An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer's equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer's model (combining a long-range term, based on the Debye–Hückel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid–liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems.     

The model of a polyelectrolyte solution with explicit account of counterions within a self-consistent field theory

A theoretical approach to calculating the thermodynamic and structural functions of solutions of polyelectrolytes based on Gaussian equivalent representation for the calculation of functional integrals is proposed. It is noted that a new analytical result of this work is the direct assumption of counterions, along with an equation for the gyration radius of a polymer chain as a function of the concentrations of monomers and added low-molecular salt. An equation of state is obtained within the proposed model. Our theoretical results are used to describe the thermodynamic and structural properties of an aqueous solution of sodium polystyrene sulfonate with additions of NaCl.     

Thermodynamic characterization of rare Earth salts of strong polyacid copolymers

Stoichiometric La3+, Ce3+, and Nd3+ salts of poly[(vinyl alcohol)-co-(vinyl sulfate)] (PVAS) copolymer polyacids have been studied in aqueous solution without added salt. All LnPVAS salts were entirely water-soluble in the composition and concentration range investigated. Ratios of the vinyl sulfate and vinyl alcohol units in the copolymers were between 1:5 and 1:107, leading to structural charge densities both above and under the critical value needed for counterion condensation of trivalent counterions. Solvent activity, a1, has been measured by the gel deswelling method in the concentration range of 5 x 10(-4) to 1 x 10(-1) mol of counterion/kg of water (0.2-9 w/w% of the polyelectrolyte). Results are unusually high for polyelectrolytes (-2 x 10(-6) > ln a1 > -3 x 10(-4)), and they are comparable with values determined in solutions of uncharged polymers. Nevertheless, the different copolymers can be clearly distinguished; the water activity is lowered in the order of the vinyl sulfate content of the polyelectrolytes, except for the one above the critical charge density. No observable difference was caused in the thermodynamic properties by the different lanthanide counterions. Reduced osmotic pressure curves and Flory-Huggins pair interaction parameters have been calculated; both of them were used to estimate degrees of dissociation at zero as well as at finite concentrations. Degrees of dissociation are decreasing with increasing concentration or vinyl sulfate content of the copolymer. They take values between 8-36% at zero polymer concentration and they reach zero value simultaneously at approximately 1 x 10(-3) mol of polymer chains/kg of water. The average number of released counterions per polymer chain (DPn = 1005) approaches to a limit of about 4.4 with increasing vinyl sulfate content. This corresponds to average charge distances of b > or = 19 nm and charge density parameters of xi < or = 0.037. The latter is, however, a very low value and indicates a 1/9 contraction compared to the rod-like assumption.     

A new approach in modelling phase equilibria and gas solubility in electrolyte solutions and its applications to gas hydrates

This paper presents a new predictive model for phase equilibria and gas solubility calculations in the presence of electrolyte solutions. It treats salts as pseudo-components in an equation of state (EoS) by defining the critical properties and acentric factor for each salt. The water–salt, gas–salt and salt–salt binary interaction parameters (BIP) have been determined by using available experimental data on freezing point depression and boiling point elevation as well as gas solubility and salt solubility data in saline solutions.The methodology has been applied in modelling sodium chloride, potassium chloride and their mixtures, as well as solubility of methane and carbon dioxide in aqueous single and mixed electrolyte solutions.The developed model is capable of accurately predicting the phase behaviour, gas hydrate stability zone and potential salt precipitation in single and mixed electrolyte solutions. The model predictions are compared with available independent experimental data, including hydrate inhibition characteristics of single and mixed electrolyte solutions, and good agreement is demonstrated.     

Polyelectrolyte conductivity

Using the de Gennes scaling model for the configuration of a polyelectrolyte chain in semidilute solution, we construct a simple model of AC conductivity for semidilute solutions of strongly charged polyelectrolytes without added salt. We compare the predictions of this model with literature data and new data on two polyelectrolytes with very different affinities for water. The sodium salt of sulfonated polystyrene in water is a hydrophobic polyelectrolyte (the uncharged monomer does not dissolve in water), where the chain is locally collapsed. The sodium salt of poly(2-acrylamido-2-methylpropanesulfonate), is a much more hydrophilic polyelectrolyte, making the chain quite expanded locally. The model describes the conductivity of both cases reasonably for concentrations below 10⁻² M (mol of monomer per liter). Deviations between experiment and theory at higher concentrations lead us to conclude that counterion condensation decreases as concentration is increased. This is qualitatively consistent with the experimental observation that the dielectric constant of the polyelectrolyte solution increases as polyelectrolyte is added. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2951–2960, 1997     

Aqueous GPC of electrolytes and polyelectrolytes

The gel permeation chromatography (GPC) of polyelectrolytes is discussed. The electrostatic exclusion is demonstrated using simple electrolytes with different eluents. The data for aqueous free salt solutions of polyelectrolytes are interpreted. The osmotic coefficient is deduced and its dependence on molecular weight and polymer concentration reported. In salt eluents, the Donnan exclusion is discussed. The universal calibration obtained with different standards in aqueous solution is shown to be valid and identical to that obtained in an organic solvent using polystyrene standards.     

A Modified Local Composition-Based Model for Correlating the Vapor-Liquid and Liquid-Liquid Phase Equilibria of Aqueous Polymer-Salt Systems

In this research, a new local composition model has been proposed to study the vapor-liquid and liquid-liquid phase equilibria of polyelectrolyte solutions. The proposed model has been used in order to obtain the activity of water in polyethylene glycol (PEG) and polypropylene glycol (PPG) solutions. The interaction parameters introduced into the proposed model have been reported. The interaction parameters between the salt and water molecule have been estimated using the experimental mean ionic activity coefficients of aqueous electrolytes studied in this work. Also, the interaction parameters between the polymer and salt molecule, and the polymer and water molecule have been computed using the experimental activity of water data in aqueous polymer solutions. The results showed that the proposed model, segment-based Wilson and segment-based NRTL models have good accuracy in correlating the vapor-liquid phase equilibria of the water-polymer and water-polymer-salt systems. Also, the liquid-liquid phase behavior of the polymer-salt aqueous two-phase systems has been correlated using the proposed model. The results show that the proposed model can more accurately correlate the phase behavior of aqueous two-phase systems than the UNIQUAC and the modified Wilson models.     

Theory of competitive counterion adsorption on flexible polyelectrolytes: divalent salts

The counterion distribution around an isolated flexible polyelectrolyte in the presence of a divalent salt is evaluated using the adsorption model [M. Muthukumar, J. Chem. Phys. 120, 9343 (2004)] that considers the Bjerrum length, salt concentration, and local dielectric heterogeneity as physical variables in the system. Self-consistent calculations of effective charge and size of the polymer show that divalent counterions replace condensed monovalent counterions in competitive adsorption. The theory further predicts that at modest physical conditions for a flexible polyelectrolytes such as sodium polystyrene sulfonate in aqueous solutions polymer charge is compensated and reversed with increasing divalent salt. Consequently, the polyelectrolyte shrinks and reswells. Lower temperatures and higher degrees of dielectric heterogeneity between chain backbone and solvent enhance condensation of all species of ions. Complete diagrams of states for the effective charge calculated as functions of the Coulomb strength and salt concentration suggest that (a) overcharging requires a minimum Coulomb strength and (b) progressively higher presence of salt recharges the polymer due to either electrostatic screening (for low Coulomb strengths) or coion condensation (for high Coulomb strengths). Consideration of ion-bridging by divalent counterions leads to a first-order collapse of polyelectrolytes in modest presence of divalent salts and at higher Coulomb strengths. The authors' theoretical predictions are in agreement with the generic results from experiments and simulations.     

Liquid–liquid equilibrium behavior of tetrabutylammonium bromide,benzene, and water mixture

Tetrabutylammonium bromide (QBr) is a weak organic salt and used as a phase-transfer catalyst in phase-transfer catalytic reaction producing the desired product of benzyl bromide in the organic phase. The distribution of QBr between the organic phase (benzene is the organic phase solvent) and the aqueous phase is the important factor influencing benzyl bromide yield. In this study, the liquid–liquid equilibrium of benzene, water, and QBr ternary mixture were measured at 318.15, 328.15, and 338.15 K, respectively. The experimental results exhibited that the solubility of QBr is very large in this heterogeneous liquid mixture and the amount of aqueous phase increases whenever more QBr was added at constant temperature. The concentration of QBr in aqueous phase decreased with the increasing temperature. The organic phase composition did not vary obviously since the solubilities of water and QBr in benzene are very low. An empirical parameter was introduced to represent the degree of dissociation of QBr in solvent while the experimental data were correlated since it is very difficult to measure the degree of dissociation of QBr attributed to the partial dissociation of a weak organic salt. Finally, the experimental data were correlated with the NRTL model of Renon and Prausnitz taking account ion–molecule and molecule–molecule interactions.     

Phase equilibria of hydrogen sulphide clathrate hydrates in the presence of single or mixed salt aqueous solution

This work reports the dissociation pressures of hydrogen sulphide clathrate hydrates in the presence of single and mixed aqueous solutions of NaCl, KCl and CaCl₂ at different temperatures and various concentrations of salt(s) in aqueous solution. The equilibrium data were generated using an isochoric pressure-search method. These data are compared with some selected experimental data from the literature on the dissociation conditions of hydrogen sulphide clathrate hydrates in the presence of pure water to show the inhibition effects of the aforementioned aqueous solutions. Comparisons between our experimental data and the corresponding literature data show some disagreements in the literature data.     

Role of linear charge density and counterion quality in thermodynamic properties of strong acid type polyelectrolytes: divalent transition metal cations

Thermodynamic properties of aqueous solutions of poly[(vinyl alcohol)-co-(vinyl sulfate)] (PVAS) copolymer polyelectrolytes with divalent transition metal (Co(II), Ni(II), and Cu(II)) counterions have been determined by the gel deswelling method in the concentration range of 0.0005-0.12 mol of counterion/kg of water (0.09-9 w/w% of the polymer). The influence of the chemical nature of the counterion as well as the effect of the composition of the copolymer from small to medium linear charge density have been systematically studied. Solvent activity, reduced osmotic pressure, the Flory-Huggins pair interaction parameter, rational osmotic coefficients, and degrees of dissociation were calculated from the measured data. No difference could have been observed between the three counterions. Reduced osmotic pressure curves are found to be convex from above, as for Na+ counterions studied previously, which is contrary to the usual behavior of neutral polymers. Intercepts are increasing, and the calculated apparent molar masses and degrees of dissociation at infinite dilution are decreasing with increasing linear charge density of the polyelectrolytes. The pair interaction parameters show a considerable negative deviation from linearity, except for the high volume fraction region. From the differences, concentration dependence of degrees of dissociation could have been calculated. The values at infinite dilution are in good agreement with those obtained from the intercepts of the reduced osmotic pressure curves. Degrees of dissociation seem to decrease approximately linearly with increasing concentration and reach zero at finite concentrations. Rational osmotic coefficients have been calculated in three different ways, both regarding and neglecting the change in the degrees of dissociation.     

Complexation of linear and poly(ethylene oxide)‐grafted poly(methacryl oxyethyl trimethylammonium chloride) with poly(ethylene oxide‐block‐sodium methacrylate)

The interactions between oppositely charged polyelectrolytes were studied in saline aqueous solutions as functions of the temperature and the salt and polymer concentrations. The polyanion was a diblock copolymer composed of a poly(ethylene oxide) block and a poly(sodium methacrylate) block. Two polycations were used, the homopolymer poly(methacryl oxyethyl trimethylammonium chloride) and its poly(ethylene oxide)‐grafted analogue. By dynamic light scattering and turbidity measurements, it was observed that the salt concentration, temperature, and counterion size had a significant effect on the formation of the polymer complexes in aqueous solutions. At a fixed salt concentration and a fixed temperature, it was possible to form completely soluble complexes of an ionic polymer in aqueous solutions between poly(ethylene oxide)‐grafted poly(methacryl oxyethyl trimethylammonium chloride)and the polyanion with a poly(ethylene oxide) block at a 1:1 anion/cation ratio. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1904–1914, 2003     

Transport properties of some cationic polysaccharides 2. Charge density effect

The charge density effect on the behavior of some cationic polysaccharides in aqueous and nonaqueous (methanol) solutions was studied by viscometric and conductometric measurements. The polyelectrolytes investigated contain quaternary ammonium salt groups, N-alkyl-N,N-dimethyl-2-hydroxypropylene ammonium chloride, attached to a dextran backbone. This new class of polyelectrolytes has various linear charge density parameters, xi, located below and above the critical threshold value of counterions condensation, xi(c)=1(xi=0.25-3.18). The viscometric data revealed that all copolymers exhibit a polyelectrolyte behavior and were plotted in the terms of Rao equation. The conductometric measurements of solutions of these copolymers were presented as a function of polymer concentration and charge density. The results were analyzed within the Manning's theory and lower experimental values of the equivalent conductivity than the theoretical ones were found. Possible reasons of this discrepancy have been discussed. The interaction parameters were evaluated and these were found to depend on both the polymer concentration and the charge density. The conductometric behavior of these cationic polysaccharides has shown that counterion condensation is not a threshold phenomenon, their association to the charged groups of the polyions taking place for xi>1 as well as xi<1.     

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.     

Thermodynamics of aqueous solutions containing poly (N-isopropylacrylamide)

Hydrogels undergo reversible and discontinuous volume changes in response to variation of solution conditions such as solvent composition, temperature, salt concentration, and pH. In this contribution we focus our attention on the experimental and theoretical investigation of these swelling equilibria of aqueous cross-linked poly (N-isopropylacrylamide) solutions as well as on the connected demixing behavior of the linear polymer dissolved in water. For the experimental study of the (liquid + liquid) equilibrium an alternative method based on refractive index measurements is suggested. In order to calculate the swelling behavior a model combining an expression for the Gibbs free energy of mixing with an expression for the elastic network is applied. As a model for the Gibbs free energy of mixing the UNIQUAC-approach and the Koningsveld–Kleintjens model are used. For the elastic network contribution again two different theories, namely the phantom network theory and the affine network theory, were applied. Whereas the type of network theory has only a small influence on the calculation results, the Gibbs free energy of mixing has a large impact. Using the UNIQUAC-approach the swelling equilibria can be correlated close to the experimental data, however, this model predicts a homogeneous mixture for linear polymer chains in water. In contrast to this situation the Koningsveld–Kleintjens model does a good job in calculating the swelling equilibria as well as the demixing curve, however, the adjustable parameter must be changed slightly.     

Evaluating alternative electrostatic potential models for polyacrylamide-co-acrylate in aqueous solution

The capabilities of three simplified analytical equations to accurately model electrostatic interactions during proton binding and release by linear anionic polyelectrolytes in aqueous solution were evaluated. The impermeable sphere (IS), Donnan (DN), and cylindrical (CY) electrostatic models were fit to experimental acid-base titration curves of linear polyacrylamide-co-acrylate having ionizable site densities ranging from ca. 10-35%. The titrations were conducted in 0.003-0.12M NaCl solutions and the sum of squared errors from modeled and experimental data was used as a comparative index of each model's capability. In addition, the relative size of each polyelectrolyte was estimated from its measured specific viscosity and then compared against the values obtained from the fitting procedure for the size parameter that each model contained. Although the IS and DN electrostatic models could be used to obtain reasonably good fits to each titration curve, the size parameter values obtained by each model were not reflective of the actual polyelectrolyte sizes, indicating that the models had limited physical meaning and that the size parameter was essentially just an additional fitting parameter in each model. In contrast, the CY model was not only more effective in its ability to fit the titration data but also provided a better physical representation of the polyelectrolyte size. Therefore, for polyelectrolytes that remain essentially linear or are only loosely coiled such that counter ions are free to travel throughout the polymer structure, we conclude that the CY model and its morphological representation of a cylindrical polyelectrolyte are more valid and realistic than the IS and DN models and their representation of polyelectrolytes as spheres.     

Reversible association of thermoresponsive gold nanoparticles: polyelectrolyte effect on the lower critical solution temperature of poly(vinyl methyl ether)

Thermoresponsive gold nanoparticles (GNPs) have been prepared by the borohydride reduction of gold salt in the presence of water-soluble polymer, poly(vinyl methyl ether) (PVME). The PVME-coated GNPs (PVME-GNPs) have been assembled into large aggregates in the presence of polyelectrolytes, viz., poly(sodium-4 styrene sulfonate) and sodium salt of carboxymethylcellulose at low pH by raising the solution temperature from 20 to 40 degrees C. Increase of temperature triggers the interparticle association due to hydrophobic interaction of pendent methyl group of the surface adsorbed PVME. This assembly process is reversible with respect to temperature and pH of the medium and was studied by monitoring the change in surface plasmon resonance band of PVME-GNPs. Three-dimensional assemblies of various architectures, depending on the concentration of polyelectrolytes, were observed through transmission electron microscopy. A mechanistic model has been suggested for the reversible assembly formation that suits well with the experimental observations. The changes in optical properties of the PVME-GNPs due to their aggregation/disaggregation enabled us to use it as an effective tool to monitor the change in lower critical solution temperature (LCST) of PVME in the presence of polyelectrolytes due to interpolymer complexation at low pH. This result agrees well with the variation of LCST of pure aqueous PVME solution in the presence of polyelectrolytes measured by conventional turbidimetric technique.     

Isothermal titration calorimetry and molecular dynamics study of ion-selectivity in mixtures of hydrophobic polyelectrolytes with sodium halides in water

Aliphatic x,y-ionenes are polyelectrolytes in which x and y denote the numbers of methylene groups separating quaternary ammonium ions. They represent useful model substances for studying hydrophobic and charge effects in aqueous solutions. We used isothermal titration calorimetry to measure the enthalpies of mixing, ΔH(mix), of 3,3- and 6,6-ionene fluorides and bromides with low molecular weight salts (NaF, NaCl, NaBr, and NaI) at 298 K in water. The signs and magnitudes of the measured enthalpies depend on the hydrophobicity of the ionene and on the nature of the added salt. For example, addition of sodium fluoride to solutions of 3,3- and 6,6-ionene fluorides produced endothermic effects, while addition of sodium bromide to 3,3-ionene bromide resulted in a strong exothermic effect. Interestingly, mixing of 6,6-ionene bromide and NaBr solutions in water gave a small exothermic heat effect. Polyelectrolyte theories, based on continuum-solvent models, predict enthalpies of mixing to be positive (endothermic) for all the solutions examined in this work. The ion-specific effect is more strongly expressed in ionene solutions with higher charge density (3,3-ionene). The most important result of this work is the finding that the enthalpy of mixing of 3,3- (and of 6,6-ionene) fluorides with sodium halides can be expressed as a linear function of the enthalpy of hydration of the halide counterions. The experimental results were complemented with an explicit water molecular dynamics simulation of solutions of oligoions modelling 3,3- and 6,6-ionenes. The computer simulation results for various nitrogen-counterion pair distribution functions were in most cases consistent with the enthalpy measurements.     

STUDIES ON SELF-ASSOCIATIVE BEHAVIOR OF A NOVEL CATION AMPHIPHILIC POLYMER

A novel associating polymer P(AEBA) was synthesized by radical polymerization of the cationic amphiphilic monomer,4-(2-(acryloyloxy)ethoxy)benzyl tri-ethyl ammonium bromide(AEBA),in aqueous solutions.P(AEBA) displays a strong tendency for self-association in aqueous solutions and is sensitive to the external stimulation such as added salt.The associative properties and morphologies of P(AEBA) were studied by fluorescnece probe technique,viscometry and TEM.In dilute salt-free solutions P(AEBA) behaves as ...     

Molecular dynamics and NMR studies of proteins in ionic solutions

The molecular dynamics of water and selected ions was studied in concentrated electrolyte solutions with, or without, proteins added. Our experimental results by multinuclear spin relaxation techniques were then compared with molecular dynamics computations for water and ions in concentrated electrolyte solutions. The mechanisms for the anionic and cationic interactions with myofibrillar proteins in aqueous solutions were investigated by nuclear magnetic resonance over a wide range of salt concentrations. The multinuclear spin relaxation data were analyzed with a thermodynamic linkage model of hydrated ion clusters of various sizes and composition. Protein amide groups were found to bind to anions with strengths in the order of the lyotropic series.