Solvation equilibria in very concentrated electrolyte solutions

A stepwise hydration-equilibrium model for aqueous electrolytes is developed and shown to give a good quantitative account of osmotic coefficients of strong, highly soluble electrolytes up to concentrations of 20–30 m. The main parameters needed are two equilibrium constants describing the stepwise hydration and the number of hydration sites. Choice of ion-size parameter has only a minor effect.This paper was presented at the symposium, The Physical Chemistry of Aqueous Systems, held at the University of Pittsburgh, Pittsburgh, Pennsylvania, June 12–14, 1972, in honor of the 70th birthday of Professor H. S. Frank.Contribution from the Diffusion Research Unit, Research School of Physical Sciences, Australian National University, Canberra, A.C.T., Australia and the University of New England, Armidale, N. S. W., Australia.     

Transference numbers of sodium chloride in concentrated aqueous solutions and chloride conductances in several concentrated electrolyte solutions

Stable chlorine electrodes with low bias potentials have been developed by introducing 25% Ir+75% Pt electrodes and an improved gas line. With their use in cells with transference, cation constituent transference numbers have been measured at 25°C in NaCl solutions from 1.7 to 6 modal. These results agree well with four other sets of data in the literature but disagree with two further sets based on emf determinations with Ag/AgCl electrodes. A table of best NaCl transference numbers is proposed. The conductances of the chloride ion-constituent in concentrated NaCl, KCl, and HCl solutions are compared.     

Surface tension of aqueous electrolyte solutions. Thermodynamics

A thermodynamic theory is developed for obtaining the enthalpic and entropic contributions to the surface excess Gibbs energy of electrolyte solutions from the dependence of the surface tension on concentration and temperature. For elaboration, accurate activity coefficients in solution as functions of concentration and temperature are required. The theory is elaborated for (1-1) electrolytes and applied to HClO(4), HNO(3), NaCl, NaBr, and LiCl, of which the first two adsorb positively and the other three negatively. One of the conspicuous outcomes is that in all cases, the surface excess entropies slightly decrease with electrolyte activity but remain close to that of pure water, whereas the enthalpy is different from that. The implication is that the driving force for positive or negative adsorption must have an enthalpic origin. This finding can be useful in developing and evaluating theoretical models for the interpretation of surface tensions of electrolyte solutions.     

Hydration forces between mica surfaces in electrolyte solutions

The forces between two molecularly smooth mica surfaces were measured over a range of concentrations in aqueous Li⁺, Na⁺, K⁺ and Cs⁺ chloride solutions. Deviations from DLVO forces in the form of additional short-range repulsive “Hydration” forces were observed only above some critical bulk concentration, which was different for each electrolyte. These observations are interpreted in terms of the corresponding ion exchange properties at the mica surface. “hydration” forces apparently arise when hydrated cations adsorbed on mica are prevented from desorbing as two interacting surfaces approach. dehydration of the cations leads to a repulsive hydration force. A simple site-binding model was successfully applied to describe the charging behavior of interacting mica surfaces . By subtraction of the DLVO-regulation theory from the total measured force the net hydration force was obtained for mica surfaces apparently fully covered with adsorbed cations. The magnitude of this extra force followed the series Na⁺ > Li⁺ > K⁺ > Cs⁺ and, in each case, could be described by a double-exponential decay.     

Calculation of electrostatic interaction forces between ellipsoidal particles

An analytical expression is presented for describing the electrostatic interaction forces between various shaped particles having mutual orientations. The expression is derived by applying the surface integration method, which is a generalization of the Derjaguin summation procedure. Based on previous theoretical considerations it is possible to calculate the electrostatic interaction force between regularly shaped bodies (both convex or concave in the vicinity of their contact point) by multiplying the interaction energy derived for paralled plates with the corresponding geometric factor. The forces acting between two equal shaped ellipsoids are described and discussed, considering three different limiting orientations, the parallel, the perpendicular, and the contact of the edges' orientation.     

Numerical values of individual activity coefficients of single-ion species in concentrated aqueous electrolyte solutions and the attempt of a qualitative interpretation on a model of electrostatic interaction

Individual activity coefficients of single-ion species can be achieved by the factorizing of a new concentration function for the mean activity coefficient to the required power applying a purely mathematical method. These single-ion activity coefficients, calculated in this manner, are listed for some aqueous strong electrolytes. The reasons for the magnitude and variation of the activity coefficients as a function of the concentration are, without a doubt, of complex nature. Activity coefficients have their meaning as practical values. In relation to the analytical concentration, the individual activity coefficients represent the macroscopic effectiveness of the single-ion species in solution an easy manner. However, with increasing deviations from Debye–Hückel conditions of an infinitely diluted electrolyte solution, a physically correct interpretation of the macroscopically visible activity coefficient is becoming more and more difficult, if not impossible to find. On the basis of a model of electrostatic interaction, an attempt has been made to create a qualitative interpretation of the individual ion activity coefficients in concentrated aqueous electrolyte solutions which were calculated applying the purely mathematical method by Ferse.     

The ionic product of water in highly concentrated aqueous electrolyte solutions

Summary The ionic product of water, , has been determined in aqueous NaCl (0.5–5.0M), KCl (3.0M), NaNO₃ (3.0 and 5.0M), and KNO₃ (2.5M) at 25 °C from high-precision potentiometric titrations carried out in cells with liquid junction using either glass or hydrogen electrodes. Measurements ofK _w provide a set of self-consistent data that can be used in the estimation of activity coefficient changes and liquid junction potentials in the study of extremely concentrated electrolyte solutions. Where comparison is possible, results obtained by hydrogen electrode measurements are in excellent agreement (ca ± 0.005 inpK _w) with other reliable experimental values and the predictions of thePitzer activity-coefficient model. The glass electrode results are, as expected, routinely lower (by 0.03–0.05pK _w units), owing to interference by Na⁺ ions. This effect virtually disappears in solutions of potassium salts. Comparison of the experimental results with thePitzer predictions shows that knowledge of the ternary interaction parameters is essential to account for specific ionic effects in the concentration dependence ofpK _w.On leave from the Abteilung für Physikalische Chemie und Theoretische Hüttenkunde, Montanuniversität Leoben, A-8700 Leoben, Austria     

Analytical theories of transport in concentrated electrolyte solutions from the MSA

Ion transport coefficients in electrolyte solutions (e.g., diffusion coefficients or electric conductivity) have been a subject of extensive studies for a long time. Whereas in the pioneering works of Debye, Hückel, and Onsager the ions were entirely characterized by their charge, recent theories allow specific effects of the ions (such as the ion size dependence or the pair association) to be obtained, both from simulation and from analytical theories. Such an approach, based on a combination of dynamic theories (Smoluchowski equation and mode-coupling theory) and of the mean spherical approximation (MSA) for the equilibrium pair correlation, is presented here. The various predicted equilibrium (osmotic pressure and activity coefficients) and transport coefficients (mutual diffusion, electric conductivity, self-diffusion, and transport numbers) are in good agreement with the experimental values up to high concentrations (1-2 mol L(-1)). Simple analytical expressions are obtained, and for practical use, the formula are given explicitly. We discuss the validity of such an approach which is nothing but a coarse-graining procedure.     

Suppression of dendritic lithium formation by using concentrated electrolyte solutions

This study examined the electrochemical deposition and dissolution of lithium on nickel electrodes in a propylene carbonate (PC) electrolyte containing different LiN(SO₂C₂F₅)₂ concentrations. The electrolyte concentration was found to have a significant effect on the reactions occurring at the electrode. The poor cycleability of the electrodes in the low-concentration solutions was improved considerably by increasing the electrolyte concentration. Transmission electron microscopy (TEM) revealed that a high-concentration solution produces a thinner solid electrolyte interphase (SEI) on the electrodeposited lithium than a low-concentration solution, e.g., ∼35 nm in 1.28 mol kg⁻¹ vs. ∼20 nm in 3.27 mol kg⁻¹ solutions. Raman spectroscopy showed that the solvation number of lithium ions differed according to the electrolyte concentration. This suggests that the structure of solvated lithium ions is an important factor in suppressing dendritic lithium formation.     

Repulsive interface forces in overlapping electric double layers in electrolyte solutions

The historical development of the problem of the electric interaction of particles in electrolyte solutions is comprehensively discussed. The existing approaches are divided into force-based methods, where the mechanical (ponderomotive) forces of the electric field are directly calculated, and energy-based methods calculating the free energy of the colloid system (at least the part of the free energy which is determined by the repulsive forces of electrical nature). The fundamental works of Langmuir, Derjaguin, Levine, Verwey and Overbeek are discussed in detail. At the same time, new original methods are proposed: the method of effective displacements; the formula of free energy of overlapping double layers.Special attention is paid to the analysis of electrostriction forces in liquids, particularly in electric double layers. The non-contradictory application of the concepts of classic macroelectrostatics is shown to result in the need to take into account electrostriction forces in overlapping double layers. The main formulas are given for force and energy of repulsion in flat surfaces with a constant density of the electric charge on them. These formulas are derived with electrostriction forces taken into account. A number of the theoretical results are new.Some experiments are discussed in measuring repulsive forces in colloid systems. A qualitative agreement is established between the experimental results of Ottewill et al. and the theory of electrostriction forces in double layers.     

Variations of activity coefficients in concentrated electrolyte solutions at constant lonic strength

Measurements of different types on various (trace) electrolytes in HClO₄–Na(Li)ClO₄ solutions at several (constant) values of the ionic strength have been used to determine the variation of their activity coefficients with changing amount of perchloric acid in the solution. These variations (with respect to the hydrogen ion) differ considerably among different cations and anions. The results for the alkali metal ions and the anions are interpreted in the light of the recent work of Pitzer on short-range ionic interactions. The results for the cations with outerd-electrons and the alkaline earth metal ions are interpreted in terms of ion-solvent interactions. It is concluded that the use of HClO₄–NaClO₄ solutions of high ionic strength (rather than the use of HClO₄–LiClO₄ solutions) is advisable in studies where the variation in activity coefficients must be accounted for. Finally, it is shown that the usual interpretation of the influence of the salt medium in studies of complex equilibria and reaction kinetics is sometimes questionable.     

Heat capacities of concentrated multicomponent aqueous electrolyte solutions at various temperatures

The specific heat capacities of the aqueous multicomponent system NaCl +KCl+MgCl₂+CaCl₂ with ionic strength between 8.3 and 9.6 (resembling Dead Sea waters) were measured between 15°C and 45°C. The obtained data were fitted to an empirical equation as a function of concentration and temperature. The thermodynamic functions of the studied multicomponent system were found to be strongly influenced by changes in MgCl₂ concentrations. The application of Young's rule to such concentrated systems was checked at 25°C. The calculated (by Young's rule) specific heat capacitiesC _p and apparent molar heat capacities C_p, of these multicomponent electrolyte solutions were in reasonable agreement with the measured values (–0.008 J-g^–1-K^–1 and –2.6 J-mol^–1-K^–1, respectively).     

Numerical analysis of thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions

Thermophoresis of colloidal particles in aqueous media is more frequently applied in biomedical analysis with processed fluids as biofluids. In this work, a numerical analysis of the thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions is presented. In a particle-fixed reference frame, the flow field of non-Newtonian fluids has been governed by the Cauchy momentum equation and the continuity equation, with the dynamic viscosity following the power-law fluid model. The numerical simulations reveal that the shear-thinning effect of pseudoplastic fluids is advantageous to the thermophoresis, and the shear-thickening effect of dilatant fluids slows down the thermophoresis. Both the shear-thinning and shear-thickening effects of non-Newtonian fluids on a thermodiffusion coefficient are pronounced for the case when the thickness of electric double layer (EDL) surrounding a particle is moderate or thin. Finally, the reciprocal of the dynamic velocity at the particle surface is calculated to approximately estimate the thermophoretic behavior of a charged particle with moderate or thin EDL thickness.     

Protonation and sodium ion-pairing of the sulfite ion in concentrated aqueous electrolyte solutions

A protocol has been developed for the reliable titration of aqueous sulfite solutions which minimizes photodecomposition effects. This procedure has been used to measure the protonation constants of the sulfite ion in aqueous solution by glass electrode potentiometry at 25.0‡C and ionic strengths (I) from 0.1 to 5.0M in NaCI media and atI = 1.0M in KC1 and Me₄NCl media. These measurements provided evidence of weak but significant ionpairing between SO2/3 -and Na⁺ with a formation constant of logK _Na = 0.431 in 1.0M Me₄NCl. This was in very good agreement with the value logK _Na = 0.410 measured directly by Na⁺ ion-selective electrode potentiometry. Evidence is also presented for an extremely weak association of K⁺ and SO ₂ ³ -with logK _k = 0.22 in 1.0M Me₄NCl.     

Sedimentation of concentrated monodisperse colloidal suspensions: role of collective particle interaction forces

The sedimentation velocities and concentration profiles of low-charge, monodisperse hydroxylate latex particle suspensions were investigated experimentally as a function of the particle concentration to study the effects of the collective particle interactions on suspension stability. We used the Kossel diffraction technique to measure the particle concentration profile and sedimentation rate. We conducted the sedimentation experiments using three different particle sizes. Collective hydrodynamic interactions dominate the particle-particle interactions at particle concentrations up to 6.5 vol%. However, at higher particle concentrations, additional collective particle-particle interactions resulting from the self-depletion attraction cause particle aggregation inside the suspension. The collective particle-particle interaction forces play a much more important role when relatively small particles (500 nm in diameter or less) are used. We developed a theoretical model based on the statistical particle dynamics simulation method to examine the role of the collective particle interactions in concentrated suspensions in the colloidal microstructure formation and sedimentation rates. The theoretical results agree with the experimentally-measured values of the settling velocities and concentration profiles.     

Modification of the Falkenhagen equation to fit conductimetric data for concentrated electrolyte solutions

A modification of the Falkenhagen equation is proposed, which fits correctly data of 29 different 1:1 aqueous electrolyte solutions up to very high concentrations. The concept of activity is used to account for deviations from ideality appearing at higher concentrations. A discussion about trends in the value of the ‘distance of closest approach between two ions’, a, and novel conductivity data for several concentrated electrolyte solutions estimated by the proposed model are also provided.