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.     

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).     

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.     

Transport Properties of Selective Membranes Reversible to Nitrogen-Containing Organic Base Cations: Permeability and Ion Flow

Main transport properties were studied for selective membranes with low dielectric constants based on liquid ion exchangers involving nitrogen-containing organic base cations. Permeabilities and ion flows through a membrane were calculated for major and interfering ions. Dependences of the transport properties of membranes on the concentrations of the ion exchanger and near-membrane solution and their potentiometric characteristics are presented. It was demonstrated that the transport properties of liquid membranes are determined by two main factors: the transfer of counterions through the phase boundary by the extraction–exchange mechanism and the leaching of the ion exchanger from the membrane.     

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.     

Equilibrium and Transport Characteristics of Perfluorinated Cation-Exchange Membranes Containing Carboxyl Groups

Equilibrium (the exchange capacity and moisture content) and transport (the ion transport numbers and the electrical conductance) properties of perfluorinated cation-exchange membranes containing carboxyl groups were studied as a function of pH and concentration of KCl solutions (10^–4–1 M). Dissociation constants of carboxyl groups, adsorption potentials of K⁺ ions, transport numbers and mobilities of counterions in the membranes, concentrations of fixed ions, co- and counterions, as well as the Donnan potentials were calculated.     

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.     

Zeta-potential measurements as a tool to quantify the effect of charged drugs on the surface potential of egg phosphatidylcholine liposomes

The binding of charged drugs to neutral phosphatidylcholine membranes was assessed by measuring their zeta-potential values in the presence of different drug concentrations. This methodology was applied to the study of the concentration effects of two nonsteroidal antiinflammatory drugs (NSAIDs). Results revealed an intense membrane charging that was proportional to the amount of negatively charged drug in the media. A mathematical formalism was adapted and an analytical expression derived to calculate directly surface potentials from zeta-potential data. The membrane loading state, expressed as the number of molecules per unit area, was calculated for the negative and for the neutral forms of the drugs. An approach was also developed that allows the determination of the maximum number of molecules per unit area by fitting a binding isotherm to the dependence of the number molecules per unit area with the drug concentration. The calculation of the maximum mol lipid/drug ratio can also be estimated and related to the binding stoichiometry, as well as to the maximum lipid loading capacity. Furthermore, the concentration profiles for both drugs can be established in terms of the distance to the liposome surface. The developed methodology allowed for the simultaneous determination of partition coefficients (Kp) for the NSAIDs in lipid/aqueous media because zeta-potential values can be related to the drug concentration at the lipid/ aqueous media interface. Alternative independent methodologies were used to determine Kp: spectrophotometric and centrifugation assays. A mathematical relation was developed to compare the Kp values determined from the zeta-potential data with those obtained from the other techniques used because in the former case they are calculated on the basis of the number of molecules per unit area and in the latter on the basis of the total drug concentrations in solution, and the values of the partition coefficients obtained from all the techniques were found to be equal, within the experimental error. This methodology constitutes a more straightforward method than the other techniques used because partition coefficients for all drug forms (charged and noncharged) can be assessed with a minimum number of experimental determinations and it allows for a characterization of the electrostatic properties of neutral membranes upon binding of charged drugs.     

Controlling the transport of cations through permselective mesoporous alumina layers by manipulation of electric field and ionic strength

The electric field-driven transport of ions through supported mesoporous gamma-alumina membranes was investigated. The influence of ion concentration, ion valency, pH, ionic strength, and electrolyte composition on transport behavior was determined. The permselectivity of the membrane was found to be highly dependent on the ionic strength. When the ionic strength was sufficiently low for electrical double-layer overlap to occur inside the pores, the membrane was found to be cation-permselective and the transport rate of cations could be tuned by variation of the potential difference over the membrane. The cation permselectivity is thought to be due to the adsorption of anions onto the pore walls, causing a net negative immobile surface charge density, and consequently, a positively charged mobile double layer. The transport mechanism of cations was interpreted in terms of a combination of Fick diffusion and ion migration. By variation of the potential difference over the membrane the transport of double-charged cations, Cu2+, could be controlled accurately, effectively resulting in on/off tunable transport. In the absence of double-layer overlap at high ionic strength, the membrane was found to be nonselective.     

Local anesthetics facilitate ion transport across lipid planar bilayer membranes under an electric field: dependence on type of lipid bilayer

In order to elucidate the role of structural change of lipid membrane bilayer in the mode of action of local anesthetic, we studied the effects of local anesthetics, charged tetracaine and uncharged benzocaine, on ion permeability across various lipid planar bilayers (PC, mixed PC/PS (4/1, mol/mol); mixed PC/PE (1/1, mol/mol); mixed PC/SM (4/1, mol/mol)) under a constant applied voltage. The membrane conductances increased in the order of PC  PC/PS ≤ PC/SM  PC/PE. When the constant voltage of −100 or −70 mV was applied through the lipid bilayer membranes in the presence of positively charged tetracaine, the fluctuating current pulses with the large amplitude generated, but not appeared in the absence of tetracaine. The addition of uncharged benzocaine generated the fluctuating currents with the small amplitude. Both charged tetracaine and uncharged benzocaine facilitated electrophoretically the transport of small ions such as KCl in the buffer solution through the fluctuating pores in the lipid bilayer membranes formed by interaction with the local anesthetic under the negative applied membrane potential. The current pulses also contained actual transport of charged tetracaine together with the transport of the small ions. The amplitude and the duration time of the electrical current generated by adding the local anesthetics were dependent on the type of the lipid, the applied voltage and its voltage polarity.     

Theory of Ion Transport in Electrochemically Switchable Nanoporous Metallized Membranes

A physicomathematical model of ion transport through a synthetic electrochemically switchable membrane with nanometric metal‐plated pores is presented. Due to the extremely small size of the cylindrical pores, electrical double layers formed inside overlap, and thus, strong electrostatic fields whose intensities vary across the cross‐sections of the nanopores are created. Based on the proposed model a relationship between the relative electrostatic energies experienced by ions in the nanopores and the potential applied to the membrane is established. This allows the prediction of transference numbers and explains quantitatively the ion‐transport switching capability of such synthetic membranes. The predictions of this model agree satisfactorily with previous experimental data obtained for this type of devices by Martin and co‐workers.     

Electrokinetic effects in membrane pores and the determination of zeta-potential

The surface charge or electrical potential properties of microfiltration, ultrafiltration and nanofiltration membranes can have a very significant influence on their separation performance. Such properties are most commonly quantified in terms of zeta-potentials obtained by calculation following experimental measurement of streaming potentials. Such calculation requires numerical solution of the equations governing fluid flow and electrical-potential distribution in the pores. A method for such calculations is presented, which includes a numerical solution of the non-linear Poisson–Boltzmann equation and allows for the mobilities of anions and cations to be individually specified. By expressing the results of such calculations in terms of a factor to be applied to a classical analytical result, it is shown to be very important to use proper numerical calculations in the interpretation of electrokinetic data for membranes. Use of a classical analytical analysis to calculate ‘relative', ‘apparent', ‘equivalent' or ‘nominal' zeta-potentials is likely to lead to substantial underestimation of the true zeta-potential and possible serious error even in the interpretation of relative changes in membrane properties. The calculations needed to avoid such difficulties may be readily carried out on a PC. It is also important to account for the individual mobilities of the anions and cations in the electrolyte used for measurements.     

Supported liquid membranes modification with sulphonated poly(ether ether ketone): Permeability,selectivity and stability

The development of a new type of composite membrane consisting of a microfiltration support membrane, an immobilised liquid membrane phase and a hydrophilic, charged polymer layer and its function as a supported liquid membrane (SLM) for copper selective transport are described. The ion-exchange layers function as stabilisation layers to improve the membrane lifetime and consist of sulphonated poly(ether ether ketone) (SPEEK). This polymer shows a high permeability for copper ions due to the presence of fixed negative charges and to its swelling capacity in an aqueous phase.A method was developed to prepare composite membranes composed of the support membranes Celgard with one stabilisation layer on either the feed or strip side of the membrane or on both sides. Good adhesion of homogeneous, negatively charged, hydrophilic SPEEK layers to the hydrophobic macroporous support membranes could only be established when the support membranes were first hydrophilised with a concentrated sulphuric acid solution containing 5 wt% free SO₃.The lifetime of the SLMs is significantly improved when one stabilisation layer is applied at the strip side or two layers at both sides of the SLM. A second advantage of this composite SLM is the increase in copper flux caused by a decrease in thickness of liquid membrane phase. However, when SPEEK penetrates entirely through some pores of the support membrane, ions diffuse non-specifically through the SPEEK matrix resulting in an undesired selectivity loss. This phenomenon occurs only when thin Celgard membranes are used as support membranes.     

Electrochemistry of capillary systems with narrow pores. VI. Convection conductivity (theoretical considerations)

Generally, the electrical convection current and the electrical convection conductivity (Smoluchowski's surface conductivity) have to be taken into account to describe transport phenomena across membranes with narrow pores although the electrical charge distribution within the pores cannot be described as a Helmholtz electrical double layer. In collodion membranes, which have a comparatively low fixed ion concentration, the contribution of the convection conductivity to the electrical conductivity of the pore fluid may be neglected. This assumption was made tacitly in the analysis of our data obtained with this type of membrane.In this communication equations are derived which take the convection conductivity into account. They are in agreement with the phenomenological transport equations developed by Staverman on the basis of the thermodynamics of irreversible processes.The electrical convection conductivity can be considered to be the contribution of the fixed ion concentration to the electrical conductivity. It is argued that this contribution cannot be neglected in ion exchange membranes with a high fixed ion concentration and a high mechanical permeability. Neglecting the electrical convection conductivity in such systems could lead to considerable differences between experimental conductivity data and the theoretical predictions. An electrical conductivity term for the fixed ions is proposed which can be used as a correction factor in the equations in which the contribution of the electrical convection conductivity has been neglected. Suggestions are made for the measurement of the electrical convection conductivity in systems with narrow pores and high electrical conductivity (e.g. ion exchange resins). The consequences of the electrical convection conductivity in practical applications of ion-exchange resins are discussed (acceleration of the rates of ion exchange; improvement of the separation properties by the application of a direct electrical current flow).     

Electrochemistry of capillary systems with narrow pores. VI. Convection conductivity (theoretical considerations)

Generally, the electrical convection current and the electrical convection conductivity (Smoluchowski's surface conductivity) have to be taken into account to describe transport phenomena across membranes with narrow pores although the electrical charge distribution within the pores cannot be described as a Helmholtz electrical double layer. In collodion membranes, which have a comparatively low fixed ion concentration, the contribution of the convection conductivity to the electrical conductivity of the pore fluid may be neglected. This assumption was made tacitly in the analysis of our data obtained with this type of membrane.

In this communication equations are derived which take the convection conductivity into account. They are in agreement with the phenomenological transport equations developed by Staverman on the basis of the thermodynamics of irreversible processes.

The electrical convection conductivity can be considered to be the contribution of the fixed ion concentration to the electrical conductivity. It is argued that this contribution cannot be neglected in ion exchange membranes with a high fixed ion concentration and a high mechanical permeability. Neglecting the electrical convection conductivity in such systems could lead to considerable differences between experimental conductivity data and the theoretical predictions. An electrical conductivity term for the fixed ions is proposed which can be used as a correction factor in the equations in which the contribution of the electrical convection conductivity has been neglected. Suggestions are made for the measurement of the electrical convection conductivity in systems with narrow pores and high electrical conductivity (e.g. ion exchange resins). The consequences of the electrical convection conductivity in practical applications of ion-exchange resins are discussed (acceleration of the rates of ion exchange; improvement of the separation properties by the application of a direct electrical current flow).     

Electrical conductivity of cation-and anion-exchange membranes in ampholyte solutions

Several laws governing ampholyte transport through ion-exchange membranes are established by a comparative analysis of the concentration dependence of electrical conductivity for homogeneous (CMX, AMX) and heterogeneous (MK-40, MA-41) membranes in NaCl, LysHCl, and NaH₂PO₄ solutions. The increase in the electrical conductivity of membranes in ampholyte solutions as the solutions become more dilute is explained by the increased fraction of divalent ions of the amino acid (cation-exchange membrane) or from phosphoric acid (anion-exchange membrane) in the membrane as a result of Donnan exclusion of hydrolysis products (hydroxide ions or protons, respectively).     

Modification of electrochemical properties of pore wall of track-etched mica membranes

The electrochemical properties of the pore wall of track-etched mica membranes are modified (a) by covalent binding of positively and negatively charged groups, and (b) by adsorption of cationic and amonic polyelectrolytes. The electrochemical properties of the pore wall are characterized by measurements of membrane potential, electrical conductivity and streaming potential.By these methods it is possible to change the sign of the surface charge density of the pore wall and to increase its absolute value by a factor of about 30 compared with that of the unmodified pore wall. Changes of electrochemical properties of the pore wall are desirable in studies of negative osmosis and incongruent electrolyte transport in membranes with known pore structure.     

Flux decline during cross flow membrane filtration of electrolytic solution in presence of charged nano-colloids: a simple electrokinetic model

An electrokinetic transport based approach for quantification of reversible flux decline due to the concentration polarization of an electrolyte solution in presence of charged colloids is presented. The model envisions the electrolyte transport across a charged cake or gel layer as transport of ions through charged cylindrical capillaries. This model is coupled with the standard theory of concentration polarization during cross flow membrane filtration. The analysis is carried out entirely in terms of generalized, non-dimensional variables. A dimensionless group termed as the scaled gel layer resistance evolves from the analysis, which accounts for the electrical properties of the charged nano-colloids and the electrolyte solution. A parametric study is performed to elucidate the coupled influence of mass transfer, membrane resistance, gel resistance, and electrical properties of the gel-electrolyte polarized layer. The effects of these parameters are examined on the filtration performance through the model equations.     

Surface modification of phenolphthalein poly(ether sulfone) ultrafiltration membranes by blending with acrylonitrile-based copolymer containing ionic groups for imparting surface electrical properties

Asymmetric ultrafiltration membranes were fabricated from the blends of phenolphthalein polyethersulfone (PES-C) and acrylonitrile copolymers containing charged groups, poly(acrylonitrile-co-acrylamido methylpropane sulfonic acid) (PAN-co-AMPS). From the surface analysis by XPS and ATR-FTIR, it was found that the charged groups tend to accumulate onto the membrane surface. This result indicated that membrane surface modification for imparting surface electrical properties could be carried out by blending charged polymer. Furthermore, with the help of a relatively novel method to measure membrane conduction, the true zeta potentials calculated on the basis of the streaming potential measurements were used to reflect the charge state of membrane surface. In addition, it was noteworthy that, from the profiles of zeta potential versus pH curves and the magnitude of zeta potentials, the determination of zeta potential was dependent not only on the electrical properties of membrane surface but also on its hydrophilicity. At last, based on a relatively elaborate study on the electrostatic interaction between the membrane surface and protein, it was found that these charged membranes could meet different demands of membrane applications, such as resisting protein fouling or protein separation, through adjusting solution pH value.     

A Comparative Study of the Electric Transport of Ions and Water in Sulfonated Cation-Exchange Polymeric Membranes of the New Generation

This work presents the results of the studies concerning the electric transport of ions and water through sulfonated cation-exchange membranes synthesized on the basis of polysulfone (PS) and poly(ether–ether–ketone) (PEEK). The concentration dependences of the water absorption capacity, specific conductance, and diffusion and electroosmotic permeabilities measured in sodium chloride solutions are compared to the analogous characteristics of some commercial membranes (MK-40, MF-4SK, CL-25T) under the same experimental conditions. The model concepts concerning the permeability of ion-conducting membranes as disperse systems are found to be applicable for interpreting the set of the electric transport properties of the membrane samples studied. A cluster–channel type of the membrane structure is identified. The polymeric films based on PS and PEEK are shown to possess characteristics comparable to those of commercial ion-exchange membrane samples and can be recommended for producing polymer compositions with an optimum set of electric transport properties.