Note on nonaqueous electrokinetic transport in charged porous media

A model for electrokinetic transport in charged capillaries is compared with experiments using nonaqueous lithium chloride solutions. The electrokinetic parameters considered are the pore fluid conductivity and the concentration potential. Methanol/water mixtures were the solvent, and track-etched mica membranes with a well-characterized pore structure were the porous medium. The electrolyte concentrations used were such that the Debye lengths of solutions in pores ranged from much smaller to much larger than the radius of pores. The space-charge model is found to be capable of qualitatively describing the trend of the electrokinetic data, but as expected, at higher concentrations the model fails, probably because the assumption that ion—ion interactions are negligible no longer holds. The experimental results show that the pore fluid conductivity depends strongly on the dielectric constant of the solvent, that the absolute value of the pore wall charge tends to decrease with the lowering of the solvent dielectric constant, and that the wall charge tends to increase with the concentration of the chloride ion.     

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).     

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.     

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.     

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.     

Colloid chemical characteristics of nanoporous glasses with different compositions in solutions of simple and organic electrolytes. 3. Calculation of electrochemical characteristics of membranes in terms of a homogeneous model

The electrosurface characteristics of nanoporous glass membranes–ion concentrations in pores with taking into account the specificity of counterions, electrokinetically mobile charge, the convective component of pore solution electrical conductivity, electroosmotic mobility of a liquid in the field of streaming potential and ion mobilities in pore space–were calculated within the homogeneous model. The effects of the type of counterion (sodium, potassium, ammonium, tetramethylammonium, and tetraethylammonium ions), solution concentration, glass composition, and pore size on the equilibrium and transport characteristics of membrane systems have been analyzed. A method for the determining of electrolyte activity coefficients in the membranes has been proposed.     

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.     

Flow of Multicomponent Electrolyte Solutions through Narrow Pores of Nanofiltration Membranes

The slow flow of a multicomponent electrolyte solution in a narrow pore of a nanofiltration membrane is considered. The well-known semiempirical method of subdivision of electrical potential into quasi-equilibrium and streaming parts and the definition of streaming concentrations and pressure are discussed. The usefulness of this tool for solving the electrohydrodynamic equations is shown and justified: the use of a small parameter enables a system of electrohydrodynamic partial differential equations to be reduced to a system of ordinary differential equations for streaming functions. Boundary conditions for streaming functions at both the capillary inlet and outlet are derived. The proposed model is developed for the flow of a multicomponent electrolyte solution with an arbitrary number of ions. This is coupled with (i) the introduction of specific interactions between all ions and the pore wall and (ii) the inclusion of the dissociation of water in both conservation and transport equations. Effective distribution coefficients of ions are introduced that are functions of both the specific interaction potentials and the surface potential of the nanofiltration membrane material. The axial dependency of surface potential is expressed by the use of a charge regulation model from which the discontinuity in electric potential and ion pore concentrations at the pore inlet and outlet can be described.A relation between the frequently used capillary and homogeneous models of nanofiltration membranes is developed. An example of application of the homogeneous model for interpretation of experimental data on nanofiltration separation of electrolyte solutions is presented, which shows a reasonable predictive ability for the homogeneous model.     

Quantifying barriers to monovalent anion transport in narrow non-polar pores

The transport of anionic drinking water contaminants (fluoride, chloride, nitrate and nitrite) through narrow pores ranging in effective radius from 2.5 to 6.5 ? was systematically evaluated using molecular dynamics simulations to elucidate the magnitude and origin of energetic barriers encountered in nanofiltration. Free energy profiles for ion transport through the pores show that energy barriers depend on pore size and ion properties and that there are three key regimes that affect transport. The first is where the ion can fit in the pore with its full inner hydration shell, the second is where the pore size is between the bare ion and hydrated radius, and the third is where the ion size approaches that of the pore. Energy barriers in the first regime are relatively small and due to rearrangement of the inner hydration shell and/or displacement of further hydration shells. Energy barriers in the second regime are due to partial dehydration and are larger than barriers seen in the first regime. In the third regime, the pore becomes too small for bare ions to fit regardless of hydration and thus energy barriers are very high. In the second regime where partial dehydration controls transport, the trend in the slopes of the change in energy barrier with pore size corresponds to the hydration strength of the anions.     

Effect of pH on hydrophilicity and charge and their effect on the filtration efficiency of NF membranes at different pH

In this work the effect of pH on membrane structure, its permeability and retention was studied. In addition, we studied whether the possible changes in the membrane properties due to the pH change are reversible. This is important for understanding the performance of nanofiltration membranes at different conditions and for the selection of cleaning processes. Moreover, the results facilitate the choice of membrane for specific applications.

Several commercial NF membranes were studied at different pH values. Their retention and flux were explained by the charge and the hydrophilic characteristics of the membranes. The filtrations were made with uncharged sugar and salt solutions.

The lower the membrane contact angle (i.e., a more hydrophilic membrane) the higher was the change in apparent zeta potential when pH was increased from 4 to 7. As a result, the retention of ions with more hydrophilic membranes changed more than hydrophobic ones when the pH was increased in the feed solution. However, some membranes retained ions well at high pH although their apparent zeta potential or hydrophilicity was relatively low. These membranes had charge inside the pores and it was not detected by streaming potential measurement along the surface or by measuring the contact angle of the surface. Thus, the apparent zeta potential of the exterior membrane surface did not sufficiently describe the ionic transport through the membrane. In addition, some membranes became significantly more open at high pH (i.e., flux increased). This was explained by the chemical nature of the polymer chains in the membrane skin layer, i.e., dissociating groups in the polymer made the surface more hydrophilic and looser when charges of the polymer chains started to repel each other at elevated pH. Generally, the retention of uncharged glucose decreased more at high pH than the salt retention. The changes in permeabilities and retentions were found to be mostly reversible in the pH range studied (very slowly in some cases, however).     

Ion separations with membranes

Ion separations are important for resource recovery, water treatment, and energy production and storage. Techniques such as chemical precipitation, selective adsorption, and solvent extraction are effective, but membranes may separate ions continuously with less waste and lower energy costs. Separation of monovalent and multivalent ions with nanofiltration or electrodialysis membranes already enables water softening and edible salt purification. Similar membranes are attractive as separators in vanadium redox flow batteries. Selective partitioning of divalent counter-ions into ion-exchange membranes even allows transport of these ions against their concentration gradients in salt mixtures. However, separations of ions with the same charge is more challenging. Recent research demonstrated highly selective ion “sieving” at small scales. Separations using electrical potentials and differences in ion electrophoretic mobilities are promising, but relatively unexplored. Carrier-mediated transport affords high selectivity in liquid membranes, but these systems are not very stable, and selective transport via hopping between anchored carriers has proven elusive. Finally, this paper discusses how concentration polarization decreases selectivities in many membrane processes. Although development of selective, inexpensive ion-separation membranes is a work in progress, successes in water softening and edible salt purification suggests that future selective membranes will serve as complementary methods to traditional purification techniques.     

Nanofiltration of biogenic amines in acidic conditions: Influence of operation variables and modeling

Biogenic amines are present in some fermented and non-fermented beverages and can cause diseases. This study analyzes the feasibility of separating biogenic amines by nanofiltration in acidic medium. Solutions of chloride salts of three biogenic amines: putrescine, histamine and tyramine were filtered through a nanofiltration membrane with a 1000 Da molecular weight cut-off (MWCO) and a positive electrical charge at pH 3. Increasing the transmembrane pressure or cross flow velocity led to an increase in solute rejection and permeate flow. Moreover, a higher electrical charge or lower concentration of amine cations caused a larger rejection indicating that membrane-solutes repulsion governs the filtration process. Finally, the experimental results were analyzed using the classic Donnan–Steric pore model. Values of 0.83 nm and 5.4 μm were estimated for pore radius and membrane effective ratio thickness-porosity from the filtration of neutral solutes. Membrane volumetric charge density and the proton diffusivity inside the pores were estimated from the experimental results.     

Pore formation coupled to ion transport through lipid membranes as induced by transmembrane ionic charge imbalance: atomistic molecular dynamics study

We have employed atomic-scale molecular dynamics simulations to address ion transport through transient water pores in phospholipid membranes. The formation of a water pore is induced by a transmembrane ionic charge imbalance, which gives rise to a significant potential difference across the membrane. The subsequent transport of ions through the pore discharges the transmembrane potential and makes the water pore metastable, leading eventually to its sealing. The findings highlight the importance of ionic charge fluctuations in spontaneous pore formation and their role in ion leakage through protein-free lipid membranes.     

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.     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

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.     

Structural and Electrosurface Properties of Porous Glasses of Various Composition in 1 : 1 Electrolyte Solutions

Complex studies of structural (the specific surface area, the volume porosity, the structural resistance coefficient, and the average pore radius), adsorption and electrokinetic (the electrical conductivity, the ion transport numbers, and the electrokinetic potential) characteristics as functions of pH and the concentration of KCl solution were carried out on porous glasses (PGs) with or without lead oxide and leached under various conditions. It was established that temperature of the leaching solution affects the colloidochemical parameters of PGs, while the addition of salt to the leaching solution exerts practically no influence on the PG behavior. It was shown that the addition of lead oxide results in the formation of membranes with thinner pores and higher surface charge.     

聚二苯基乙炔耐溶剂纳滤膜的制备与性能

聚二苯基乙炔(PDPA)不溶于有机溶剂,是理想的新型耐溶剂纳滤膜材料。采用溶液浇铸法制备聚[1-(4-三甲基硅基)苯基-2-苯乙炔](PTMSDPA)均质膜,经脱硅反应得到PDPA膜,研究其乙醇渗透性能和染料截留性能。结果表明,乙醇渗透通量与压力呈正相关性,传质机理可能介于孔流机理和溶解扩散机理之间的过渡区。染料的分子尺寸、电荷性质以及染料和膜之间的相互作用共同影响PDPA膜的截留性能。