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.     

Diffusion of electrolytes of different natures through the cation-exchange membrane

Diffusion of different electrolytes through a negatively charged (cation-exchange) membrane into distilled water has been studied. It has been established theoretically (with no regard to the presence of diffusion layers) that the integral diffusion permeability coefficient of an electrolyte depends on the diffusion coefficients and the ratio between the charge numbers of a cation–anion pair, the ratio between the density of charges fixed in the membrane and electrolyte concentration, and the averaged coefficient of equilibrium distribution of cation?anion ion pairs in the membrane matrix. It has been found that, when co-ions have a higher mobility, the dependence of diffusion permeability on electrolyte concentration passes through a maximum. Derived equations have been compared with experimental dependences of the diffusion permeability of an MC-40 membrane with respect to different solutions of inorganic 1: 1 and 2: 1 electrolytes. The developed method has been shown to be applicable for describing diffusion of any electrolytes (including asymmetric ones) through arbitrary uniformly charged membranes.     

Determination of Activation Energy for the Diffusion of Fe<Superscript>3+</Superscript> Ions in Agar Gel Medium Containing Various Transition Metal Sulfates

The study of the diffusion of ferric ions in agar gel containing transition metal sulfates was carried out. The effect of gel concentration, electrolyte concentration and temperature on the diffusion of Fe³⁺ ions in various transition metal sulfates was studied with a view to verify Wang’s model of diffusion and the applicability of transition state theory to diffusion in a gel medium. The diffusion coefficients were measured using the zone diffusion technique. For a given concentration of electrolyte the activation energy (E) is found to decrease with an increase in the charge density of the cation of the supporting electrolyte and for a given system it is found to decrease with increasing electrolyte concentration in agreement with Wang’s model. This observation is explained on the basis of the distortion in the water structure caused by ions and agar molecules. At a given electrolyte concentration the magnitude of the Arrhenius parameters, E and D _o, is found to decrease with increasing gel concentration in agreement with the transition state theory of diffusion.     

Transport in polymer-gel composites: response to a bulk concentration gradient

This paper examines the response of electrolyte-saturated polymer gels, embedded with charged spherical inclusions, to a weak gradient of electrolyte concentration. An electrokinetic model was presented in an earlier publication, and the response of homogeneous composites to a weak electric field was calculated. In this work, the influence of the inclusions on bulk ion fluxes and the strength of an electric field (or membrane diffusion potential) induced by the bulk electrolyte concentration gradient are computed. Effective ion diffusion coefficients are significantly altered by the inclusions, so-depending on the inclusion surface charge or zeta potential-asymmetric electrolytes can behave as symmetrical electrolytes and vice versa. The theory also quantifies the strength of flow driven by concentration-gradient-induced perturbations to the equilibrium diffuse double layers. Similarly to diffusiophoresis, the flow may be either up or down the applied concentration gradient.     

Effective concentration difference model to study the effect of various factors on the effective diffusion coefficient in the dialysis membrane

Cellulose acetate dialysis membrane (CDM) has been used in the diffusive gradients in thin films (DGT) technique, where accurate diffusion coefficients are essential for the assessment of the concentrations of labile metal in solution. Effective concentration difference model (ECDM), based on the assumption that the effective diffusion coefficient of metal ion in the dialysis membrane is determined by the effective concentration difference (ΔC(e)) across the dialysis membrane, is proposed and applied to study the effect of ionic strength, binding agent, ligands and Donnan potential on the effective diffusion coefficient. The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in receptor solutions with binding agent were almost the same as those in receptor solutions without binding agent at higher ionic strengths (0.01-1 M) but much higher than those at lower ionic strengths (0.001-0.0001 M). The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in deionized water receptor solutions with binding agent were not significantly different from those in synthetic receptor solutions (receptor solutions with various ionic strengths) with binding agent. The DGT-labile fractions were measured in synthetic solutions and natural waters, which indicated that the effective diffusion coefficients, through the dialysis membrane immersed in the deionized water solution with binding agent as receptor solution and in the spiked natural water as source solution, were more suitable for DGT application.     

Theoretical study of interdiffusion of aqueous solutions of 1 : 1 electrolytes having the same anion through a cation-exchange membrane

The interdiffusion of aqueous 1: 1 electrolytes having the same anion through a negatively charged (cation-exchange) membrane has been studied without taking into account the diffusive layers. It has been established that the interdiffusion coefficients of the cations depend (in addition to their own diffusion coefficients in the membrane) on the ratio of the diffusion coefficients of both cations to the diffusion coefficient of the anion and the ratio of the density of charges fixed in the membrane to the equal concentration of the electrolytes on both sides of the membrane, as well as the equilibrium distribution coefficients of cationanion ion pairs in the membrane matrix. The conditions have been found under which the membrane plays the role of a “blocking system” (like a diode) that is impenetrable to cations located on both sides of the membranes in spite of the existence of their concentration gradients. The developed approach can be used to describe the interdiffusion of 1: 1 electrolytes through any uniformly charged membrane.     

Electrochemical behaviour of cellulosic cation membranes: Bi-ionic potentials in alkali systems

The behaviour of cationic ion-exchange membranes in bi-ionic systems formed by pairs of alkali ions was studied. The membrane was prepared by grafting vinyl monomers on parchment paper, which gives it a marked hydrophilic character. The selectivity coefficients and bi-ionic potentials of the membrane in the presence of the ten possible pairs of alkali ions was measured in a wide range of electrolyte concentrations (10⁻³−1 molal). The magnitude of these parameters is governed by the ions forming the bi-ionic system and their values are the higher the greater the difference in size of the ions. For those ion-pair systems formed from identical ions, both selectivity coefficients and bi-ionic potentials remain constant as the electrolyte concentration increases, whereas for those systems made up of dissimilar ions, the values are dependent on the concentration of electrolyte. The results are justified on the basis of the hydrophilic character of the membrane matrix.     

Modification of the GV-MSA model in obtaining the activity and osmotic coefficients of aqueous electrolyte solutions

In this work a modified form of the Ghotbi–Vera Mean Spherical Approximation model (MGV-MSA) has been used to correlate the mean ionic activity coefficients (MIAC) for a number of symmetric and asymmetric aqueous electrolyte solutions at 25 °C. In the proposed model the hard sphere as well as the electrostatic contributions to the MIAC and the osmotic coefficient of the previously GV-MSA model has been modified. The results of the proposed model for the MIAC of the electrolyte solutions studied in this work are used to directly calculate the values of the osmotic coefficients without introducing any new adjustable parameter. In the MGV-MSA model the cation diameter as well as the relative permittivity of water depends on the electrolyte concentration. Having considered such dependency for both cation and relative permittivity for water in an electrolyte solution the modification of the GV-MSA has been made. It should be stated that in the MGV-MSA model the anion diameter in the solution similar to that in the GV-MSA model remains constant and independent of the electrolyte concentration. The results obtained from the proposed model have been favorably compared with those of the GV-MSA model. The results showed that the MGV-MSA model can more accurately correlate the MIAC of the single electrolyte solutions than those of the GV-MSA model. The same comparison has been observed in case of the osmotic coefficients for the electrolyte solutions studied in this work. It should be noted that in order to do an unequivocal comparison between the results obtained from the models used in this work the same minimization procedure and the same experimental data for the MIAC and the osmotic coefficients have been used. Also it should be mentioned that in the MGV-MSA model the conversion from the McMillan–Mayer (MM) framework to that of the Lewis–Randall (LR) has been performed. It has been concluded that such transformation can affect the results in particular at higher electrolyte concentrations.     

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).     

Stripping Voltammetry for the Real Time Determination of Zinc Membrane Diffusion Coefficients in High pH: Towards Rapid Screening of Alkaline Battery Separators

An anodic stripping voltammetry (ASV) sensing platform which provides real time determination of zincate diffusion through membrane separators in alkaline electrolyte with total experimental times on the order of hours is presented. Advanced separators are essential for future rechargeable alkaline zinc batteries. In order to be screened, these membranes need to be evaluated for their zincate blocking performance. Current complexometric titration and elemental analysis methods for zincate membrane diffusion characterization can take days to weeks to obtain results as well as include large sample dilution factors and require additional sample processing. The anodic stripping voltammetry (ASV) sensing platform presented here provides real time determination of zincate diffusion in alkaline electrolyte with total experimental times on the order of hours. This method eliminates the need for sample dilution and post experiment sample processing. This technique significantly increases the throughput for the screening of advanced alkaline battery separators resulting in rapid turnaround times in the analysis of these vital membranes. To evaluate the utility of this method, zincate diffusion through commercial Celgard 3501 and Cellophane 350P00 was monitored using both ASV and inductively coupled plasma‐mass spectrometry (ICP‐MS) methods. The obtained zincate diffusion coefficients for both techniques were found to compare favorably.     

Studies on the Response Dynamics of a Gas-Sensing Membrane Probe

The present paper covers the response dynamics of a gas-sensing membrane probe, which is described by the dynamic differential equation based upon a steady-state diffusion process. The theoretical results indicate that the response time is dependent upon membrane properties, membrane geometry, internal electrolyte composition, the dissociation constant of the conjugate reaction, the initial gas concentration in the internal electrolyte, and the gas concentration in the evaluation sample. The theoretical prediction is in good agreement with the experimental result. A method for determining a gas-sensing probe' s dynamic parameter is proposed in this paper also.     

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.     

Diffusion coefficients of lithium chloride and potassium chloride in hydrogel membranes derived from acrylamide

Diffusion of non-associated electrolytes (potassium chloride and lithium chloride) in concentrated aqueous solutions (0.1-1.0 mol dm⁻³) has been studied in hydrogels derived from acrylamide and methyl methacrylate to study the mechanism of electrolyte transport. The preparation of two gels with different monomer ratio compositions resulted in obtaining membranes of substantially different hydrophilic character with polymer fractions of 0.3 and 0.5.Cukier hydrodynamic model was applied to explain the dependence of the diffusion coefficients of KCl and LiCl on the electrolyte concentration in hydrogel obtained experimentally. It was shown that the increase of the diffusion coefficients is accompanied with a decrease of the mean distance of approach of the ions. This can be explained by the formation of ion-pairs, resulting in a further contribution to diffusion once there is a decrease in the hydrodynamic resistance of the medium to the diffusing particles. Parameters, which characterise such a behaviour quantitatively, are different for different electrolytes and depend on water content in the gel.     

Tracer diffusion of Co2+ ions in agar gel containing multi-electrolyte systems

Tracer diffusion coefficients of cobalt ions have been measured in the supporting medium containing multi-electrolyte systems of alkali bromides. The electrolyte concentration was varied between 10^–6-0.1M at 25°C and the diffusion coefficients were determined by zone-diffusion technique using agar gel medium. The trend in the theoretical values of diffusion coefficients is accounted for by considering the relative contribution of mobility function, ionic strength as well as ion size parameter to the theoretical value in different systems. While the deviations between theoretical and experimental values of diffusion coefficients are explained on the basis of various co-occurring effects in ion-gel-water system.     

Transport of Acids through Polyether-Sulfone Anion-Exchange Membrane

Diffusion dialysis of sulfuric acid and hydrochloric acid into water with a polyether-sulfone anion-exchange membrane was studied. Transport of sulfuric acid and hydrochloric acid through the membrane has been quantified by diffusion coefficients and mass transfer coefficients. The mass transfer coefficients were investigated as a function of the rotational speed of the stirring rate of both sides of the membrane and with different pH ranges. It was observed that the diffusion dialysis seems to be dependent on the rotational speed of the stirrer; in contrast, the membrane mass transfer coefficients are independent of rotational speed, but they are slightly affected by the initial acid concentration in donor phase. Copyright 2001 Academic Press.     

Prediction of collective diffusion coefficient of bovine serum albumin in aqueous electrolyte solution with hard-core two-Yukawa potential

A new method to predict concentration dependence of collective diffusion coefficient of bovine serum albumin (BSA) in aqueous electrolyte solution is developed based on the generalized Stokes-Einstein equation which relates the diffusion coefficient to the osmotic pressure. The concentration dependence of osmotic pressure is evaluated using the solution of the mean spherical approximation for the two-Yukawa model fluid. The two empirical correlations of sedimentation coefficient are tested in this work. One is for a disordered suspension of hard spheres, and another is for an ordered suspension of hard spheres. The concentration dependence of the collective diffusion coefficient of BSA under different solution conditions, such as pH and ionic strength is predicted. From the comparison between the predicted and experimental values we found that the sedimentation coefficient for the disordered suspension of hard spheres is more suitable for the prediction of the collective diffusion coefficients of charged BSA in aqueous electrolyte solution. The theoretical predictions from the hard-core two-Yukawa model coupled with the sedimentation coefficient for a suspension of hard spheres are in good agreement with available experimental data, while the hard sphere model is unable to describe the behavior of diffusion due to its neglect of the double-layer repulsive charge-charge interaction between BSA molecules.     

Electrostatic interaction of ion-penetrable membranes. Effects of ionic solubility

An analytic, approximate expression for the electrostatic interaction between two membranes immersed in an electrolyte solution is derived on the basis of a simple membrane model. This model assumes that the membrane has a surface layer in which charged groups are uniformly distributed and that electrolyte ions can penetrate into the surface layer. The partition coefficients of cations and anions between the solution and the surface layer, which are related to their solubilities in the surface layer, may be different from unity.The electrostatic interaction depends on the ionic partition coefficients between the solution and the surface layer, and the relative permittivity of the surface layer, as well as on the membrane-fixed charges, the electrolyte concentration in the solution, and the surface layer thickness. It is shown, in particular, that even where the charge layer has no fixed charges, the electrostatic interaction force can be produced if the solubilities of cations and anions are different in the surface layer.     

Intradiffusion coefficients for perchlorate ions in zinc perchlorate and zinc chloride solutions at 25°C: Comparing transport properties of zinc chloride and zinc perchlorate systems

Intradiffusion coefficients for³⁶ClO ₄ ^– have been measured in solutions of zinc perchlorate of concentration 0.1 to 3 mol dm^–3 at 25°C by the diaphragm cell technique. In addition, intradiffusion coefficients for perchlorate ions in zinc chloride solutions have been measured over a concentration range at 25°C. The results confirm previous work on the effect of complexation on diffusion in zinc chloride solutions above a salt concentration of 0.1M. The present data, together with literature data for diffusion coefficients of the other species present in the zinc perchlorate electrolyte system, have enabled a simple analysis of the hydration around the zinc ions to be carried out. This indicates that the water diffusion data are consistent with the zinc ions having an effective hydration sphere of 11 (±2) water molecules. This is in keeping with values obtained for other simple divalent electrolytes using the same model. The model is extended here to allow analysis of water diffusion in zinc chloride solutions taking into account the presence of complexed chloro-zinc species. The experimental data are consistent with the effective hydration of the chloro-zinc complexes being independent of the number of chloride ligands and equal to 18±3 over a concentration range of 0 tol mol-dm^–3. This postulate is discussed in terms of its consequences on the water ligand dynamics for the complex equilibria.     

Diffusion in dilute aqueous acetic acid solutions at 25°C

A conductimetric technique has been used to measure diffusion coefficients for aqueous solutions of acetic acid at concentrations from 0.002 to 0.02 mol-dm^–3 at 25°C. The acetic acid component diffuses more rapidly at lower concentrations where a higher proportion of the slower acid molecules are converted by dissociation to acetate ions and highly mobile hydrogen ions. The observed concentration dependence of the diffusion coefficient verifies the limiting law for weak electrolyte diffusion. A new type of conductimetric diffusion cell with several practical advantages over earlier designs is described together with an improved procedure for the conductimetric determination of accurate diffusion coefficients for weak electrolyte systems.     

Permeation of aromatic compounds in aqueous solutions through thin,dense cellulose acetate membranes

The partition and diffusion coefficients of aqueous solutions of aromatic compounds through a thin, dense cellulose acetate membrane were measured at 20°C. The water content and the thickness of the prepared membranes varied from 0.121 to 0.610 by volume fraction and from 17 to 88 μm, respectively. The aromatic solutes used were phenol, aniline, hydroquinone and p-chlorophenol. The solute concentration ranged between 9.0 x 10^-5 and 1.0 x 10^-3 mol/l. The partition coefficients had the following order: p-chlorophenol, phenol, aniline, hydroquinone; they were experimentally correlated with the water content of the swollen membranes.The dependence of the diffusion coefficients on the water content of the membrane was examined using as basis a pore model and a free volume model, respectively. The diffusion coefficients were adequately correlated with the water content of the membrane according to the relation given by the free volume model.