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.     

Hofmeister effects in surface tension of aqueous electrolyte solution

The surface tension of electrolyte solutions shows marked specific ion effects. We here show an important role for both ionic solvation energies and ionic dispersion potentials in determining this ion specific surface tension of salt solutions. The ion self-free energy changes when an ion moves from bulk solution into the interfacial region, with its decreasing water density profile. We will show that the solvation energies of different ions correlate very well with the surface tension of salt solutions. Inclusion of this distance-dependent self-free energy contribution brings qualitative agreement with experiments and the right Hofmeister series. This is so not only for surface tension changes but also for measured surface potentials. The inclusion of ionic dispersion interaction potentials further improves the agreement with experiments. We discuss how further progress in the theory of the surface tension of salts can be achieved.     

Electrolysis at the interaface of two immiscible electrolyte solutions and extraction kinetics

The problem of the interfacial step of salt extraction has been solved using the ideas of the kinetics of individual ion transfer across the interface of two immiscible electrolyte solutions (ITIES). A new concept, the extraction potential has been introduced. The values of extraction rate constants for several tetraalkylammonium picrates have been presented.     

Dispersion self-free energies and interaction free energies of finite-sized ions in salt solutions

The role for many-body dipolar (dispersion) potentials in ion-solvent and ion-solvent-interface interactions is explored. Such many-body potentials, accessible in principle from measured dielectric data, are necessary in accounting for Hofmeister specific ion effects. Dispersion self-energy is the quantum electrodynamic analogue of the Born electrostatic self-energy of an ion. We here describe calculations of dispersion self-free energies of four different anions (OH-, Cl-, Br-, and I-) that take finite ion size into account. Three different examples of self-free energy calculations are presented. These are the self-free energy of transfer of an ion to bulk solution, which influences solubility; the dispersion potential acting between one ion and an air-water interface (important for surface tension calculations); and the dispersion potential acting between two ions (relevant to activity coefficient calculations). To illustrate the importance of dispersion self-free energies, we compare the Born and dispersion contributions to the free energy of ion transfer from water to air (oil). We have also calculated the change in interfacial tension with added salt for air (oil)-water interfaces. A new model is used that includes dispersion potentials acting on the ions near the interface, image potentials, and ions of finite size that are allowed to spill over the solution-air interface. It is shown that interfacial free energies require a knowledge of solvent profiles at the interface.     

Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations

We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.     

Interfacial dilational properties of partly hydrolyzed polyacrylamide and gemini surfactant at the decane–water interface

The dilational viscoelastic properties of partly hydrolyzed polyacrylamide (HPAM) and surfactant (C₁₂COONa-p-C₉SO₃Na) in the absence or presence of electrolyte were investigated at the decane–water interface by means of longitudinal method and the interfacial tension relaxation method. The polymer plays different roles in influencing the structure of HPAM–surfactant mix-adsorbed layer at different surfactant concentration. At low surfactant concentration, the addition of polymer could sharply decrease the dilational elasticity mainly due to the weakening of the “entanglement” among long alkyl chains in surfactant molecules, while the addition of the polymer may enhance the dilational elasticity due to the slow diffusivity of the polymer chains at higher surfactant concentration. And the added electrolyte, which results in screening of electrostatic interactions between the ionized groups, generally decreases the interfacial dilational elasticity and increases the dilational viscosity. The data obtained on the relaxation processes via interfacial tension relaxation measurement can explain the results from dilational viscoelasticity measurements very well.     

Concentration dependence of ionic transport in dilute organic electrolyte solutions

Ion transport is studied in dilute organic liquid electrolyte solutions in which close cation-anion interactions are minimized either through steric hindrance imposed by the bulky tetrabutylammonium cation or by strong solvation of alkali metal cations by DMSO or 1-propanol. In these solutions, the molar conductivity does not appear to depend on either the solvent viscosity or the size of the solvated charge carrier in a manner consistent with Walden's rule. The molar conductivities plotted as a function of the solvent dielectric constant from epsilon = 5.48 to 63.5 appear to lie on a smooth curve for a set of 0.0055 M solutions of tetrabutylammonium trifluoromethanesulfonate in a variety of aprotic solvents. The molar conductivity smoothly increases with increasing dielectric constant to a maximum at roughly epsilon = 33 and then decreases with further increase of the dielectric constant. The conductivity appears to depend only on the dielectric constant and not the specific functional group in this broad family of solvents. A similar plot for a series of linear alcohols as solvents also led to a smooth curve, although the values of the molar conductivity were lower than values in the aprotic solvents by almost an order of magnitude at corresponding values of the solvent dielectric constant.     

A study on orientation and absorption spectrum of interfacial molecules by using continuum model

In this work, a numerical procedure based on the continuum model is developed and applied to the solvation energy for ground state and the spectral shift against the position and the orientation of the interfacial molecule. The interface is described as a sharp boundary separating two bulk media. The polarizable continuum model (PCM) allows us to account for both electrostatic and nonelectrostatic solute-solvent interactions when we calculate the solvation energy. In this work we extend PCM to the interfacial system and the information about the position and orientation of the interfacial molecule can be obtained. Based on the developed expression of the electrostatic free energy of a nonequilibrium state, the numerical procedure has been implemented and used to deal with a series of test molecules. The time-dependent density functional theory (TDDFT) associated with PCM is used for the electron structure and the spectroscopy calculations of the test molecules in homogeneous solvents. With the charge distribution of the ground and excited states, the position- and orientation-dependencies of the solvation energy and the spectrum have been investigated for the interfacial systems, taking the electrostatic interaction, the cavitation energy, and the dispersion-repulsion interaction into account. The cavitation energy is paid particular attention, since the interface portion cut off by the occupation of the interfacial molecule contributes an extra part to the stabilization for the interfacial system. The embedding depth, the favorable orientational angle, and the spectral shift for the interfacial molecule have been investigated in detail. From the solvation energy calculations, an explanation has been given on why the interfacial molecule, even if symmetrical in structure, tends to take a tilting manner, rather than perpendicular to the interface.     

Dielectric exclusion of ions from membranes

Dielectric exclusion is caused by the interactions of ions with the bound electric charges induced by ions at interfaces between media of different dielectric constants. It is considered as one of mechanisms of nanofiltration. The transport properties of capillary model are expressed through ion distribution and diffusion coefficients. Due to local equilibrium the distribution coefficient is directly related to the excess solvation energy of ion. First, this energy is considered for single ions in single neutral pores in terms of pore size, ion charge, dielectric constants of solvent and membrane matrix and pore geometry. The dielectric exclusion from pores with closed geometry like circular cylinders is shown to be essentially stronger than that from pores with relatively open geometry like slits. Furthermore, the role of finite membrane porosity is analysed for the model of infinite slabs with alternating dielectric constants. The presence of other ions is accounted for within the scope of a mean-field approach, and the screening of dielectric exclusion is thus introduced and considered in some detail. A fixed electric charge is shown to cause additional screening. At the same time the dielectric exclusion makes the Donnan exclusion of ions stronger. Therefore the interaction between those two rejection mechanisms turns out to be non-trivial. Finally, the effect of solvent molecular structure is considered within the scope of non-local electrostatics. It is shown that the solvent non-locality typically results in somewhat stronger dielectric exclusion, however, its most important effect is slowing down the decline of dielectric exclusion with increasing bulk electrolyte concentration.     

Effect of Na+, Mg2+, and Zn2+ chlorides on the structural and thermodynamic properties of water/n-heptane interfaces

The effect on the structural and thermodynamic properties in water/n-heptane interfaces on addition of NaCl, MgCl(2), and ZnCl(2) has been examined through five independent 100-ns molecular dynamics simulations. Results indicate that the interfacial thickness within the framework of the capillary-wave model decreases on addition of electrolytes in the order Na(+) < Mg(2+) < Zn(2+), whereas the interfacial tension increases in the same order. Ionic density profiles and self-diffusion coefficients are strongly influenced by the strength of the first hydration shell, which varies in the order Na(+) < Mg(2+) < Zn(2+). On the other hand, the Cl(-) behavior, that is, diffusion and solvation sphere, is influenced by its counterion. Accordingly, cations are strongly expelled from the interface, which is especially remarkable for the small divalent cations. This fact alters the water geometry near the interface and in a lesser extent n-heptane order and number of hydrogen bonds per water molecule close to the interface.     

Experimental Study of the Effect of Strong Alkali on Lowering the Interfacial Tension of Oil/Heavy Alkylbenzene Sulfonates System

Experimental studies were conducted to explore the fundamental mechanisms of alkali to lower the interfacial tension of oil/heavy alkylbenzene sulfonates (HABS) system. Sodium hydroxide was used as the strong alkali chemical to investigate the interfacial tension (IFT) of oil/HABS system. The influences of salt and alkali on the interfacial activity were studied by the measurement of interfacial tension and partition coefficient. Moreover, the alkali/surfactant solutions were measured by dynamic laser scattering. The results showed that compared with the salt, the function of alkali to lower the interfacial tension and improve partition coefficient is more significant. The micelles formed by surfactants could be disaggregated because of adding alkali, so the size of micelles decreases and the number of mono‐surfactants increases, then more surfactant molecules move to the interface of oil/surfactant system and the adsorption of surfactants at oil‐water interfaces increases, which can lead to the decrease of IFT.     

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.     

Interface tension of silica hydroxylated nanoparticle with brine: a combined experimental and molecular dynamics study

We have used molecular dynamics simulations to calculate the interfacial tension of hydroxylated SiO(2) nanoparticles under different temperatures and solutions (helium and brine with monovalent and divalent salts). In order to benchmark the atomistic model, quartz SiO(2) interfacial tension was measured based on inverse gas chromatography under He atmosphere. The experimental interfacial tension values for quartz were found between 0.512 and 0.617 N/m. Our calculated results for the interfacial tension of silica nanoparticles within helium atmosphere was 0.676 N/m, which is higher than the value found for the system containing He∕α-quartz (0.478 N/m), but it is similar to the one found for amorphous silica surface. We have also studied the interfacial tension of the nanoparticles in electrolyte aqueous solution for different types and salts concentrations (NaCl, CaCl(2), and MgCl(2)). Our calculations indicate that adsorption properties and salt solutions greatly influence the interfacial tension in an order of CaCl(2) > MgCl(2) > NaCl. This effect is due to the difference in distribution of ions in solution, which modifies the hydration and electrostatic potential of those ions near the nanoparticle.     

Influence of electrolyte on interfacial and rheological properties and shear stability of highly concentrated W/O emulsions

The effect of the electrolyte concentration on the interfacial interactions, rheological properties and emulsion shear stability was investigated. The increase of the electrolyte concentration leads to the growth of storage modulus and the yield stress of emulsions and enhances the emulsion stability to shearing, while interfacial tension decreases. The observed effects were attributed to the interfacial interaction of a surfactant and an electrolyte that was confirmed by the IR-analysis. The interaction between an electrolyte and a surfactant provides a stable interface.     

Association of ionic liquids in solution: a combined dielectric and conductivity study of [bmim][Cl] in water and in acetonitrile

Ion association of the ionic liquid [bmim][Cl] in acetonitrile and in water was studied by dielectric spectroscopy for salt concentrations c ≤ 1.3 M at 298.15 K and by measurement of molar electrical conductivities, Λ, of dilute solutions (c ≤ 0.006 M) in the temperature range 273.15 ? T/K ≤ 313.15. Whilst acetonitrile solutions of [bmim][Cl] exhibit moderate ion pairing, with an association constant of K°(A) ≈ 60 M(-1) and increasing with temperature, [bmim][Cl] is only weakly associated in water (K°(A) ≈ 6 M(-1)) and ion pairing decreases with rising temperature. Only contact ion pairs were detected in both solvents. Standard-state enthalpy, entropy and heat capacity changes of ion association were derived, as well as the activation enthalpy of charge transport and the limiting conductivity of the cation, λ(∞)?([bmim](+)). These data, in conjunction with effective solvation numbers obtained from the dielectric spectra, suggest that the solvation of [bmim](+) is much weaker in water than in acetonitrile.     

Repulsion between oppositely charged macromolecules or particles

The interaction of two oppositely charged surfaces has been investigated using Monte Carlo simulations and approximate analytical methods. When immersed in an aqueous electrolyte containing only monovalent ions, two such surfaces will generally show an attraction at large and intermediate separations. However, if the electrolyte solution contains divalent or multivalent ions, then a repulsion can appear at intermediate separations. The repulsion increases with increasing concentration of the multivalent salt as well as with the valency of the multivalent ion. The addition of a second salt with only monovalent ions magnifies the effect. The repulsion between oppositely charged surfaces is an effect of ion-ion correlations, and it increases with increasing electrostatic coupling and, for example, a lowering of the dielectric permittivity enhances the effect. An apparent charge reversal of the surface neutralized by the multivalent ion is always observed together with a repulsion at large separation, whereas at intermediate separations a repulsion can appear without charge reversal. The effect is hardly observable for a symmetric multivalent salt (e.g., 2:2 or 3:3).     

The effect of salting out and micellization on interfacial tension

We consider a system consisting of oil and water phases with nonionic surfactant distributed between them and present a model for the effect of salt on the interfacial tension. The model accounts for the salting out of surfactant from water to oil and also for the occurrence of micelles in the aqueous phase. In addition, it is shown that salting out affects micellization in interesting ways, e.g. micelles may form as the salt concentration increases even though none are present initially and then disappear at higher concentrations. The effect of chain length and head group size (and hence of HLB) on the interfacial tension is examined for surfactants of the polyoxyethylene type. The calculated interfacial tension decreases continuously and may become negative under certain condition, indicating that the oil-water interface becomes unstable and a microemulsion forms.     

Impurity effects at hydrophobic surfaces

The effective charge of hydrophobic surfaces and in particular of the air–water interface is a crucial parameter for electrochemistry, colloidal chemistry and interfacial science, but different experiments give conflicting estimates. Zeta-potential and disjoining-pressure measurements point to a strongly negative surface charge, often interpreted as being due to adsorbing hydroxide ions. In contrast, surface tension measurements of acids and bases suggest the hydronium ion to be surface active, in agreement with some surface-specific non-linear spectroscopy results. The air–electrolyte interfacial tension exhibits a characteristic minimum at millimolar electrolyte concentration for all salts, the so-called Jones–Ray effect, which points to competitive adsorption mechanisms present in dilute electrolyte solutions. We show that all these puzzling experimental findings can be explained by the presence of trace amounts of surface-active charged impurities, most likely anionic surfactants.