1·bar−1), which is better than that of the most membranes reported in the literature. Overall, this work is expected to promote the practical application of NF membranes in lithium extraction from salt-lake brines and industrial lithium production.

Characterizing Oscillatory and Excitability Regimes in a Protein-Free Lipid Membrane

Observations of electric potential oscillations in artificial lipid bilayers near the order-disorder transition indicate the existence of a stable limit cycle and, therefore, the possibility of producing excitable signals close to the bifurcation. We present a theoretical investigation of membrane oscillatory and excitability regimes induced by an increase in ion permeability at the order-disorder transition. The model accounts for the coupled effects of state-dependent permeability, membrane charge density, and hydrogen ion adsorption. A bifurcation diagram shows a transition between fixed-point and limit cycle solutions, enabling both oscillatory and excitability responses at different values of the acid association parameter. Oscillations are identified in terms of the membrane state, electric potential difference, and ion concentration near the membrane. The emerging voltage and time scales agree with measurements. Excitability is demonstrated by applying an external electric current stimulus, and the emerging signals display a threshold response and the appearance of repetitive signals upon using a long-lasting stimulus. The approach highlights the important role of the order-disorder transition, enabling membrane excitability in the absence of specialized proteins.

Enhanced salt rejection of hydroxylated BaTiO3/Ti3C2Tx@polyvinyl alcohol composite nanofiltration membranes under electrochemical assistance

The influence of surface charge density of nanofiltration (NF) membranes could due to enhanced electrostatic interaction through electrically assisted. In this study, the hydroxylated BaTiO3/Ti3C2Tx (HBT)@polyvinyl alcohol (PVA) (HBTA) composite NF membranes were prepared by crosslinking HBT on the surfaces of NF membranes. The optimized HBTA-0.06 sample exhibited a water contact angle of 43.7°, zeta potential of −13.73 mV (pH = 6.5), average effective pore size of 0.319 nm, and pure water permeance of 55.1 L·m–2·h–1. At an applied electric field of 3 V, the rejection rates of LiCl, NaCl, KCl, RbCl, and MgCl2 determined for HBTA-0.06 reached 73.3%, 60.1%, 53.6%, 49.4%, and 59.8%, respectively. HBTA-0.06 has good stabilization properties that are especially advantageous for water purification, indicating good long-term filtration stability within 168 h. Furthermore, HBT doping significantly increased the charge density of the HBTA membranes and the rejection efficiency of chloride salts, both chlorine radicals (·Cl) and hydroxyl radicals (·OH) generation pathways were proposed under electrochemical assistance. Hence, electrical assistance represents a novel and effective technique for enhancing the salt rejection properties of multifunctional composite NF membranes.

Characterization of the surface charge property and porosity of track-etched polymer membranes.

As an important property of porous membranes, the surface charge property determines many ionic behaviors of nanopores, such as ionic conductance and selectivity. Based on the dependence of electric double layers on bulk concentrations, ionic conductance through nanopores at high and low concentrations is governed by the bulk conductance and surface charge density, respectively. Here, through the investigation of ionic conductance inside track-etched single polyethylene terephthalate (PET) nanopores under various concentrations, the surface charge density of PET membranes is extracted as ∼-0.021C/m2 at pH 10 over measurements with 40 PET nanopores. Simulations show that surface roughness can cause underestimation in surface charge density due to the inhibited electroosmotic flow. Then, the averaged pore size and porosity of track-etched multipore PET membranes are characterized by the developed ionic conductance method. Through coupled theoretical predictions in ionic conductance under high and low concentrations, the averaged pore size and porosity of porous membranes can be obtained simultaneously. Our method provides a simple and precise way to characterize the pore size and porosity of multipore membranes, especially for those with sub-100nm pores and low porosities.

Global optimization for accurate and efficient parameter estimation in nanofiltration

One of the most well-established frameworks for modeling multicomponent transport in nanofiltration (NF) is the Donnan-Steric Pore Model with Dielectric Exclusion (DSPM-DE). Conventional DSPM-DE characterizes transport across NF membranes through four governing membrane parameters: (1) pore radius; (2) effective membrane thickness; (3) membrane charge density; and (4) the dielectric constant inside the membrane pores. The process for quantifying these parameters is typically sequential. First, neutral solute experiments are performed to determine pore radius and effective membrane thickness. Next, charged species experiments are conducted, and the data is used to regress out the remaining parameters. The resulting regressions are often performed using local search algorithms that can struggle to provide low residuals with robust fits. In addition, this two-step approach tends to: (1) require a substantial number of charged and uncharged solute experiments; and (2) introduce assumed relationships between pore size and water flux, such as the Hagen-Poiseuille equation, which may not be representative of transport through complex pore networks. To address these issues, we propose the use of metaheuristic global optimization techniques supplemented with gradient-free local search and maximum likelihood estimation to simultaneously regress all four membrane parameters directly from charged species experiments. We validate our approach against eight independent datasets across diverse input salinities, compositions, and membranes.