Activity Coefficient Of Counterions Research Articles

Ion size effect on counterion condensation around a spherical colloidal particle in a salt-free medium containing only counterions

A theory of counterion condensation around a spherical colloidal particle in a salt-free medium containing only counterions developed by Imai and Oosawa as reported by Busseiron Kenkyu 52:42, 1952 ibid. 59:99, 1953) and later by Ohshima (J Colloid Interface Sci 247:18, 2002) is extended to incorporate the ion size effect on the basis of the modified Poisson-Boltzmann equation using the Carnahan-Starling activity coefficient of counterions. The potential distribution depends on the particle surface charge, the particle volume fraction, and the average counterion volume fraction. It is shown that for a dilute particle suspension, the counterion condensation occurs, leading to a decrease in the particle surface potential when the following two conditions are both satisfied: (i) the scaled particle surface charge is greater than the logarithm of the inverse of the particle volume fraction and (ii) the average counterion volume fraction is much smaller than the particle volume fraction.

Effect of hydrotrope on the electrochemical behavior of Dowex-50 membrane in aqueous solution of uni–univalent electrolyte

Membrane potential and membrane conductance measurements have been carried out using Dowex-50Kynar membrane, sodium chloride and urea as a hydrotrope, mixture of varying composition to examine the hydrotrope effect on electrochemical character of the membrane. A significant change on membrane electrochemical character is observed in the presence of hydrotrope due to changed co-ion exclusion. The Donnan equilibrium has been incorporated to estimate the activity coefficient of counter ion, ypm, and solute, y±m in the membrane phase along with the parameter, so called Ф expressing non-ideality. Solute rejection performance of the membrane is examined when electrolyte concentration remains constant and hydrotrope concentration varies and vice-versa. In both cases, membrane specific conductance depends on NaCl and hydrotrope concentrations differently. Friction caused through the membrane by the variation in concentration of hydrotrope is greater than friction caused by the variation in concentration of NaCl. Zeta potential is sensitive to the variation of hydrotrope concentration but insensitive to the variation of electrolyte concentration. The membrane system shows the behavior of NF membrane because Pe≪1 is estimated in both cases.

Self-diffusion and activity coefficients of ions in charged disordered media

Self-diffusion and single ion activity coefficients of ions of size symmetric electrolytes were studied in the presence of a collection of charged obstacles (called matrix) within a "soft" version of the primitive model of electrolyte solutions. The matrix subsystem possesses a net charge, depending on the concentration and charge of obstacles. The brownian dynamics method was used to calculate the self-diffusion coefficients of mobile species. The replica Ornstein-Zernike theory for the partly quenched systems was used to calculate the individual activity coefficients of mobile ionic species. The results reflect the competition between attractive (obstacle-counterion, co-ion-counterion), and repulsive (obstacle-co-ion) interactions in these model systems. For the simplest possible system of symmetric monovalent ions the latter effect wins: Co-ions are excluded from the area around obstacles, and this slows down their diffusion compared to that of counterions. Introduction of divalent charges into the system changes this result when the concentration of obstacles is low. We compare these results to those obtained for the corresponding fully annealed systems, i.e., where all the species are mobile. In most cases the self-diffusion and activity coefficients of counterions and co-ions in the presence of charged obstacles follow the trends of the fully annealed solution, which are dictated by the composition of the mixture. In few situations, however, the presence of charged obstacles modifies these trends. Our study allows us to clearly identify the effects due to obstacles, and to separate them from those arising from the composition of the solution. In the case of charge and size symmetric systems, the results for the individual activity coefficients fully support the hypothesis of the "electrostatic excluded volume". Thermodynamic and dynamic results are consistent in explaining the behavior of the systems studied.

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, ypM, and solute, y±M in the membrane phase along with the parameter, so called ϕ 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, Kds and Kdf. It has been found that membrane surface charge density σs 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 (fij) of Spiegler's frictional pore model. In our case, an fwm<fsm<fsw-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±MCM⋅δ)≫2. A slightly higher value of solute rejection is found in Membrane-2.

Osmotic Properties of Aqueous Ionene Solutions

Osmotic coefficients of aqueous solutions of 3,3-, 4,5-, 6,6-, and 6,9-ionenes with bromide and chloride counterions were measured at 298 K and in the concentration range from 0.001 to 0.1 mol/dm 3 . The measured osmotic coefficients are very low, indicating large deviations from ideality caused by strong interactions in these systems. The solutions with chloride counterions have a higher osmotic coefficient than the corresponding bromide solutions, which is in agreement with experimental data for the counterion activity coefficient of these solutions. The experimental results for osmotic coefficients were analyzed using a cylindrical cell model where a fixed charge is assumed to be uniformly distributed along the z-axis of a rigid and impenetrable polyion, in conjunction with the classical Poisson-Boltzmann equation. More refined models in which discrete charges are located periodically along the z-axis of the polyion were also studied. In the latter case the canonical Monte Carlo method was used to calculate the osmotic coefficient. In agreement with previous studies of weak and moderately charged polyelectrolytes, we found the theoretically predicted osmotic coefficients to be too high in comparison with the experimental data for aqueous ionene solutions.

Conductance and Counterion Activity of Ionene Solutions

The conductance and counterion activity of aliphatic ionenes with counterions of F - , Cl - , Br - , I - , and NO 3 - in both the absence and presence of salts were measured and compared with Manning's equations for both cases. Samples used were 3,3-, 4,5-, 6,6-, and 6,9-ionenes, where the numbers are those of methylene groups between the quaternized nitrogen atoms. The activity coefficients of counterions for ionenes in the absence of salts were lower than the theoretical values, and experimentally determined values of the charge density parameters, higher than the theoretical ones, could explain the departure between the experimental and the theoretical values at least semiquantitatively. The conductance of ionenes in the presence of salts deviated from the additivity rules, dependent on charge density of the ionenes as well as the counterions used. It also deviated from the theoretical prediction in which the interaction between small ions was taken into account. On the other hand, the additivity holds approximately for the counterion activity irrespective ofthe species ofionenes and counterions, in marked contrast to the case of conductivity. The viscosity of the ionene solution exhibited a strong dependence on the salts added. The effect of salts on the viscosity was more prominent in the samples with higher charge density parameter, corresponding to larger conformational change in the polyion. These results may give useful information on the conformation of ionenes in solution as well as the mechanism of the electrical conductivity of polyelectrolytes.

(4- O-Methyl- α- d-glucurono)- d-xylan from Rudbeckia fulgida, var. sullivantii (Boynton et Beadle)

From the medicinal plant Rudbeckia fulgida, var. sullivantii (Boynton et Beadle) a low-molecular-mass (4- O-methyl- α- d-glucurono)- d-xylan was isolated by alkaline extraction, followed by ethanol precipitation, ion-exchange chromatography, and gel filtration. The results of compositional and linkage analyses, supported by those of 1H and 13C NMR measurements of oligomers generated on partial acid hydrolysis, showed the (1→4)-linked β- d-xylopyranosyl backbone with about 18% of 4- O-methyl- d-glucuronic acid attached to O-2 of the xylose residues. From the mean distance of adjacent carboxyl groups, obtained from experimentally determined single-ion activity coefficients of calcium counterions, it followed that the uronic acid units are separated and distributed regularly along the xylan chain, i.e. approximately each sixth d-xylose unit bears a 4- O-methyl- d-glucuronic acid residue.

Colligative properties of polyelectrolyte solutions

The solution properties of polyelectrolytes are not well understood despite increasing theoretical and experimental effort, particularly during the last 10 years. Some of the current models for polyelectrolyte solutions are valid only at infinite dilution because they account only for long-range interactions. Nagvekar and Danner [M. Nagvekar, R.P. Danner, An Excess Gibbs Free Energy Model for Polyelectrolyte Solutions, Fluid Phase Equilibria 53 (1989) 219.] have developed an excess Gibbs free energy model for polyelectrolyte solutions. The key feature of the model is to express the excess Gibbs free energy as the sum of the contributions from long-range and short-range interactions. The `limiting laws' of Manning [G.S. Manning, Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions. I. Colligative Properties, J. Chem. Phys. 51 (1969a) 924; G.S. Manning, Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions. II. Self-diffusion of Small Ions, J. Chem. Phys. 51 (1969b) 934.] were used to account for the long-range interactions while a local composition model of the Non-Random Two Liquid (NRTL) type was used for short-range interactions. In this work, we present the expressions for counterion activity coefficients and the motic coefficients in polyelectrolyte solutions with and without added salts at finite concentrations. Data for a number of polyelectrolyte systems with univalent and divalent counterions are analyzed using Nagvekar's proposed model. In the low concentration regime, the osmotic coefficient data are practically independent of concentration, and are in reasonable agreement with the Manning model. With increasing polyelectrolyte concentration, the osmotic coefficient data are a strong function of concentration, and the local composition model is shown to successfully represent the data.

Relationship between protonation and ion condensation for branched poly(ethylenimine)

The chloride ion activity, pH and conductance of an aqueous solution of branched poly(ethylenimine) (BPEI) were measured as a function of polymer concentration C p and degree of protonation α or degree of neutralization β. BPEI is a highly branched polyelectrolyte and has ionizable groups mainly on the main chain. The conductometric titration curve shows a sharp increase before complete protonation, and its starting point, β c, depends on C p and does not coincide with the equivalent point determined by potentiometric titration. The chloride ion activity coefficient is very low and decreases with β, but it has a minimum point at about 0.6–0.8, roughly corresponding to β c. The sharp conductance increase, in the region of β < 1, is explained in terms of the weakness of the bases in the higly branched spherical polyion. The low values of the counterion activity coefficient is explained in terms of the two-phase model of spherical polyelectrolytes.

Limiting-laws of polyelectrolyte solutions. Ionic distribution in mixed-valency counterions systems. I: The model

An extension of the counterion-condensation (CC) theory of linear polyelectrolytes has been developed for the case of a system containing a mixture of counterions of different valency, i and j. The main assumption in the derivation of the model is that the relative amount of the condensed counterions of the type i and j is strongly correlated and it is determined by the overall physical bounds of the system. The results predicted by the model are consistent, in the limiting cases of single species component, with those of the original CC theory. The most striking results are obtained for the cases of low charge density and excess of counterion species: in particular, an apparent positive “binding” cooperativity of divalent ions is revealed for small, increasing additions of M 2+ ions to a solution containing a swamping amount of monovalent salt and a polyelectrolyte of low charge density. Apparent “competitive binding” of mono- and divalent ions derives as a bare consequence of the electrostatic interactions. Theoretical calculations of experimentally accessible quantities, namely single-(counter) ion activity coefficients, confirm the surprising predictions at low charge density, which qualitatively agree with the measured quantities.

Electrostatic effects in dilute solutions containing charged colloidal entities

The Donnan osmotic pressure of a solution containing charged colloidal entities is divided into electrostatic and non-electrostatic contributions. The expression adopted for the former contribution is obtained from a general thermodynamic treatment of the diffuse double layer. Expressions are derived which allow for specific binding and which also provide a definition of amounts bound electrostatically. When the approximation is made that the electrostatic binding of indifferent coions Γcoions is negligible the equations which result have the same form as those that apply to non-interacting uncharged systems and can be handled in the same way. The treatment provides a basis for a successful but somewhat arbitrary approach developed previously. In particular an expression for the activity coefficient of unbound counterions and coions is justified. The prediction (based on the application of the Poisson—Boltzmann equation to cell models) that Γcoions is negative is contradicted by work concerning the significance of single ionic chemical potentials.

Using Oligomeric Surfactants To Improve Oil Recovery

Summary Oligomeric surfactants are a unique class of surfactants that differ from conventional surfactants in their molecular structures. The hydrophilic portion of conventional surfactant molecules is usually smaller than their hydrophobic portion. For oligomeric surfactants, however, several polar and ionic functional groups, distributed along a hydrocarbon chain, form the hydrophilic part of the molecule. In addition, the hydrophilic part has a size comparable with or greater than the hydrophobic counterpart. A number of surfactant/alcohol/oil/brine systems were investigated to evaluate the efficacy of oligomeric surfactants as cosurfactants in surfactant formulations. When used at a concentration of about 110 of the active surfactants, the resultant formulation exhibited higher solubilization capacity, lower interfacial tension (IFT), somewhat higher optimal salinity, higher salt tolerance, higher viscosity, and lower adsorption loss. These benefits may improve the economics of the surfactant flooding process and broaden its application range. The mechanisms by which oligomeric surfactants affect the properties of surfactant formulations were investigated. Surface tension and potentiometric measurements showed that they formed mixed micelles with other surfactants and that they bound with divalent cations. These interactions lowered the activity coefficients of surfactants and counter-ions, thereby increasing the salt tolerance of the surfactant formulation while lowering the adsorption of surfactants on rock surfaces. Oligomeric surfactants may also be used at low concentrations to improve waterflood performance in oil-wet reservoirs. Oil recovery in preferentially oil-wet Berea cores was significantly increased by use of a low-concentration surfactant slug. The higher oil recovery resulted from alteration of the rock wettability.

A new model of counterion condensation in polyelectrolyte solutions: III. Theoretical predictions of competitive condensation between counterions of different valences

Our model has been extended for theoretical estimation of competitive condensation of counterions of different valences onto polyelectrolytes in solution. The estimations are compared with those obtained from Manning theory and with experimental data on counterion activity coefficients. The agreement with the data for sodium polystyrenesulfonate/MgCl 2, CaCl 2 is satisfactory.

A New Model of Counterion Condensation in Polyelectrolyte Solutions I. Comparison with Other Condensation Theories and Experimental Data on Counterion Activity Coefficients

A new model of counterion condensation (Intermediate Model, IMM) is proposed as a modification of our corrected previous model (CPM). The theoretical predictions of IMM and CPM for the degree of condensation, θ, and the counterion activity coefficient, γ, are compared with those of Manning and Iwasa et al. It is found that γ’s in the absence of added salts estimated by IMM and CPM for infinitely long polyions are hardly dependent on the polymer concentration, Cp, while those for polyions with finite length increase with decreasing Cp. It is the latter that is experimentally observed. This fact indicates that polymer models, in which end effects are considered, should be employed to treat dependence of the condensation phenomena on the ionic strength.

The cell model for polyelectrolytes with added salt

Using a comparison theorem from the theory of elliptic equations, we obtain rigorous bounds for the exact solution to the Poisson–Boltzmann equation for the cylindrical cell model, and error bounds for approximations to the exact solution. We present a method for obtaining perturbative solutions, formally to any order, from the exact solution to the salt-free case, and we obtain an explicit solution for the potential correct to the first order. We derive formulas for thermodynamic quantities and compare them with experimental values. We find that the predicted counterion activity coefficients agree well with experimental results; however, agreement of the predicted coion activity coefficient with experiment is only qualitative. We rigorously show that as the concentration of excess salt tends to zero, and as the polyion’s radius becomes very small in comparison to the cell’s radius, the coion activity coefficient given by the Poisson–Boltzmann equation approaches 16/13 for polyion charge densities above a critical value; for subcritical charge densities the limiting value depends on the charge density and lies between 1 and 16/13.

Sodium and calcium counterion activity in the presence of xanthan polysaccharide

This work concerns the activity coefficient determination for sodium and calcium ions in a semi-dilute solution of xanthan when they are mixed in various ratios, and their correlation with the conformational structures. From these values we show that the conformation can be related to the dissociation of the polymer carboxylic acid sites. Below an apparent dissociation coefficient of about 0.29, the conformation is ordered and above 0.55 the xanthan conformation is entirely disordered. The value of the counterion activity coefficient in pure solution of sodium or calcium xanthan salts agrees fairly well with the theoretical ones derived from Manning's and Lifson-Katchalsky's theories if we make the assumption that the Na form is a stretched coil and the Ca form a single fivefold helix.

The molal osmotic coefficients and counterion activity coefficients of arabate with various counterions.

The interaction of arabic acid with counterions was studied by measuring the molal osmotic coefficients and counterion activity coefficients. The molal osmotic coefficients, φ, of various salt solutions were measured with a vapor pressure osmometer. In the monovalent salts, the φ value slightly decreased with decreasing hydration radii of counterions, but in divalent salts, the φ value was similar to each other and was about a half of those of monovalent salts. The counterion activity coefficients, γ+, for Na and/or Ca arabate with or without added salts were determined by measuring electromotive force with cation-selective electrodes. In the absence of added salts, γ+ was slightly larger than φ. In the presence of added salts, the additivity rule held very well for Na and Ca arabate solutions. In such a system with two kinds of counterions, Na and Ca, coexisting in arabate solution, Ca ion was preferentially adsorbed onto the polyions and consequently Na ion was less subject to the influence of the polyion. These results suggest that the interaction of arabic acid with counterions is due to the electrostatic free force alone, and not by any other specific force, and further suggest that Manning's theory for cylindrical polyelectrolytes seems to be applicable to the case of a branched polysaccharide, arabate, if the intercharge distance, b, can be assumed to be a parameter reflecting a spatial intercharge distance.

Counter-ion activity in a cationic polyelectrolyte solution

The counterion transport properties, represented by the chloride ion activity coefficient in cationic polyelectrolyte solutions were studied. The effect of polymer concentration and ionic strength of the media in non-dilute regime were examined. The relative counterion activity coefficient (γ/γ0) decreased with a decrease in ionic strength, but remained unchanged with polymer concentrations. Chloride ions bound per monomer of polymer (n) were estimated from the activity coefficient. The bound ion (n) decreased with decreases in ionic strength and increases in polymer concentration. This phenomenon demonstrates the effect of intermolecular interactions in polyelectrolytes on the charge shielding process of polyions.

Structural study of the solutions of acidic polysaccharides

A study was made of the effect of NaCl on the counterion activity coefficient in solutions of acidic polysaccharide sodium salts. The counterion activity coefficient in the sodium salt solutions of polyuronic acids was shown to be determined by electrostatic interactions only. Consequently it can be supposed that the counterion-polyion interaction is also of an electrostatic nature.

Interactions in clay suspensions: The distribution of ions in suspension and the influence of tactoid formation

Mean ionic activity and anion exclusion data based on membrane equilibria are reported for a series of alkali- and alkaline earth-forms of montmorillonite. Mean ionic activity coefficients can be described rather well by a simple additivity principle, from which counterion activity coefficients are estimated. These latter varied in a regular fashion from 0.1 for Li-form suspensions to as low as 0.01 for the Ca-form. The trend of low counterion activity coefficients for the more strongly preferred ions is reflected as well in the calculated anion exclusion volumes. The results are discussed in terms of the formation of clay tactoids which can be observed in such suspensions. It is demonstrated that tactoid formation model can describe the ionic distributions in suspension for the cases where diffuse double layer theory for single clay plates is inappropriate.