Prediction of physical properties of nanofiltration membranes using experiment and theoretical models

Two commercial nanofiltration (NF) membranes, viz., Desal-HL and NF 700 MWCO were investigated experimentally using neutral and charged solutes, viz., glucose, sodium chloride and magnesium chloride. Effect of pH was studied for sodium chloride rejection and isoelectric point of the membrane was deduced. Experimental results were analyzed using Donnan steric pore and dielectric exclusion models. Dielectric exclusion arises due to the difference in dielectric constant between the bulk and the nano-pore. Born dielectric effect was used as dielectric exclusion phenomena in the present investigation. Stokes–Einstein, Born effective and Pauling radii were used for theoretical simulation, which accurately predicted different charge densities. Empirical correlations were proposed between charge density, concentration and pH for each radius. Charge density decreased drastically when dielectric exclusion term was included in the theoretical model, which showed the real physical characteristics of the membranes employed. Charge density and radius of pore was found to be an important surface parameter in predicting the separation effects in NF membranes.     

Streaming potential measurements as a characterization method for nanofiltration membranes

The streaming potentials of two different nanofiltration membranes were studied with several electrolyte solutions to investigate the influence of salt type and concentration on the zeta potential and kinetic surface charge density of the membranes. The zeta potentials decreased with increasing salt concentration, whereas the kinetic surface charge densities increased. The kinetic surface charge densities could be described by Freundlich isotherms, except in one case, indicating that the membranes had a negligible surface charge. The kinetic surface charge density observed was caused by adsorbed anions. Salt retention measurements showed different mechanisms for salt separation for the two investigated membranes. One membrane showed a salt retention that could be explained by a Donnan exclusion type of separation mechanism, whereas for the other membrane the salt rejection seemed to be a combination of size and Donnan excluion. Comparing the results obtained by the streaming potential measurements with those of the retention measurements, it could be concluded that the membrane with the highest kinetic surface charge density showed the Donnan exclusion type of separation, whereas the membrane with the lower surface charge density showed a separation mechanism that was not totally determined by Donnan exclusion, size effects seemed to play a role as well.     

纳滤膜对电解质溶液分离特性的理论研究(II): 混合电解质溶液

假定纳滤膜具有狭缝状孔, 使用纯水透过系数、膜孔径及膜表面电势来表征纳滤膜的分离特征, 用流体力学半径和无限稀释扩散系数表征了离子特性. 采用扩展Nernst-Planck方程、Donnan平衡模型和Poisson-Boltzmann理论描述了混合电解质溶液中离子在膜孔内的传递现象, 计算了三种商用纳滤膜(ESNA1-LF, ESNA1和LES90)对同阴离子、同阳离子和含四种离子的混合电解质体系中离子的截留率, 并与实验数据进行了比较. 计算结果表明, 电解质溶液中离子在纳滤膜孔内传递的主要机理是离子的扩散和电迁移, 纳滤膜对混合电解质溶液中离子的分离效果主要由空间位阻和静电效应决定. 该模型在低浓度时对含一价离子的混合电解质溶液通过纳滤膜的截留率计算结果比较准确, 但对高浓度或含高价离子的混合电解质溶液则偏差较大.     

Computer program for simulation of mass transport in nanofiltration membranes

A computer program, NanoFiltran, was developed to simulate the mass transport of multi-ionic aqueous solutions in charged nanofiltration (NF) membranes, based on the Donnan steric partitioning pore and dielectric exclusion (DSPM&DE) model, with incorporation of the non-ideality of electrolyte solutions and concentration polarization effects in the membrane/feed-solution interface. With this computer program, the extended Nernst–Planck (ENP) equations are discretized inside the membrane, using the finite-difference scheme. The discretized ENP equations together with the other model equations are linearized in order to obtain a system of equations that are solved simultaneously. The linearized system of equations is based on an initial guess for the electrical potential and ions concentrations profiles, which are updated iteratively. A robust method of under-relaxation of the electrical potential and ions concentrations ensures that the convergence is achieved even for NF systems that exhibit a very stiff numerical behaviour.     

Dielectric exclusion of ions from membranes

Dielectric exclusion is caused by the interactions of ions with the bound electric charges induced by ions at interfaces between media of different dielectric constants. It is considered as one of mechanisms of nanofiltration. The transport properties of capillary model are expressed through ion distribution and diffusion coefficients. Due to local equilibrium the distribution coefficient is directly related to the excess solvation energy of ion. First, this energy is considered for single ions in single neutral pores in terms of pore size, ion charge, dielectric constants of solvent and membrane matrix and pore geometry. The dielectric exclusion from pores with closed geometry like circular cylinders is shown to be essentially stronger than that from pores with relatively open geometry like slits. Furthermore, the role of finite membrane porosity is analysed for the model of infinite slabs with alternating dielectric constants. The presence of other ions is accounted for within the scope of a mean-field approach, and the screening of dielectric exclusion is thus introduced and considered in some detail. A fixed electric charge is shown to cause additional screening. At the same time the dielectric exclusion makes the Donnan exclusion of ions stronger. Therefore the interaction between those two rejection mechanisms turns out to be non-trivial. Finally, the effect of solvent molecular structure is considered within the scope of non-local electrostatics. It is shown that the solvent non-locality typically results in somewhat stronger dielectric exclusion, however, its most important effect is slowing down the decline of dielectric exclusion with increasing bulk electrolyte concentration.     

Retention measurements of nanofiltration membranes with electrolyte solutions

Retention measurements with single salt solutions of CaCl₂, NaCl and Na₂SO₄ revealed that the rejection mechanism of commercial polymeric nanofiltration membranes investigated in this study may be divided into two categories:

• 1.Membranes for which Donnan exclusion seems to play an important role.
• 2.Membranes for which retention is determined by both Donnan exclusion and size effects.

In category 1 both positively and negatively charged membranes were found.Ceramic γ-Al₂O₃ ultrafiltration membranes with a pore size of 3 nm showed a same type of salt retention behavior as the positively charged polymeric membranes.The extended Nernst–Planck equation in combination with the Donnan equilibrium has been used to model the flux-retention experiments for the salt solutions. The numerical calculations resulted in a good agreement with experimental data and acceptable values for the fixed charge densities have been determined. The effective membrane thicknesses calculated were higher than those observed by scanning electron microscopy.     

Theory of pressure-driven transport of neutral solutes and ions in porous ceramic nanofiltration membranes

Hindered transport theory and homogeneous electro-transport theory are used to calculate the limiting, high volume flux, rejection of, respectively, neutral solutes and binary electrolytes by granular porous nanofiltration membranes. For ceramic membranes prepared from metal oxides it is proposed that the membrane structural and charge parameters entering into the theory, namely the effective pore size and membrane charge density, can be estimated from independent measurements: the pore radius from the measured hydraulic radius using a model of sintered granular membranes and the effective membrane charge density from the hydraulic radius and the electrophoretic mobility measurements on the ceramic powder used to prepare the membrane. The electro-transport theory adopted here is valid when the membrane surface charge density is low enough and the pore radius is small enough for there to be strong electrical double layer overlap in the pores. Within this approximation the filtration streaming potential is also derived for binary electrolytes.     

Evaluation of the "DSPM" model on a titania membrane: measurements of charged and uncharged solute retention, electrokinetic charge, pore size, and water permeability

The DSPM (Donnan steric partitioning pore model) was evaluated in the case of a titania membrane with "nanofiltration properties" by measuring the electrokinetic charge, pore size, and water permeability of the membrane, along with charged and uncharged solute retention. The zeta potential values (zeta) were determined from measurements of the electrophoretic mobility (EM) of titania powder forming the filtering layer of the membrane. Zeta potential values were converted into membrane volume charge (X) by assuming two limiting cases: a constant surface charge (sigma(s)(cst)) and a constant surface potential (psi(s)(cst)). The mean pore radius and thickness/porosity ratio of the membrane were determined by permporometry and from water permeability measurements, respectively. Retention measurements were carried out as a function of the permeate volume flux for both neutral solutes (polyethylene glycol PEG of different size) and salts (KCl, MgSO4, K2SO4, and MgCl2) at various pH values. Ionic retentions showed minimum values near the IEP of the membrane. Retention data were analyzed using the DSPM. Very good agreement was found between the pore radius calculated by the model and that determined by permporometry. X values calculated from fitting retention data using the DSPM were also in satisfactorily agreement with X values calculated from EM measurements assuming a constant surface potential for a large pH range. Furthermore, the DSPM leads to X values (X(DSPM)) between those calculated from EM (X(EM)) using the two limiting bounds. In other words, X(DSPM) was higher than X(EM) assuming psi(s)(cst) at pH values far from the isoelectric point (IEP) and lower than X(EM) assuming sigma(s)(cst). These results show that the DSPM is in qualitative agreement with the charge regulation theory (increase of the pore surface potential and decrease of the pore surface charge density with decreasing the pore size). On the other hand, the thickness/porosity ratio of the membrane calculated from solute retention data differed significantly from that determined from water permeability measurements. Moreover, a single value of Deltax/Ak could not be determined from PEG and salt retention data. This means that the Deltax/Ak parameter loses its physical meaning and includes physical phenomena which are not taken into account by the DSPM. Nevertheless, the model satisfactorily predicted the limiting retention, as this is not influenced by the Deltax/Ak parameter.     

Tangential streaming potential as a tool in modeling of ion transport through nanoporous membranes

Tangential streaming potential (TSP) measurements have been carried out so as to assess the electrokinetic properties of the active layer of organic nanofiltration (NF) membranes. Due to the porous structure of NF membranes, cares must be taken to convert the experimental data into zeta potential. Indeed, an assumption that is implicitly made in Smoluchowski's theory (or in related approaches accounting for the surface conduction phenomenon) is that both streaming and conduction currents involved in the streaming potential process flow through an identical path. Such an assumption does not hold with porous membranes since the conduction current is expected to flow wherever the electric conductivity differs from zero. Consequently, a non-negligible share of the conduction current is likely to flow through the membrane body filled with the electrolyte solution. This phenomenon has been taken into account by carrying out a series of TSP measurements at various channel heights. Experiments have been conducted with various electrolyte solutions. The inferred zeta potentials have been further converted into membrane volume charge densities which have been used to predict the membrane performances in terms of rejection rates. The conventional NF theory, i.e. based on a steric/Donnan exclusion mechanism, has been found to be unable to describe the experimental rejection rates. Using the volume charge density of the membrane as an adjustable parameter, it has been shown that the conventional theory even predicts the opposite sign for the membrane charge. On the other hand, the experimental rejection rates have been well described by including dielectric effects in the exclusion mechanism. In this case, a noticeable lowering of the effective dielectric constant of the electrolyte solution inside pores has been predicted (with respect to the bulk value).     

Electroviscous Effects in Ceramic Nanofiltration Membranes

Membrane permeability and salt rejection of a γ‐alumina nanofiltration membrane were studied and modeled for different salt solutions. Salt rejection was predicted by using the Donnan‐steric pore model, in which the extended Nernst–Planck equation was applied to predict ion transport through the pores. The solvent flux was modeled by using the Hagen–Poiseuille equation by introducing electroviscosity instead of bulk viscosity. γ‐Alumina particles were used for ζ‐potential measurements. The ζ‐potential measurements show that monovalent ions did not adsorb on the γ‐alumina surface, whereas divalent ions were highly adsorbed. Thus, for divalent ions, the model was modified, owing to pore shrinkage caused by ion adsorption. The ζ‐potential lowered the membrane permeability, especially for membranes with a pore radius lower than 3 nm, a ζ‐potential higher than 20 mV, and an ionic strength lower than 0.01 m . The rejection model showed that, for a pore radius lower than 3 nm and for solutions with ionic strengths lower than 0.01 m , there is an optimum ζ‐potential for rejection, because of the concurrent effects of electromigration and convection. Hence, the model can be used as a prediction tool to optimize membrane perm‐selectivity by designing a specific pore size and surface charge for application at specific ionic strengths and pH levels.     

静电位阻模型在纳滤膜跨膜电位解析中的应用

采用静电位阻模型对纳滤膜的跨膜电位进行了理论解析, 考察了溶液体积通量密度、原料液浓度、阴阳离子扩散系数比、膜孔半径和膜体积电荷密度对KCl(1-1型电解质)和MgCl2(2-1型电解质)中的纳滤膜跨膜电位的影响. 研究结果表明, 随着通量密度的增大, KCl和MgCl₂的跨膜电位线性程度增强; 两种电解质的跨膜电位均随着原料液浓度和膜孔半径的增大而下降; 在不同的考察范围内, 阴阳离子扩散系数比对1-1型和2-1型电解质的跨膜电位的影响差别较大; KCl的跨膜电位随着膜体积电荷密度的变化关于零点呈现出对称性, 而MgCl₂的跨膜电位零点则出现在膜体积电荷密度为负的条件下.     

Evaluating the charge of nanofiltration membranes

In this study, several methods were used to determine the charge of commercially available nanofiltration membranes, and were compared. First the ion-exchange capacity was determined by titration, this method is able to distinguish between positively and negatively charged functional groups on the membrane. Secondly, measurements of the streaming potential gave a value for the charge density at the exterior membrane surface; the effect of the pH of the solution on the membrane charge was studied. Finally, measurements of the membrane potential allowed to evaluate the total membrane charge density.The results of the three methods were used to compare the membrane charge of nanofiltration membranes mainly in a qualitative way. It is shown that measurements of the membrane potential are preferred for the evaluation of the membrane charge.     

Nanofiltration membranes synthesized from hyperbranched polyethyleneimine

Four nanofiltration membranes, two negatively and two positively charged, were fabricated by interfacial polymerization. Three different amines, ethylenediamine (EDA), diethylenetriamine (DETA), and hyperbranched polyethyleneimine (PEI) were selected to react with two acyl chlorides, trimesoyl chloride (TMC) and terephthaloyl chloride (TPC). The two membranes containing hyperbranched PEI, PEI/TPC and PEI/TMC, are positively charged at the operational pH. But the other two membranes, EDA/TMC and DETA/TMC, are negatively charged. It is found that the two PEI membranes own special rejection characters during nanofiltration. The PEI/TPC membrane has a similar pore size to the EDA/TMC membrane but owns simultaneously the higher salt rejection and permeation flux. The PEI/TMC has a pore size as large as 1.5 nm and still has a higher NaCl rejection than the EDA/TMC membrane of which the pore size as small as 0.43 nm. We consider that the special rejection characters are derived from the special structure of PEI. The hyperbranched structure allows some of the charged amine groups drifting inside the pores and interacting with the ions in the pathway. The drifting amines increase salt rejection but have little effect on water permeation. It implies that a high flux and high rejection membrane for desalting can be obtained by attaching freely rotating charged groups.     

Free energies of the ion equilibrium partition of KCl into nanofiltration membranes based on transmembrane electrical potential and rejection

The free energies of ion equilibrium partition between an aqueous KCl solution and nanofiltration (NF) membranes were investigated on the basis of the relationship of the transmembrane electrical potential (TMEP) and rejection. The measurements of TMEP and rejection were performed for Filmtec NF membranes in KCl solutions over a wide range of salt concentrations (1-60 mol·m(-3)) and pH values (3-10) at the feed side, with pressure differences in the range 0.1-0.6 MPa. The reflection coefficient and transport number, which were used to obtain the distribution coefficients on basis of irreversible thermodynamics, were fitted by the two-layer model with consideration of the activity coefficient. Evidence for dielectric exclusion under the experimental conditions was obtained by analyzing the rejection of KCl at the isoelectric point. The free energies were calculated, and the contribution of the electrostatic effect, dielectric exclusion, steric hindrance, and activity coefficient on the ion partitioning is elucidated. It is clearly demonstrated that the dielectric exclusion plays a central role.     

Influence of membrane fouling by (pretreated) surface water on rejection of pharmaceutically active compounds (PhACs) by nanofiltration membranes

The effects of surface water pretreatment on membrane fouling and the influence of these different fouling types on the rejection of 21 neutral, positively and negatively charged pharmaceuticals were investigated for two nanofiltration membranes. Untreated surface water was compared with surface water, pretreated with a fluidized anionic ion exchange and surface water, pretreated with ultrafiltration. Fouling the nanofiltration membranes with anionic ion exchange resin effluent, resulted in the deposition of a mainly colloidal fouling layer, with a rough morphology. Fouling the nanofiltration membranes with ultrafiltration permeate, resulted in the deposition of a smooth fouling layer, containing mainly natural organic matter. The fouling layer on the nanofiltration membranes, caused by the filtration of untreated surface water, was a combination of both colloids and natural organic matter.Rejection of pharmaceuticals varied the most for the membranes, fouled with the anionic ion exchange effluent, and variations in rejection were caused by a combination of cake-enhanced concentration polarisation and electrostatic (charge) effects. For the membranes, fouled with the other two water types, variations in rejection were smaller and were caused by a combination of steric and electrostatic effects.Changes in membrane surface hydrophobicity due to fouling, changed the extent of partitioning and thus the rejection of hydrophobic, as well as hydrophilic pharmaceuticals.     

349 - Membrane potential and ion permeability of lipid bilayer membranes

In order to clarify the components consisting of transmembrane potential of membranes, measurements of surface potentials of phospholipid monolayers and concentration potentials of phospholipid bilayer membranes measurements were carried out with respect to salt concentrations.It was concluded that, for a highly charged membranes symmetrical with respect to the surface charge density, the observed transmembrane potential is due mostly to the difference between the two surface potentials on both sides of the membrane. On the other hand, for an uncharged membrane, the transmembrane potential is due to the ion diffusion potential through the membrane.Some discussion concerning ion permeabilities through the membranes is also made in relation to the observed transmembrane potentials.     

Pore assembled multilayers of charged polypeptides in microporous membranes for ion separation

In this study, highly permeable ion-selective membranes are prepared via immobilization of polyelectrolyte multilayer networks within the inner pore structure of a microporous (pore size = 0.2 microm) support. Electrostatic layer-by-layer assembly is achieved through alternate adsorption of cationic and anionic polyelectrolytes under convective flow conditions. To initiate pore assembly, the first layer consists of covalently bound charged polypeptides (poly(L-glutamic acid) (PLGA) or poly(L-lysine) (PLL)) establishing a charged support for subsequent adsorption. Nonstoichiometric immobilization of charged multilayers within a confined pore geometry leads to an enhanced volume density of ionizable groups in the membrane phase. This overall increase in the effective charge density allows for Donnan exclusion of ionic species (especially divalent co-ions) using microporous materials characterized by permeability values that exceed conventional membrane processes. Multilayer assemblies are fabricated using both PLGA/PLL and synthetic polyelectrolytes (poly(styrenesulfonate)/poly(allylamine)) in an attempt to compare the level of adsorption and separation properties of the resulting materials. The role of salt concentration in the carrier solvent on overall polyelectrolyte adsorption was examined to determine its effect on both solute (Cl-, SO4(2-), As(V)) and water transport. Constriction of the pore size induced by multilayer propagation was monitored through permeability measurements and dextran rejection studies at each stage of the deposition process.     

Contribution of convection,diffusion and migration to electrolyte transport through nanofiltration membranes

Transport mechanisms through nanofiltration membranes are investigated in terms of contribution of convection, diffusion and migration to electrolyte transport. A Donnan steric pore model, based on the application of the extended Nernst-Planck equation and the assumption of a Donnan equilibrium at both membrane-solution interfaces, is used. The study is focused on the transport of symmetrical electrolytes (with symmetric or asymmetric diffusion coefficients). The influence of effective membrane charge density, permeate volume flux, pore radius and effective membrane thickness to porosity ratio on the contribution of the different transport mechanisms is investigated. Convection appears to be the dominant mechanism involved in electrolyte transport at low membrane charge and/or high permeate volume flux and effective membrane thickness to porosity ratio. Transport is mainly governed by diffusion when the membrane is strongly charged, particularly at low permeate volume flux and effective membrane thickness to porosity ratio. Electromigration is likely to be the dominant mechanism involved in electrolyte transport only if the diffusion coefficient of coions is greater than that of counterions.