Surface tension of general electrolyte solutions

A simple analytic expression is derived for the surface tension of a solution of general electrolytes including symmetrical and unsymmetrical electrolytes. Following the theory of Levin and Flores-Mena (Europhys Lett (2001) 56:187), we have introduced an ion-free layer of thickness just below the Gibbs dividing surface at the air/electrolyte solution interface. We use the linearized Poisson-Boltzmann equations for the mean potential and for the local fluctuation potential around an ion in the electrolyte solution, together with the Laplace equation for these potentials in the ion-free layer. It is found that the contribution of the mean potential as well as the tangential Maxwell stress along the interface vanishes for low potentials. Experimental data by Matubayasi et al (J Colloid Interf Sci (1999) 209:398, ibid (1999) 209:403, ibid (2001) 243:444) are analyzed with the present theory in order to estimate the values of for several electrolytes.     

Towards a modellisation of the solvation energy in multi-component solvents. The interesting case of a charged solute imbedded in a polymer-containing electrolyte solution

In this paper we propose a mean-field theory to calculate the solvation free energy of a charged solute imbedded in a complex multi-component solvent. We considered a solvent made up of a mixture of small (electrolyte solution) and large (polymer) components. The presence of macromolecules ensures reduced mixing entropy among the different solvent components, an effect due to polymer connectivity. The reduced entropy favours strong preferential distribution of a particular solvent even in the presence of weak preferential solute–solvent interactions. In addition, two energy terms must be considered: (a) the interaction between the solute electrostatic potential and the electrolyte solution and (b) the formation of a polymer–solute interface. Because of the different dielectric permittivity of the solvent components, the electrolyte and polymer distribution functions are strongly coupled: ions, indeed, are more solvated in regions of higher local dielectric permittivity arising from the inhomogeneous mixing of solvent and polymer. We combined together the different energy terms in the framework of the de Gennes free energy functional for polymer solutions along with a generalised Poisson–Boltzmann equation developed for inhomogeneous dielectric media. Moreover, the preferential electrolyte solvation in regions of greater polarity was considered by an extension of the Born equation. Setting the polymer dielectric permittivity smaller than the solvent one and making null the specific polymer–solute interactions, we calculated enhanced electrolyte concentration and reduced polymer concentration near the solute surface on raising the solute surface charge density. The theory shows also the breakdown of the widely used separation between electrostatic and surface tension-dependent contributions to solvation energy when non-ideal mixed solvents are considered. In fact, according to the model, the surface tension of such mixed solvents strongly depends on the solute surface charge density: at high potentials the interfacial tension may increase rather than decrease on raising the polymer volume fraction. The theoretical results have been compared with experimental data on polymer+electrolyte solution surface tension and with solubility data of colloidal particles. The comparison evidences the complex behaviour of multi-component solvents going well beyond the trivial weighted average of the dielectric permittivity and surface tension of the isolated chemical components. Deviations from the simple behaviour predicted by an average picture of multi-component solvents could be understood by developing more sophisticated, but still simple, approaches like that proposed in this paper.Contribution to the Jacopo Tomasi Honorary Issue. This paper is dedicated to Jacopo Tomasi. I learned much of the difficult art of transforming complex problems into simple models after reading his early works on solvation energy.     

Simulating Coadsorption of Surface Active Anions and Organic Molecules Capable of Forming Two-Dimensional Condensed Layers on the Electrode

Within the framework of the Alekseev–Popov–Kolotyrkin model combined with a set of Frumkin isotherms, the adsorption of adamantanol (AdOH) molecules is studied in the presence of a surface-inactive electrolyte and chloride ions at the Hg/H₂O interface. The position of points at the beginning and in the end of an equilibrium two-dimensional phase transition is shown to be determined by the equality of (a) surface tension and (b) calculated electrode potentials. With these conditions fulfilled in the phase-transition region, the model of two parallel capacitors with a common diffuse layer (in the AdOH + NaF system) transforms into the classical model of two parallel capacitors with two independent diffuse layers. Taking into account the lateral interaction between adsorbed chloride anions and AdOH molecules makes no difference to the two-dimensional phase transition potential at fixed adsorption parameters. The effect of the diffuse layer on the position of two-dimensional phase transition potentials is analyzed.     

A discussion on ion conductivity at cation exchange membrane/solution interface

By Gouy–Chapman–Stern–Grahame (CGSG) model, the electric double layer at ion exchange membrane/solution interface consists of two parts: the Stern layer and the diffusion layer. The ions in Stern layer are compacted and considered to be immobile. The relation of diffusion layer mean conductivity K with outer Stern layer potential φ₀, the boundary potential φ_δ and the electrolyte concentration C₀ is educed for symmetric electrolyte system. The results show that K is higher than that of the bulk solution and is greatly influenced by φ₀, φ_δ and C₀.The examination of PE01 cation exchange membrane/solution interface resistance R_e measured by ac impedance technique, shows that R_e value decreases quickly as the KCl electrolyte concentration rises. The effect of electrolyte concentration on the resistance of EDL can be explained by the electrical interactions between ions and charged groups of the membrane. Since the membrane/solution interface resistance is much higher than that of bulk solution, therefore, a further analysis based on the theory developed in this study proves that the ion transfer resistance R_e of membrane–solution interface predominantly occurs at Stern layer as a result of static electrical interaction.     

The Hofmeister series effect in adsorption of cationic surfactants--theoretical description and experimental results

Interfacial properties of cationic surfactants show strong dependence on the type of surfactant counterion or on the type of anion of a salt added to the surfactant solution. In the paper, the models of ionic surfactant adsorption that can take into account ionic specific effects are reviewed. Model of ionic surfactant adsorption based on the assumption that the surfactant ions and counterions undergo nonequivalent adsorption within the Stern layer was selected to describe experimental surface tension isotherms of aqueous solutions of a number of cationic surfactants. The experimental isotherms for: n-alkyl trimethylammonium cationic surfactants, namely: C(16)TABr (CTABr or CTAB), C(16)TACl, C(16)TAHSO(4), C(10)TABr and C(12)TABr as well as decyl- and dodecylpyridinium salts with and without various electrolyte anions as Cl(-), Br(-), F(-), I(-), NO(3)(-), ClO(4)(-) and CH(3)COO(-) were described in terms of the model and a good agreement between the theory and experiment was obtained for a wide range of surfactants and added electrolyte concentrations. A very pronounced Hofmeister effect in dependence of surface tension of cationic surfactants on the type of anion was found. Analysing this dependence in terms of the proposed model of ionic surfactant adsorption, strong correlation between "anion surface activity" (the model parameter accounting for ion penetration into the Stern layer), and the ion polarizability was obtained. That suggests that the mechanism related to the dispersive interaction of polarized ion with electric field at interface is responsible for Hofmeister series effects in surface activity of cationic surfactants. The same mechanism was proposed recently to explain the dependence of surface tension increase with electrolyte concentration on anion and cation type.     

Surface tension and adsorption of electrolytes at the aqueous solution-gas interface

The surface tension of aqueous solutions of hydrogen, sodium, and potassium chlorides was measured. The excess adsorption isotherms for electrolyte adsorption at the liquid-gas interface were obtained. The dependence of the surface tension on the solute concentration exhibits an extremal character, with the onset surface-inactivity of electrolytes being observed at concentrations above 0.3 M. The composition of the surface layer was demonstrated to be governed by the energy of solvation, while the extrema in the surface tension and excess adsorption isotherms are associated with the behavior of individual ions in the adsorption layer of the interphase interface.     

Structure of nonpolarizable water/nitrobenzene interface: potential distribution, ion adsorption, and interfacial tension

Adsorption of hydrophobic and hydrophilic ions at the nonpolarizable interface between two immiscible electrolyte solutions was investigated. The results were analyzed in three different models: (i) Gouy-Chapman model, (ii) ions as hard spheres, and (iii) ion pair formation at the interface. In the Gouy-Chapman model, an analytical expression for the interfacial tension was obtained. It predicts that interfacial tension should be proportional to the square root of the electrolyte concentration, which does not agree with experimental data. Modeling ions as hard spheres only slightly improves the agreement. The third model of interfacial ion pairing as the main origin of adsorption was analyzed using the amphiphilic isotherm (Markin-Volkov isotherm). A good agreement between ion-pairing theory and experimental values was achieved. The MV isotherm takes into account the limited number of adsorption sites, final size of molecules, complex formation at the interface, and interaction between adsorbed particles. The analysis revealed repulsion between adsorbed tetraalkylammonium ions at the nitrobenzene/water interface and demonstrated linear dependence between adsorption site area and the size of a molecule.     

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

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

Molecular dynamics simulations of electrolyte solutions at the (100) goethite surface

Molecular dynamics simulations of electrolyte solutions in contact with a neutral (100) goethite (alpha-FeOOH) surface were used to probe the structure of the mineral-water interface and gain insight into the adsorption properties of monovalent ions. Three electrolyte solutions were considered: NaCl, CsCl, and CsF. The electrolyte ions were chosen to cover a range of ionic sizes and affinities for the aqueous phase. The molecular dynamics simulations indicate the presence of a structured interfacial region resulting from the strong interaction of water with the mineral surface. The specific arrangement and preferred orientation of water that arise from this interaction create adsorption sites in the interfacial region, i.e., as far as 15 A away from the surface, and hence give rise to a strong correlation between the water and ion distributions. The structure of the hydrated ion, its effect on the water arrangement at the interface, and the strength of the ion-water bond are found to be key factors that determine the location and extent of ion adsorption at the interface. Additionally, in all simulations, we find a build up of positive charges near the surface due to cation adsorption, which is compensated by an accumulation of anions in the next few angstr?ms. This creates an excess of negative charges, which is in turn compensated by an excess of positive charges, and so on. As we modeled a neutral surface, the structure of the electrolyte distribution arises from the complex interplay of the interactions between the surface, water, and the electrolyte ions rather than from the need to neutralize a surface charge. In addition, our simulations indicate that the electrolyte distribution does not resemble that of a classical electrical double layer. Indeed, our calculations predict the presence of several condensed layers and oscillations in the net charge away from the surface.     

Adsorption and Micellization in Solutions of Dodecylpyridinium Bromide–Nonionic Surfactant Mixtures

Dependences of the surface tension of aqueous solutions of cationic (dodecylpyridinium bromide) and nonionic (Tween 80, Triton X-100) surfactants and their mixtures on total surfactant concentration and solution composition were studied. The values of critical micellization concentration (CMC) and excess free energy of adsorption were determined from tensiometric measurements. Based on Rubingh–Rosen model (approximation of the theory of regular solutions), the compositions of micelles and adsorption layers at the solution–air interface as well as parameters of interaction between the molecules of cationic and nonionic surfactants were calculated for the systems indicated above. It was established that, in the case of surfactant mixtures with considerable difference in the CMCs, the micelles of individual surfactant with lower CMC value are formed. The effect of negative deviation from the ideality during the adsorption of surfactants from mixed solutions at the solution–air interface was disclosed. It was shown that the interaction energy depends significantly on the composition of mixed systems.     

The conditions governing the specific adsorption of counter-ions in the interaction of two parallel plate-like colloidal particles

Frens and Overbeek have proposed that during the Brownian collision of two colloidal particles in a hydrophobic sol, the surface charge density due to potential-determining (p.d.) ions remains virtually unchanged. It is argued here that the cause of this behaviour is the low concentration of p.d. ions in the diffuse layer. However, equilibrium can be maintained with respect to counter-ions adsorbed into the Stern region from the supporting electrolyte, because the concentration of such electrolyte in the dispersion medium is considerably greater than that of p.d. ions.A general expression is quoted from earlier work for the electric double layer interaction between two parallel plate-like particles in the case where surface charge due to p.d. ions is fixed, but where counter-ions adsorbed into the Stern region can equilibrate with ions of the same species in the diffuse layer. Incorporating discreteness-of-charge and ion-size effects into the adsorption isotherm of the counter-ions, the double layer interaction energy of the two plates is calculated at contact of the two outer Helmholtz planes (o.h.p.'s). It is shown that although this energy exceeds the classical expression obtained by assuming the potential at the o.h.p. to be independent of plate separation, it remains finite.     

Surface Activity of sp-Metals in Molten Intermetallic Compounds

The dependence of the surface-layer composition of a molten binary intermetallic compound (IMC) on factors determining electrochemical properties of liquid electrodes in indifferent electrolytes is studied. The segregation of the binary melt components at the interface with vacuum is considered in terms of physical materials technology. The interface state of the molten IMC is described by the Landau–Ginzburg functional for a surface excess of the Gibbs free energy. An examination of the functional shows that a minimum energy at a given temperature and system volume is reached by depositing the component with the lowest surface tension at the plain component's mp on the melt surface. The deposit has the character of a mesophase; therefore, it remains liquid at temperatures much lower than the plain component's mp in the bulk phase. The dilation interactions between atoms near the interface, caused by different atomic volumes of components, favor the deposition of the metal with a higher atomic volume. The calculated change of the surface tension of Ga–Tl IMC as related to plain Ga is close to relevant experimental value obtained on neutral Ga and Ga–Tl electrodes in an indifferent electrolyte.     

Surface tension of electrolytes: hydrophilic and hydrophobic ions near an interface

We calculate the ion distributions around an interface in fluid mixtures of highly polar and less polar fluids (water and oil) for two and three ion species. We take into account the solvation and image interactions between ions and solvent. We show that hydrophilic and hydrophobic ions tend to undergo a microphase separation at an interface, giving rise to an enlarged electric double layer. We also derive a general expression for the surface tension of electrolyte systems, which contains a negative electrostatic contribution proportional to the square root of the bulk salt density. The amplitude of this square-root term is small for hydrophilic ion pairs but is much increased for hydrophilic and hydrophobic ion pairs. For three ion species, including hydrophilic and hydrophobic ions, we calculate the ion distributions to explain those obtained by x-ray reflectivity measurements.     

Phase equilibria and surface tension of pure fluids using a molecular layer structure theory (MLST) model

This paper presents a new model based on thermodynamic and molecular interaction between molecules to describe the vapour–liquid phase equilibria and surface tension of pure component. The model assumes that the bulk fluid can be characterised as set of parallel layers. Because of this molecular structure, we coin the model as the molecular layer structure theory (MLST). Each layer has two energetic components. One is the interaction energy of one molecule of that layer with all surrounding layers. The other component is the intra-layer Helmholtz free energy, which accounts for the internal energy and the entropy of that layer. The equilibrium between two separating phases is derived from the minimum of the grand potential, and the surface tension is calculated as the excess of the Helmholtz energy of the system. We test this model with a number of components, argon, krypton, ethane, n-butane, iso-butane, ethylene and sulphur hexafluoride, and the results are very satisfactory.     

Contact angles in thin liquid films : III. Interaction forces in Newton black soap films

The interaction parameters of Newton black soap films stabilized by NaDS, as derived from contact angle experiments, have been interpretated in terms of the structure and the interaction forces in the films. From the film thickness and the difference between the surface excess of the salt in the film and at the bulk surface it is concluded that (a) the diffuse double-layer overlap in the film is practically complete; (b) the film only contains absorbed DS⁻ ions and an equal amount of Na⁺ counterions, but no salt; and (c) the double layer at the bulk surface is still partly diffuse. A model for the structure of the NB films is proposed according to which the adsorbed DS⁻ ions with their counterions form a two-dimensional square lattice at each film surface. It is found that the interaction free energy of the NB films can be explained by taking into account the electrostatic interactions between the discrete ions in the two opposing surface lattices. The model of the NB film is qualitatively in agreement with the experimental results of other workers.     

Transient natural convection induced by electrodeposition of Li+ ions onto a lithium metal vertical cathode in propylene carbonate

Transient natural convection caused by Li⁺ electrodeposition at constant current along a vertical Li metal cathode immersed in a 0.5 M LiClO₄–PC (propylene carbonate) electrolyte was compared with that by Cu²⁺ ion electrodeposition in aqueous CuSO₄ solution. The concentration profile of the Li⁺ ions was measured in situ by holographic interferometry. The interference fringes start to shift with time at a higher current density. The concentration boundary layer thickness for Li⁺ ions was successfully determined. With the progress of electrodeposition, the density difference between the electrolyte at the cathode surface and the bulk electrolyte increased to induce upward natural convection of the electrolyte. The electrolyte velocity was measured by monitoring the movement of tracer particles. The measured transient behavior of the ionic mass and momentum transfer rates normalized with respect to the steady-state value was numerically analyzed. Transient natural convection along a vertical cathode due to Li metal electrodeposition can be reasonably explained by boundary layer theory, similar to the case of Cu electrodeposition in aqueous CuSO₄ solution.     

Electrolyte effect on mixed micelle and interfacial properties of binary mixtures of cationic and nonionic surfactants

In the present work, the adsorption behavior at the liquid-air interface and micellization characteristics of mixtures of cetyltrimethylammonium bromide (CTAB) and p-(1,1,3,3-tetramethylbutyl) polyoxyethylene (TritonX-100) in aqueous media containing different concentrations of NaBr were investigated by surface tension and potentiometry measurements. From plots of surface tension (gamma) as a function of solution composition and total surfactant concentration, we determined the critical micelle concentration (CMC), minimum surface tension at the CMC (gamma(CMC)), surface excess (Gamma(max)), and mean molecular surface area (A(min)). On the basis of regular solution theory, the compositions of the adsorbed film (Z) and micelles (X(M)) were estimated, and then the interaction parameters in the micelles (beta(M)) and in the adsorbed film phase (beta(sigma)) were calculated. For all mole fraction ratios, the results showed synergistically enhanced ability to form mixed micelles as well as surface tension reduction. Furthermore beta was calculated by considering nonrandom mixing and head group size effects. It was observed that, for both the planar air/aqueous interface and micellar systems, the nonideality decreased as the amount of electrolyte in the aqueous medium was increased. This was attributed to a decrease of the surface charge density caused by increasing the concentration of bromide ions.     

Isotopic Exchange and Oxygen Diffusion in the La0.88Sr0.12Ga0.82Mg0.18O3 – α–Molecular Oxygen System

The oxygen isotopic exchange kinetics in La_0.88Sr_0.12Ga_0.82Mg_0.18O_{3 –} and in the same electrolyte whose surface layer is enriched with cobalt ions is studied. Rates of different types of exchange and oxygen isotope diffusion coefficients in oxide are determined at 970–1200 K and oxygen pressures of 400–1200 Pa. The activation energy for the interphase oxygen exchange and the order of heteroexchange vs. oxygen pressure relationship are determined. The presence of cobalt ions in the near-surface layer alters the surface exchange parameters, such as the oxygen heteroexchange rate (which increases), order of the heteroexchange vs. oxygen pressure relationship, and the ratio between rates of different exchange types. The oxygen isotope diffusion coefficients coincide in both electrolytes but differ from those calculated from the electroconductivity data with the Nernst–Einstein equation.     

The enthalpy and entropy interaction parameters of cesium chloride with saccharides ( -glucose, -fructose and sucrose) in water at 298.15 K

The transfer enthalpies have been measured for cesium chloride from pure water to aqueous saccharides ( -glucose, -fructose and sucrose) solutions at 298.15 K. The McMillan–Mayer theory was employed to relate the excess thermodynamic function with a series of interaction parameters of solutes to obtain the enthalpy pair interaction parameters of cesium chloride with saccharides in water. Entropy interaction parameters can be evaluated through the enthalpy interaction parameters and the Gibbs free energy parameters. These parameters are discussed in detail to provide some information for the interaction of solute–solute and solute–solvent in CsCl–saccharide–water ternary system, and to investigate the influence of the size of metal ions and the number of hydroxyl in saccharides on these parameters.