Hindered diffusion of synthetic polyelectrolytes in charged microporous membranes

To examine electrostatic effects on the diffusion of macromolecules in membranes, diffusivities of narrow molecular-size fractions of the polyelectrolytes ficoll sulfate and dextran sulfate were measured in polycarbonate track-etch membranes. Radius, number density, and surface charge density of membrane pores were determined from a combination of hydraulic permeability, glucose diffusion, and streaming potential measurements. Molecular charge and Stokes—Einstein radius for each macromolecule fraction were determined from free-solution electrophoretic mobility and diffusivity in a large pore radius membrane, D∞, respectively. As ionic strength was increased from 0.005 to 0.1 M, D∞ for ficoll sulfate remained constant while D∞ for dextran sulfate increased slightly (15-18%). Macromolecule diffusivities in small pore membranes, D, were much more sensitive to ionic strength. For membranes where the ratio of Stokes—Einstein radius to pore radius ranged from 0.08 to 0.29, D/D∞ for ficoll sulfate and dextran sulfate increased by factors ranging from 2.5 to 14 for the same increase in ionic strength. Recent theoretical results for electrostatic double layer interactions in hindered diffusion are in good quantitative agreement with these findings.     

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.     

Preparation and evaluation of effective fixed charge density of titanium phosphate membranes for uni-univalent electrolytes in aqueous solutions

The preparation of polystyrene-based titanium phosphate membranes at different pressures with varying amounts of material has been explained. The membrane potentials of inorganic membranes were measured with uni-univalent electrolytes (KCl, NaCl and LiCl) solution using saturated calomel electrodes (SCEs). The TMS method was used for the evaluation of the effective fixed charge density of these membranes with increasing pressure, and the surface charge density of membrane appeared to be increased due to gradually diminution in surface opening channels. The order of surface charge density for electrolytes used is found to be KCl > NaCl > LiCl. In addition to the effective fixed charge density, distribution coefficient, transport numbers, charge effectiveness and other related parameters were calculated for characterizing the ion exchange membranes by utilizing the TMS method. The theoretical prediction is consistent well with the experimental data. The SEM of these membranes at various pressures has been presented.     

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.     

Calculation of the salt separation by negatively charged gel-filled membranes

The salt separations of negatively charged gel-filled membranes composed of poly(2-acrylamido-2-methylpropanesulfonic acid) gels anchored within a polypropylene microporous substrate have been determined experimentally and modeled theoretically. The separation of these membranes were calculated by both the Teorell, Meyer and Sievers (TMS) model and the Donnan–Steric Pore (DSP) model coupled with the extended Nernst–Planck equation. For modeling, the membrane effective thickness, effective charge density, and pore radius were either directly measured or calculated from theories without the use of fitting procedures. Good agreement between the experimental measurements and the theoretical calculations of salt separation was observed. For the theoretical calculations, the TMS model is suitable for membranes with moderate gel polymer volume fractions, while the DSP model is more suitable for membranes with high gel polymer volume fractions. Moreover, with a calculated constant effective charge density, the salt separation with different salt concentrations could be accurately predicted. The separation of various other salts could also be predicted with good accuracy.     

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.     

Influence of steric, electric, and dielectric effects on membrane potential

The membrane potential arising through nanofiltration membranes separating two aqueous solutions of the same electrolyte at identical hydrostatic pressures but different concentrations is investigated within the scope of the steric, electric, and dielectric exclusion model. The influence of the ion size and the so-called dielectric exclusion on the membrane potential arising through both neutral and electrically charged membranes is investigated. Dielectric phenomena have no influence on the membrane potential through neutral membranes, unlike ion size effects which increase the membrane potential value. For charged membranes, both steric and dielectric effects increase the membrane potential at a given concentration but the diffusion potential (that is the high-concentration limit of the membrane potential) is affected only by steric effects. It is therefore proposed that membrane potential measurements carried out at high salt concentrations could be used to determine the mean pore size of nanofiltration membranes. In practical cases, the membrane volume charge density and the dielectric constant inside pores depend on the physicochemical properties of both the membrane and the surrounding solutions (pH, concentration, and chemical nature of ions). It is shown that the Donnan and dielectric exclusions affect the membrane potential of charged membranes similarly; namely, a higher salt concentration is needed to screen the membrane fixed charge. The membrane volume charge density and the pore dielectric constant cannot then be determined unambiguously by means of membrane potential experiments, and additional independent measurements are in need. It is suggested to carry out rejection rate measurements (together with membrane potential measurements).     

Preparation and characterization of N-methylene phosphonic and quaternized chitosan composite membranes for electrolyte separations

Chitosan was functionalized either by introducing a phosphonic acid group or by quaternization of existing primary ammonium groups in order to make it a water-soluble material. Functionalized chitosans and poly(vinyl alcohol) (PVA)-based nanoporous charged membranes were prepared in aqueous media and gelated in methanol at 10 degrees C to tailor their pore structure. These membranes were extensively characterized for their physicochemical, electrochemical, and permeation characteristics using FTIR, TGA, DSC, water content, ion-exchange capacity, ionic transport properties, and membrane permeability studies. N-Methylene phosphonic chitosan (NMPC)/PVA-based membranes exhibited mild cation selectivity and quaternized chitosan (QC)/PVA composite membranes had mild anion selectivity, while a blend of NMPC-QC/PVA membranes exhibited weak cation selectivity because of formation of zwitterionic structure. Viscosity measurements and interaction studies for individual and mixed solutions of NMPC and QC were carried out for the prediction of charge interactions between -PO3H2 and -N+(CH3)3 groups and effect on molecular weight due to functionalization. Elaborate electrochemical and permeation experiments were conducted in order to predict suitability of these membranes for the separation of mono- and bivalent electrolytes based on their hydrated ionic radius, and it was found that among all the synthesized membranes, PC/QC-30 had the highest relative permeability, which may extend its suitability for electrolyte separations. Observations were correlated with equivalent pore radius of the different membranes as estimated by membrane permeability measurements.     

Synthesis,characterization and electrochemical properties of cation selective ion exchange composite membranes

In this work polystyrene based strontium phosphate membranes (SPMs) were prepared by applying different pressures. The membrane potential is measured with uni-univalent electrolytes (KCl, NaCl, and LiCl) solutions using saturated calomel electrodes (SCEs). The effective fixed charge density of these membranes is determined by the Torell, Meyer and Sievers method and it showed the dependence of membrane potential on the porosity, the charge on the membrane matrix, charge and size of permeating ions. The membranes are characterized by X-ray diffraction, scanning electron microscopy and IR spectroscopy. The order of surface charge density for electrolytes is KCl > NaCl > LiCl. Other parameters such as transport number, distribution coefficient, charge effectiveness and related parameters are calculated. The membrane was found to be mechanically stable, and can be operated over a wide pH range.     

Characterization of the pore area distribution in porous membranes using transport measurements

An approach originally proposed by Mason and coworkers has been applied to model porous membranes to show that transport measurements with small and large solutes can be used to distinguish between porous membranes with the same average pore size but different pore size distributions. In addtion, it is shown that such measurements can be used to account for membrane heteroporosity when predicting the sieving characteristics of a membrane. This is done by applying moment theory to results from flux measurements for a small solute at Pe ≈ 1 or to results from measurements of the reflection coefficient for a large solute at infinite Pe. No a priori assumptions about the nature of the distribution of pore areas are necessary.In this paper, the results from calculations performed with three different model membranes with log-normal pore size distribution are reported. These results show that one can begin to distinguish between membranes by measuring the hydraulic and diffusive permeability and performing at least one additional flux measurement — with either a small, non-hindered solute at Pe ≈ 1 or a large solute at infinite Pe. Results also show that a fairly narrow window can be placed on the sieving curve for a heteroporous membrane without performing any sieving measurements. This is an interesting and encouraging result because it means that many of the problems that arise from measuring and interpreting pore size distributions using more traditional techniques can be avoided by using small solute flux measurements to predict the separation characteristics of many porous membranes.     

Streaming potential and surface charge density of microporous membranes with pore diameter in the range of thickness

A system formed by two phases bathing a microporous membrane is studied considering its behavior as a dynamic system. So, the natural frequencies for each used membrane is determined and then, applying a flow ramp with a rate sufficiently small, the streaming potential can be obtained from the slope of the pressure values versus electrical potential.The determination of the electric potential inside the pores, φ, requires to solve the Poisson–Böltzmann equation in the case of membranes with pore diameter in the range of thickness, for which the radial components of velocity of the fluid must be considered. Since there is no analytical solution, a numerical method was used to obtain φ. The electrical potential value at a distance equal to hydrodynamic radius from pore axis (zeta potential) is used to evaluate the streaming potential by the Helmholtz–Smoluchowsky relation. These values were compared with the experimental data accomplishing the suitable iterations over the surface charge density until coincidence.The values of the surface charge density for the studied membranes show a concentration dependence described by Langmuir’s model for the greatest pore diameters and Freundlich’s model for the smallest pore diameters.     

Determining the Zeta Potential of Porous Membranes Using Electrolyte Conductivity inside Pores

The zeta potential is an important and reliable indicator of the surface charge of membranes, and knowledge of it is essential for the design and operation of membrane processes. The zeta potential cannot be measured directly, but must be deduced from experiments by means of a model. The possibility of determining the zeta potential of porous membranes from measurements of the electrolyte conductivity inside pores (lambda(pore)) is investigated in the case of a ceramic microfiltration membrane. To this end, experimental measurements of the electrical resistance in pores are performed with the membrane filled with KCl solutions of various pHs and concentrations. lambda(pore) is deduced from these experiments. The farther the pH is from the isoelectric point and/or the lower the salt concentration is, the higher the ratio of the electrolyte conductivity inside pores to the bulk conductivity is, due to a more important contribution of the surface conduction. Zeta potentials are calculated from lambda(pore) values by means of a space charge model and compared to those calculated from streaming potential measurements. It is found that the isoelectric points are very close and that zeta potential values for both methods are in quite good agreement. The differences observed in zeta potentials could be due to the fact that the space charge model does not consider the surface conductivity in the inner part of the double layer. Measurements of the electrolyte conductivity within the membrane pores are proved to be a well-adapted procedure for the determination of the zeta potential in situations where the contribution of the surface conduction is significant, i.e., for small and charged pores. Copyright 2001 Academic Press.     

Effects of dip coating parameters on the morphology and transport properties of cellulose acetate–ceramic composite membranes

This work presents the fabrication of cellulose acetate (CA)–ceramic composite membranes using dip coating technique. Ceramic supports used in this work were prepared from kaolin with an average pore size of 560 nm and total porosity of 33%. The dip coating parameters studied experimentally were the concentration of CA solution (varying from 2 wt% to 8 wt%) in acetone and dipping time (varying from 30 s to 150 s). The fabricated composite membranes were characterized using scanning electron microscope, gas permeation, pure water flux and ultrafiltration (UF) experiments using bovine serum albumin (BSA). It was observed that the membrane prepared with 2 wt% and 4 wt% CA were suitable for microfiltration applications and those with 6 wt% and 8 wt% were for ultrafiltration applications. Theoretical investigation was conducted to know the macroporous and mesoporous structure of the prepared membranes using Knudsen and viscous permeability analysis of air. A resistance in series model was applied to identify different resistances responsible for the flux decline. Phenomenological models were proposed to illustrate the dependency of hydraulic resistance of membrane on the structural parameters such as average pore size, effective porosity as well as dip coating parameters like dipping time and concentration of CA. It was found that, the growth rate of CA film on the ceramic support followed exponential growth law with respect to dipping time. The total hydraulic resistance of the membrane was evaluated to be inversely proportional to the ratio of pore sizes of top layer and ceramic support. The resistance due to the CA film was found to be depended to the order of 1.73 with respect to concentration of CA. An increase in the concentration of CA was found to be more effective than dipping time to reduce the membrane pore size.     

Estimation and Comparison of Pore Charge on Titania and Zirconia Membranes Prepared by Sol-Gel Route Using Zeta Potential Measurement

An attempt has been made to synthesize ceramic titania and zirconia membranes by sol-gel process by filtering respective viscous colloidal sol through microporous alumina support and gelling followed by sintering at 400°C and 470°C respectively. The static charge on the pores of the so formed membranes and the pore size distribution determine the applicability in filtering colloidal solution. The mean pore size from SEM were found to be 0.65 m and 0.54 m for titania and zirconia membranes respectively with 1.47 × 10⁷/cm² as pore density for both. The filtration characteristics during membrane layer formation showed that the membrane layer formation started after 35 minutes in the case of titania membrane and 40 minutes in the case of zirconia membrane. From the gravimetric estimation of water content of the membranes the thickness of the membrane was found out to be 3 m and the porosity was found out to be 0.30 for both the cases. The particle charge density was estimated from the zeta potential and the particle size. The pore charge density was estimated from the particle charge density, pore density, pore diameter and the thickness of the membrane layer. The membrane pore charge density was found to vary between 3 to –1 Coulombs/cm² in the case of titania membrane and 7 to –0.5 Coulombs/cm² in the case of zirconia membrane in the pH range 1–12.     

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.     

Transport Studies with Composite Membrane by Sol-Gel Method

The preparation of polystyrene-based composite membrane at different pressures with varying amounts of material has been described. In order to understand the mechanism of transport of ions, membrane potential measurements were carried out using different concentrations of 1:1 electrolyte (KCl, NaCl, and LiCl) solutions and also to evaluate various membrane parameters such as mobility, distribution coefficient, and charge effectiveness controlling the transport phenomena. The membrane potential offered by the electrolytes is in the order of LiCl > NaCl > KCl, and the membrane is found to be cation selective. The large deviation in the value of K _± at the lower concentration of electrolytes was attributed to the high mobility of comparatively free charges of the strong electrolyte. Teorell, Meyer, and Sievers (TMS) method was used for the estimation of the thermodynamically fixed charge density of membranes. The data were then utilized to calculate membrane potential using the TMS theory. It was interesting to note that the theoretical predictions were borne out quite satisfactorily with experimental results.     

Pore size distribution of ceramic UF membranes by liquid–liquid displacement porosimetry

Commercial ceramic tubular membranes made by Tami^® have been characterized by several techniques. Their pore size distributions (PSD) have been obtained by liquid–liquid displacement porosimetry (LLDP).

Computerized image analysis (CIA) of SEM pictures has been used to get information on the width of the active layer of the studied membranes. These values of thickness have helped to evaluate the porosity of the membranes and to get representative radii from measurements of the permeability to several gases and liquids. A fully automated porosimeter designed by us has been used in the determination of pore size distributions. Results show a good accuracy and reproducibility of LLDP measurements.

Binary and ternary liquid mixtures have been used to wet and penetrate into the membrane pores when performing LLDP leading to quite similar results when an effective surface tension is assigned for the ternary mixture. This procedure can be used to calibrate the technique to be extended to thick ultrafiltration and even to nanofiltration membranes.     

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.     

Temperature and concentration effects on electrolyte transport across porous thin-film composite nanofiltration membranes: Pore transport mechanisms and energetics of permeation

The influence of temperature and concentration on nanofilter charge density and electrolyte pore transport mechanisms is reported. Crossflow filtration experiments were performed to measure transport of several electrolytes (NaCl, NaNO3, NaClO4, CaCl2, MgCl2, and MgSO4) across two commercially available thin-film composite nanofiltration membranes in the range 5-41 degrees C. Experiments were also performed with selected salts in the range 1-50 meq/L to quantify concentration effects. Three different approaches, irreversible thermodynamics, extended Nernst-Planck formulation, and theory of rate processes, were employed to interpret retentions of these symmetric and asymmetric electrolytes at varying temperature and concentration. Increasing feed water temperature slightly increased electrolyte reflection coefficients and only weakly increased permeability compared with neutral solutes. Electromigration and convection tended to counteract each other at high fluxes explaining the weak temperature dependence of the reflection coefficient. Changes in membrane surface charge density with temperature were attributed to increased adsorption of electrolytes on the polymer constituting the active layer. Activation energy of permeation for charged solutes was primarily determined by the Donnan potential at the membrane-feed water interface. Electrolyte permeation was shown to be an enthalpy-driven process that resulted in small entropy changes. Increasing sorption capacity with temperature and low sorption energies indicated that co-ion sorption on polymeric membranes was an endothermic physicosorption process, which appears to determine temperature dependence of electrolyte permeation at increased feed concentrations.     

Fabrication and characterization of single layer and multi-layer anodic alumina membranes

Porous alumina films containing parallel capillary pores of uniform size were fabricated by anodically oxidizing high purity aluminum films in phosphoric acid and sulfuric acid solutions. These films were formed into membranes by post-oxidation processing that removes unoxidized aluminum as well as a barrier layer of alumina from the base of the pores. Symmetric membranes were made by oxidizing at constant current density conditions. Two layer composite membranes were made by changing current density during the oxidation process. The thickness, pore density and porosity of each membrane were predicted from the relationships between structural characteristics and processing conditions that were developed in previously reported kinetic studies of anodic oxidation of aluminum.Each membrane was then characterized using permeability measurements. The hydraulic permeability of membranes formed in phosphoric acid and the diffusive permeability of membranes formed in sulfuric acid were measured. A comparison of the measured permeability values to those predicted using the structural characteristics calculated using relationships developed in the kinetic studies shows excellent agreement. These results illustrate that porous alumina membranes can be fabricated with transport characteristics that can be predicted from the processing conditions used during membrane formation.