Activity coefficients and coion exclusion in charged polymeric membranes with macroscopic inhomogeneities

 We consider a simple model to evaluate mean activity coefficients in charged polymeric membranes with an inhomogeneous distribution of the fixed charge concentration on the macroscopic spatial scale, and apply the results obtained to the coion exclusion characteristic of the Donnan equilibrium. Model calcula-tions with two fixed charge distributions of experimental interest (the asymmetric and the skin-core distributions) show that the inhomogeneity effects can be important when M28.8n the external salt solution concentration is lower than the membrane-fixed charge concen-tration, especially if spatial regions of low charge concentration exist within the membrane. The results obtained appear to be in qualitative agreement with previous experiments. Received 1 October 1996 Accepted 5 February 1997     

Donnan equilibrium of ionic drugs in pH-dependent fixed charge membranes: theoretical modeling

We have studied theoretically the partition equilibrium of a cationic drug between an electrolyte solution and a membrane with pH-dependent fixed charges using an extended Donnan formalism. The aqueous solution within the fixed charge membrane is assumed to be in equilibrium with an external aqueous solution containing six ionic species: the cationic drug (DH(+)), the salt cations (Na(+) and Ca(2+)), the salt anion (Cl(-)), and the hydrogen and hydroxide ions. In addition to these mobile species, the membrane solution may also contain four fixed species attached to the membrane chains: strongly acid sulfonic groups (SO(3)(-)), weakly acid carboxylic groups in dissociated (COO(-)) and neutral (COOH) forms, and positively charged groups (COO...Ca(+)) resulting from Ca(2+) binding to dissociated weakly acid groups. The ionization state of the weak electrolyte groups attached to the membrane chains is analyzed as a function of the local pH, salt concentration, and drug concentration in the membrane solution, and particular attention is paid to the effects of the Ca(2+) binding to the negatively charged membrane fixed groups. The lipophilicity of the drug is simulated by the chemical partition coefficient between the membrane and external solutions giving the tendency of the drug to enter the membrane solution due to hydrophobic interactions. Comparison of the theoretical results with available experimental data allows us to explain qualitatively the effects that the pH, salt concentration, drug concentration, membrane fixed charge concentration, and Ca(2+) binding exert on the ionic drug equilibrium. The role of the interfacial (Donnan) electric potential difference between the membrane and the external solutions on this ionic drug equilibrium is emphasized throughout the paper.     

Effect of proton concentration on membrane potential across a weak amphoteric polymer membrane

An amphoteric membrane consists of both positively and negatively fixed charge groups chemically bound to the polymer chains. If the external solution is changed from alkali to acid, it is possible to obtain an experimental result in which the membrane potential changes from positive to negative through the isoelectric point. It was characterized by examining the relationship between membrane potential and proton concentration (pH) obtained from both experimental and theoretical considerations. The Nernst-Planck flux equation and the Donnan equilibrium theory were also solved for a four-component system combined with the dissociation constant, in order to discuss the pH dependence of membrane potential in a weak amphoteric membrane by comparing the experimental results with the calculated results. It was proven that the calculated results substantially deviated from the theoretical results despite a similar tendency. Such a deviation was caused by the fact that the original theory disregarded the activity coefficient and the ionic mobility, which were dependent on the fixed charge concentration in a membrane. The original theoretical model was modified by adding the effect of a fixed charge group to the activity coefficient and ionic mobility. The calculated results using the modified model explained well the experimental results if the parameter called charge effectiveness, phi, was introduced into the equations. Introduction of phi into the prediction of membrane potential was already done by Kobatake et al. in a system of a strong polyelectrolyte monopolar membrane/salt aqueous solution. In this study, it was proved that phi can also be introduced into a weak amphoteric polymer membrane/salt aqueous solution system. Finally it was also concluded that the Donnan equilibrium and the Nernst-Planck flux equation were still applicable for examining the transport phenomena for the system of a weak amphoteric charged membrane and electrolyte solutions at various pH.     

Synthesis and characterization of an amphoteric ion-exchange membrane

An amphoteric ion-exchange membrane was prepared by chemical grafting of acrylic acid and dimethyl amino-2-ethyl methacrylate on ozonized polyethylene. The effects of the variation of external pH on the physicochemical properties of this membrane were studied (exchange capacity, electrical resistance, water and electrolyte content, and membrane potential). The determination of the mean activity coefficient of the NaCl in the membrane phase using the Donnan equilibrium equation reveals that this coefficient increases with the NaCl concentration in the external solution. Fundamental electrochemical properties of the amphoteric membrane are discussed on the basis of the variation of the membrane selectivity with the external electrolyte concentrations and the pH. The properties at neutral pH are accounted for by a mutual neutralization of some acidic and basic groups in the membrane phase.     

Buffer salt effect on pH in the interior of an anion exchange resin

The internal pH of Q Sepharose Fast Flow anion exchange resin in equilibrium with a bis-tris acetate buffer solution is investigated as a function of buffer salt concentration. Direct evidence of a resin phase pH shift is presented. At low buffer salt concentrations of 20 mM NaCl the resin phase pH is found to be as much as 1.1 pH units greater than that of the buffer phase, approaching to within 0.1 units of the buffer phase at salt concentrations greater than 250 mM. An ideal model with no adjustable parameters based on the Boltzmann distribution and the electroneutrality condition provides excellent agreement with experimental observations. The model assumes that small ions do not bind to the resin fixed charge sites and the agreement between the model predictions and observed resin internal pH suggests that strong electrolytes do not form ion pairs with the resin fixed charge sites.     

Characterisation of zirconium/poly(acrylic acid) low pressure dynamically formed membranes by use of the extended Nernst-Planck equation

The rejection of a single electrolyte solution, by a hydrous zirconium oxide/poly(acrylic acid) (Zr/PAA) dual layer dynamically formed membrane (DFM), has been investigated. A flat sheet titania-coated sintered stainless steel (IMAS UK) was used as a substrate for DFM formation. Flux and rejection were recorded for a series of experiments at different transmembrane pressures, feed solution cross-flow rates and salt concentration. Experimental data was interpreted using a model based on the extended Nernst-Planck equation. This interpretation allows characterisation of the membrane in terms of two parameters, the effective membrane charge density and a structural parameter which combines porosity and membrane thickness. Good correlation between experimental data and theory has been obtained. Calculation of the effective membrane charge density and the structural parameter at pH 6.7 and 9.0 for a range of salt concentrations provides conclusive evidence that membrane pore size decreases with increasing salt concentration and that the degree of ionisation of the PAA contained within the membrane increases with increasing pH and salt concentration.     

Passive Transport of Ionic Drugs through Membranes with pH-Dependent Fixed Charges

We have studied both theoretically and experimentally the passive transport of ionic drugs through membranes with pH-dependent fixed charge. The system considered constitutes a simplified model for pH-controlled drug delivery through membranes of biochemical and pharmaceutical interest. The theoretical approach employed is based on the Nernst-Planck flux equations and all of the species present in the system (the neutral or ionic drug and the hydrogen and hydroxide ions) have been taken into account together with a Langmuir-type isotherm for the adsorption of the ionic drug onto the membrane surface. The membrane permeabilities of cationic, anionic, and neutral drugs through porous membranes with graft-polymerized weak polyelectrolytes have been measured as a function of the external pH. According to the nature of the grafted polyelectrolyte, the ionized membrane fixed groups can be negative or positive. For the amphoteric membrane, both fixed charge groups are present in the grafted chains. In all cases, the ionization state of the weak polyelectrolyte fixed groups changes with the local pH within the membrane. A comparison of the theoretical results with the experimental data allows one to explain qualitatively the changes of the membrane flux with the external pH and gives new physical insights into the transport problem. Copyright 2000 Academic Press.     

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).     

Variable Charge-Densities in Hydrophilic Weak-Base Ion-Exchange Membranes. V. Equilibrium Properties with Pure 1-1 Electrolytes. Swelling and Ion-Exclusion

Abstract

The equilibrium distribution of chloride or nitrate counter-ions of K or NH₄ co-ions and of water is determined experimentally at different degrees of ionization X[xbar] of hydrophylic weak-base aminated polyvinyl-alcohol membranes. These data are analyzed and explained in terms of thermodynamics interrelating the molality of fixed-charge densities and of counter-ions to that of the amount of water and of diffused salt in the membrane.

Three domains have to be considered: the polyelectrolyte domain with small external concentration compared to the internal net fixed charge concentration (notion of “net-charge” densities), the domain of homogeneous interstitial liquid of the concentrated electrolyte type with sufficiently concentrated salt solution, and the intermediate domain.     

Partition Equilibrium on the Interface Between a Charged Membrane and a Mixed Electrolyte Aqueous Solution

Ionic partition equilibrium on a charged membrane immersed in a mixed electrolyte solution was systematically investigated and several models were established for the determination of partition coefficients.On the basis of theoretical models,the effects of the concentration ratio λof the fixed group(charged density) to reference electrolyte,the concentration ratio η between the two electrolytes existing in the solution and the valence of the electrolyte ions on the partition equilibrium in a positively charged membrane were analyzed and simulated within the chosen parameters in detail.The obtainable results can also be applicable to a sytem of mixed electrolytes contacting with a negatively charged membrane.The theoretical calculations were confirmed with the experimental data of model mixed electrolytes,NaCl HCl and CaCl2 NaCl partitioned in the system of self-made negatively charged membrane-sulphonated poly (phenylene oxide)(SPPO) with different charge densities.     

Studies on electrochemical characterization and performance prediction of cellulose acetate and Zeocarb-225 composite membranes in aqueous NaCl solutions

We have mixed cellulose acetate and Zeocarb-225 in different ratios, leading to the preparations of Membrane-1 and Membrane-2. Membrane potential, water content, and conductance measurements have been carried out to estimate and analyze the data in terms of equilibria and important electrochemical parameters. The Donnan equilibrium has been incorporated to estimate the activity coefficient of counterions, y(p)M, and solute, y(+/-)M in the membrane phase along with the parameter, so called varphi expressing non-ideality. Dependence of the extent of hydrophilicity of both membranes on mean electrolyte concentrations has been examined. Selectivity in membranes is discussed in terms of dissociation equilibria, K(d)s and K(d)f. It has been found that membrane surface charge density sigma(s) increases with increasing of external NaCl concentration. Dependence of water transport number and cationic transport number on electrolyte concentration shows a similar trend of variation. At higher mean concentration of electrolyte, water transport number in Membrane-2 has a negative value. Membrane-2 has a higher value of water transport number than Membrane-1. The entropy production due to solute and water transport has been quantified for both the membranes in the light of nonequilibrium thermodynamics. The various type of interactions such as solute-membrane, solute-water, and water-membrane are analyzed in terms of friction coefficients (f(ij)) of Spiegler's frictional pore model. In our case, an f(wm) < f(sm) < f(sw)-like trend is observed in both membranes. These frictional coefficients show close dependence on external electrolyte concentrations. Pore potential values of Membrane-1 and Membrane-2 have been worked out using the Poisson-Boltzmann equation. In both systems pore potential values increase with increasing mean electrolyte concentrations. The transport through Membrane-1 and Membrane-2 tends to follow diffusion-control criteria, i.e., (D(+/-) . C. d/D(+/-)M C(M) . delta) > 2. A slightly higher value of solute rejection is found in Membrane-2.     

Electrochemical characterization of an asymmetric nanofiltration membrane with NaCl and KCl solutions: influence of membrane asymmetry on transport parameters

Electrochemical characterization of a nanofiltration asymmetric membrane was carried out by measuring membrane potential, salt diffusion, and electrical parameters (membrane electrical resistance and capacitance) with the membrane in contact with NaCl and KCl solutions at different concentrations (10(-3)< or =c(M)< or =5 x 10(-2)). From these experiments characteristic parameters such as the effective concentration of charge in the membrane, ionic transport numbers, and salt and ionic permeabilities across the membrane were determined. Membrane electrical resistance and capacitance were obtained from impedance spectroscopy (IS) measurements by using equivalent circuits as models. This technique allows the determination of the electrical contribution associated with each sublayer; then, assuming that the dense sublayer behaves as a plane capacitor, its thickness can be estimated from the capacitance value. The influence of membrane asymmetry on transport parameters have been studied by carrying out measurements for the two opposite external conditions. Results show that membrane asymmetry strongly affects membrane potential, which is attributed to the Donnan exclusion when the solutions in contact with the dense layer have concentrations lower than the membrane fixed charge (X(ef) approximately -0.004 M), but for the reversal experimental condition (high concentration in contact with the membrane dense sublayer) the membrane potential is practically similar to the solution diffusion potential. The comparison of results obtained for both electrolytes agrees with the higher conductivity of KCl solutions. On the other hand, the influence of diffusion layers at the membrane/solution interfaces in salt permeation was also studied by measuring salt diffusion at a given NaCl concentration gradient but at five different solutions stirring rates.     

Charge regulation and local dielectric function in planar polyelectrolyte brushes

Understanding the effect of inhomogeneity on the charge regulation and dielectric properties, and how it depends on the conformational characteristics of the macromolecules is a long-standing problem. In order to address this problem, we have developed a field-theory to study charge regulation and local dielectric function in planar polyelectrolyte brushes. The theory is used to study a polyacid brush, which is comprised of chains end-grafted at the solid-fluid interface, in equilibrium with a bulk solution containing monovalent salt ions, solvent molecules, and pH controlling acid. In particular, we focus on the effects of the concentration of added salt and pH of the bulk in determining the local charge and dielectric function. Our theoretical investigations reveal that the dipole moment of the ion-pairs formed as a result of counterion adsorption on the chain backbones play a key role in affecting the local dielectric function. For polyelectrolytes made of monomers having dipole moments lower than the solvent molecules, dielectric decrement is predicted inside the brush region. However, the formation of ion-pairs (due to adsorption of counterions coming from the dissociation of added salt) more polar than the solvent molecules is shown to increase the magnitude of the dielectric function with respect to its bulk value. Furthermore, an increase in the bulk salt concentration is shown to increase the local charge inside the brush region.     

Limiting current density and water dissociation in bipolar membranes

The behaviour of bipolar membranes in NaCl and Na₂SO₄ solutions is discussed. The membranes are characterized in terms of their limiting current densities. Below the limiting current density the electric current is carried by salt ions migrating from the transition region between the anion and the cation exchange layer of the bipolar membrane. In steady state these ions are replaced by salt ions transported from the bulk solutions into the transition region by diffusion and migration due to the fact that the ion-exchange layers are not strictly permselective. When the limiting current density is exceeded, the salt transport from the transition region can no longer be compensated by the transport into the region and a drastic increase in the membrane resistance and enhanced water dissociation is observed. This water dissociation is described as being a combination of the second Wien effect and the protonation and deprotonation of functional groups in the membrane. The limiting current density is calculated from a mass balance that includes all components involved in the transport. The parameters used in the mathematical treatment are the diffusion coefficients of salt ions and water, the ion mobilities in the membrane, the fixed charge densitiy of the membrane, the pK_b values of the functional groups and the solution bulk concentrations.     

Study of pH correction process of chloride-bicarbonate dilute solutions by electrodialysis with bipolar membranes

The pH of a dilute chloride-hydrocarbonate solution and the concentrations of chloride ions and carbonic acid anions at the outlet of the alkaline and acid chambers of the electrodialysis cell formed by bipolar and anion-exchange membranes were determined. The decrease in the concentration of hydrocarbonate ions in the alkaline chamber with growth of current density was not equal to its increase in the acid chamber. This disbalance was caused by two concurrent processes: the electromigration ion transport through the anion-exchange membrane and the chemical reactions of hydrocarbonate ions with the water dissociation products formed on the bipolar and anion-exchange membranes. A mathematical model was suggested to describe the electrodialysis correction of the pH of a dilute chloride-hydrocarbonate solution. The experimental data on the correction of pH of the chloride-hydrocarbonate solution were well approximated by both the model that takes into account water dissociation on the anion-exchange membrane and the simplified model that neglects water dissociation. The experimental data agreed well with the results of calculations by the model in which the effective anion transport numbers were calculated only from ion concentrations and diffusion coefficients in solution. This reflects the outer diffusion character of the kinetics of ion transport through the anion-exchange membrane, with pH of dilute solutions corrected by electrodialysis.     

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.     

Comparison of osmotic pressures from EMF measurements,obtained according to cell-model considerations and exact Gibbs-Duhem integrations

Osmotic pressures of aqueous solutions of poly(diethylaminoethyl methacrylate) hydrochloride, in equilibrium with a precipitate of the un-ionized polybase, at various concentrations of polymer and NaCl in solution and at different values of pH are derived from emf measurements and the “cell” theory for polyelectrolytes. Single-ion activities are evaluated according to two procedures. The first is based on measurements with ion-specific electrodes versus a calomel electrode. The second makes use of a salt bridge, but assumes that the co-ions have activity coefficients equal to the mean activity coefficient of the salt in a polyelectrolyte-free solution of the same concentration. The results show that the calculated values of the osmotic pressures are consistent with those obtained by the exact integration of the Gibbs-Duhem relationship, when the first procedure is employed. If, however, the single-ion activities are evaluated by the second procedure, the osmotic pressures obtained are consistently lower by about 10%. These differences arise because the two methods yield different values of the activity coefficients of the single ions.     

A novel measurement method of Donnan potential at an interface between a charged membrane and mixed salt solution

We developed a novel measurement method of the Donnan potential difference at a charged membrane/salt solution interface. The method can measure the potential under the condition that the membrane charge density is much lower than the KCl concentration of the salt bridge. This method is very useful for obtaining the effective charge density of each layer of a bipolar membrane. The present experiments in a system of a negatively charged poly(vinyl alcohol) membrane and a single salt solution of KCl, NaCl, LiCl, CaCl₂ and LaC₃ revealed that the membrane effective charged density has the same value for all the ions. The experiments in mixed KCl and CaCl₂ solution revealed that the potential in the system is governed mainly by the concentration of the counterion having the highest valence in the system.     

Effects of ion solvation on phase equilibrium and interfacial tension of liquid mixtures

We study the bulk thermodynamics and interfacial properties of electrolyte solution mixtures by accounting for electrostatic interaction, ion solvation, and inhomogeneity in the dielectric medium in the mean-field framework. Difference in the solvation energy between the cations and anions is shown to give rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The ion solvation affects the phase equilibrium of the solvent mixture, depending on the dielectric constants of the solvents, reflecting the competition between the solvation energy and translation entropy of the ions. Miscibility is decreased if both solvents have low dielectric constants and is enhanced if both solvents have high dielectric constant. At the mean-field level, the ion distribution near the interface is determined by two competing effects: accumulation in the electrostatic double layer and depletion in a diffuse interface. The interfacial tension shows a nonmonotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations and decreases approximately as the square root of the salt concentration for dilute solutions, reaching a minimum near 1 mM. We also find that, for a fixed cation type, the interfacial tension decreases as the size of anion increases. These results offer qualitative explanations within one unified framework for the long-known concentration and ion size effects on the interfacial tension of electrolyte solutions.