Binding Mean Spherical Approximation Research Articles

Description of electrolytes at high temperatures within the binding mean spherical approximation (BiMSA)

In this work, the binding mean spherical approximation (BiMSA) theory is used to describe osmotic and activities coefficients for electrolytes solutions up to high temperatures. Four salts are analysed: NaCl, LiCl, MgCl2 and CaCl2, in the temperature range of 25∘C to 300∘C and molalities from 0.05 to 6 molal. A good representation of experimental data is obtained for all salts and temperatures considered by introducing temperature-dependent cation size and permittivity in a suitable way. The proportion of ion pairs (that are formed at sufficiently high temperature in these solutions) for each salt is predicted from the theory, showing a pronounced increase for temperatures above 100∘C. A good agreement is found between the values of optimised and experimental association constants given in the literature.

Association in electrolyte solution: Implementing inner sphere ion pairing into the mean spherical approximation

In many electrolyte solutions, ions of opposite signs can be paired due to electrostatic or more specific interactions. The pairing may occur in competition with the individual solvation of the ions. Some of the solvent molecules, initially present around each of the ions, may be excluded between pairing ions. The resulting complexes can be seen as dumbbells with a strong overlap between the spheres representing each of the hydrated ions involved in the association. The thermodynamic description of electrolyte solutions containing such pairing ions is described in this paper with a variational generalisation of the binding mean spherical approximation.

Mean ionic activity coefficient of associative electrolyte solutions: A comparison study

The performance of four implicit solvent models for associative and two models for non-associative electrolyte solutions has been compared and analyzed for the mean ionic activity coefficient (MIAC) of electrolytes in the solution. Two of these models for associative electrolyte solutions are based on a chemical approach (Fisher-Levin-Guillot-Guissani (FLGG) and Ebeling-Grigo (EG)), and one of them is based on the reference cavity approximation (Zhou-Yeh-Stell (ZYS)). The last one is based on the thermodynamic perturbation theory (Binding mean spherical approximation, BiMSA). Models without ion-pairing also consist of hard sphere (HS) contribution in addition to the electrostatic contribution from the Debye-Hückel (HS + DH) and the mean spherical approximation (HS + MSA) theories. To this aim, the models’ predictions are compared with the numerical solution of the Poisson-Boltzmann equation, the Monte Carlo simulations, and the experimental data. We have shown that considering the ion pairing results in a better agreement of the predicted MIAC against both simulations and experimental data of 2:2 electrolytes. We have also adjusted the ionic diameter and the distance between ion pairs to the MIAC experimental data and validated the estimated fractions of free ions with the electrical conductivity measurements. We have shown that the FLGG model captures the physics of the system more accurately compared to other models.

Semi-clathrate hydrate phase equilibria of carbon dioxide in presence of tetra-n-butyl-ammonium chloride (TBAC): Experimental measurements and thermodynamic modeling

The promotion effect of TBAC on the dissociation condition of the studied system is determined under the present experimental data. A combination of the van der Waals–Platteeuw solid solution theory, binding mean spherical approximation electrolyte model and modified Peng–Robinson equation of state is used for calculation of the hydrate, aqueous solution and gaseous phases properties, respectively. The results are also compared with the experimental data for other salts such as tetra-n-butyl-ammonium bromide (TBAB) and tetra-hydro furan (THF). A good agreement between the model predictions and experimental data is found with an absolute average relative deviation of 13.1%.

110th Anniversary: Theory of Activity Coefficients for Lithium Salts in Aqueous and Nonaqueous Solvents and in Solvent Mixtures

On the basis of work by Bernard and Blum [Bernard, O.; Blum, L. Binding Mean Spherical Approximation for Pairing Ions: An Exponential Approximation and Thermodynamics. J. Chem. Phys. 1996, 104, 474...

Association of counterions on polyelectrolytes: Thermodynamic properties in the binding mean spherical approximation

We present a model for polyelectrolyte solutions within the binding mean spherical approximation. An approach developed previously, to describe polyelectrolytic chain solutions and on the other hand to describe the association of counterions on spherical polyions is generalized, considering both the polyelectrolytic chain formation and the association of counterions on the chains. Thermodynamic properties deduced from this model are presented. The associative part of the Helmholtz energy is deduced from the thermodynamic perturbation theory. Analytic expressions for the electrostatic contributions to the internal and Helmholtz energies are established.

Organic electrolyte solutions: Modeling of deviations from ideality within the binding mean spherical approximation

Deviations from ideality in organic electrolyte solutions are described within the Binding Mean Spherical Approximation (BiMSA) theory, in which ions are regarded as charged hard spheres and unlike ions may associate to form an ion pair. Association is modeled within the Wertheim theory (as done in SAFT-type models). The model includes a mass action law with a thermodynamic association constant. The literature about the thermodynamic properties of this type of solution is reviewed. Besides, it is attempted to gain some insight into the solvation of ions by computing their Stokes hydrodynamic diameters from conductivity experiments, and by employing an original analysis introduced by Fawcett. The BiMSA model is used to represent the osmotic coefficient of 1-1 electrolytes in pure methanol, ethanol, 2-propanol, acetone and acetonitrile. The optimized cation sizes in the solvents are compared with their hydrodynamic diameters. The regressed association constants are compared with literature values derived from conductivity and vapor pressure experiments.

An Evaluation of Four Electrolyte Models for the Prediction of Thermodynamic Properties of Aqueous Electrolyte Solutions

In this work, the performance of four electrolyte models for prediction the osmotic and activity coefficients of different aqueous salt solutions at 298 K, atmospheric pressure and in a wide range of concentrations are evaluated. In two of these models, (electrolyte Non-Random Two-Liquid e-NRTL and Mean Spherical Approximation-Non-Random Two-Liquid MSA-NRTL), association between ions of opposite charges for simplification purposes is ignored and in the other two ones, (Associative Mean Spherical Approximation-Non-Random Two-Liquid AMSA-NRTL and Binding Mean Spherical Approximation BiMSA) association and solvation effects are considered. The predictions of these four models for the osmotic and activity coefficients of electrolyte solutions at 298 K and atmospheric pressure are compared with the experimental data reported in the literature. This comparison includes, 28 different aqueous salt solutions including thio-cyanates, perchlorates, nitrates, hydroxides, quaternary ammonium salts and others. The results show, the performance of models that consider association effects are better than others especially for higher salt concentrations. However, the best performance belongs to BiMSA model which has some parameters with physical meaning.

Thermodynamic properties of ring polyelectrolytes in the binding mean spherical approximation

Abstract A simple model for charged ring polyelectrolyte is proposed, to describe their thermodynamic properties. Starting from an analytical expressions previously obtained for charged chains within the binding mean spherical approximation, we present a method to determine suitable modifications in order to describe charged rings. It is shown that the electrostatic excess thermodynamic properties can still be computed from relatively simple formulas which involve a screening parameter ΓB.

Theoretical and experimental study of phase equilibrium of semi-clathrate hydrates of methane + tetra-n-butyl-ammonium bromide aqueous solution

In this study, the phase stability conditions of semi-clathrate hydrate of methane + tetra-n-butyl-ammonium bromide (TBAB) + water system is investigated. New experimental data on the hydrate–liquid–vapor equilibrium conditions of this system is measured. The measured data is for the pressure range of 2.88–14.1 MPa, temperature range of 285.6–295.9 K and TBAB mass fractions of 0.05, 0.15 and 0.3. A thermodynamic model is also developed to predict the phase stability conditions of hydrate for this system. In the developed model, the phase equilibrium of the hydrate of pure TBAB in water is predicted based on the Gibbs free energy minimization technique. This model is then combined with the statistical thermodynamic model of van der Waals–Platteeuw (vdW–P) to predict the phase stability conditions of semi-clathrate hydrate of methane with TBAB in aqueous solution. Binding mean spherical approximation (BiMSA) electrolyte model is used for aqueous phase properties prediction and modified Peng–Robinson equation of state (PR-EoS) is used for calculation of the gaseous phase properties. The results show that the developed model satisfactorily predicts the experimental data with Average Absolute Relative Deviation (AARD) of 12%. Moreover, the model is able to predict the different types of pure TBAB semi-clathrate hydrates and also the inhibition and promotion effects of this salt. The results also show that considering the association effect in the electrolyte model, can improve the predictions of the developed thermodynamic model for hydrate phase equilibrium of methane in the presence of TBAB aqueous solution.

Aqueous solutions of ionic liquids. Description of osmotic coefficients within the Binding Mean Spherical Approximation

The Binding Mean Spherical Approximation (BiMSA) is used to describe osmotic coefficients of aqueous solutions of salts containing imidazolium cations and bulky anions over the whole concentration range at temperature in the range (25 to 60)°C. A total of 13 salts have been considered altogether. The ion diameters, the permittivity of solution and the association constant were taken as adjustable parameters. Ionic liquids are described as being weakly associated in water, and association constants values obtained within the BiMSA model are in good agreement with those from the literature. Diameter values were assigned to 1-alkyl-3-methylimidazolium cations. The adjusted values obtained for the cation diameters increased with the number of carbons on the alkyl chain. For all systems studied, average relative deviations were found to be satisfactory.

Multiply associating electrolytes in the binding mean spherical approximation: thermodynamic properties and speciation.

Ionic solutions exhibiting multiple association are described within the binding mean spherical approximation (BiMSA). This model is based on the Wertheim formalism, in the framework of the primitive model at the McMillan-Mayer level. The cation and the anion form the various complexes according to stepwise complexation-equilibria. Analytic expressions for the Helmholtz energy, the internal energy, the speciation, and for the osmotic and activity coefficients are given considering a binary solution with an arbitrary number of association sites on one type of ion (polyion) and one site on the ions of opposite sign (counterions). As an alternative, mean field expressions, as developed in SAFT-type theories, are also presented. The result obtained from the latter approximate method exhibits a reasonable agreement with those from BiMSA for the speciation, and a remarkable one for the osmotic coefficient.

Speciation in aqueous solutions of nitric acid

In this study, speciation in aqueous solutions of nitric acid at 25 °C was assessed in two independent ways. First, Raman experiments were carried out and interpreted in terms of free nitrate ions, ion pairs and neutral HNO(3) molecules. In parallel, a model was developed to account for the formation of these two kinds of pairs. It was based on an extension of the binding mean spherical approximation (BiMSA), or associative MSA (AMSA), in which the size and the charge of the ions in the chemical pair may differ from those of the free ions. A simultaneous fit of the osmotic coefficient and of the proportion of free ions (obtained from Raman spectroscopy experiments) led to an estimation of the speciation in nitric acid solutions. The result obtained using this procedure was compared with the estimation obtained from the Raman experiments.

Solutions of Alkylammonium and Bulky Anions: Description of Osmotic Coefficients within the Binding Mean Spherical Approximation

The binding mean spherical approximation (BiMSA) is used to describe osmotic coefficients for aqueous solutions of salts containing alkylammonium cations or bulky anions. A total of 35 salt solutions is accurately described at 25 °C over the whole concentration range, up to very high concentrations such as 20 mol·kg–1 for methylammonium chloride or 24 mol·kg–1 for ammonium thiocyanate. The ion diameters, the permittivity of solution, and the association constant are adjustable parameters within the BiMSA model. New diameter values are assigned to alkylammonium cations and bulky anions such as tetrafluoroborate, alkanesulfonates, methylsulfate, trifluoroacetate, or trifluoromethanesulfonate anions. Alkylammonium sizes are in reasonable agreement with literature values. Besides, association constants values obtained within the BiMSA model compare well with literature values when available.

Speciation in Aqueous Solutions of Nitric Acid Estimated Within the Binding mean Spherical Approximation (BiMSA)

This work is aimed at a description of the thermodynamic properties of highly concentrated aqueous solutions of nitric acid salts at 25¡C. The predictive capability of the binding mean spherical approximation (BIMSA) was examined. First, Raman spectroscopy was used to study the proportion of associated nitric acid as a function of concentration. The corresponding apparent association constant values were compared with literature values. Besides, the BIMSA model led to an assessment of the degree of association. The so-calculated amount of associated nitric acid coincides accurately with our Raman experimental results up to a high concentration of acid.

Thermodynamics of Binary and Ternary Solutions of Multivalent Electrolytes with Formation of 1:1 and 1:2 Complexes, within the Mean Spherical Approximation

The mean activity (γ±) and osmotic (Φ) coefficients for binary and ternary aqueous solutions of trivalent electrolytes (mainly made up of lanthanide salts) are described in the framework of the primitive model of ionic solutions, using the binding mean spherical approximation (BiMSA). This model, based on the Wertheim formalism, accounts for (chemical or electrostatic) association of ions. In this work, the multivalent cation and the anion are allowed to form 1:1 (pairs) and 1:2 (trimers) complexes. Expressions for γ± and Φ are given which satisfy the Gibbs−Duhem relation. The model involves concentration-dependent cation size and effective relative permittivity, variations that can be interpreted in terms of solvent effects. The theory is applied to aqueous solutions of binary and ternary mixtures at 25 °C with common anion.

Nitric acid: modeling osmotic coefficients and acid–base dissociation using the BIMSA theory

This work is aimed at a description of the thermodynamic properties of highly concentrated aqueous solutions of nitric acid salts at 25 °C within the binding mean spherical approximation (BIMSA) theory. The predictive capability of this model was examined. First, Raman spectroscopy was used to study the proportion of associated nitric acid as a function of concentration. The corresponding apparent association constant values were compared with literature values. Besides, the BIMSA model, taking into account complex formation, was used to represent literature experimental osmotic coefficient variation with concentration. This theoretical description led to an assessment of the degree of association. The so calculated amount of associated nitric acid coincides accurately with our Raman experimental results up to a high concentration of acid.

Description of the Thermodynamic Properties of Aqueous Ionic Solutions within the Mean Spherical Approximation

The thermodynamic properties of ionic solutions are described within the mean spherical approximation (MSA). The original MSA and binding MSA (BiMSA) have been supplemented so as to include solvation effects. The model is shown to be capable of representing ionic solution thermodynamics in a wide range of concentration, generally up to saturation, in the case of strong and associating electrolytes. It constitutes an interesting alternative to the Pitzer model.

Ionic Association of Hydroperoxide Anion HO2- in the Binding Mean Spherical Approximation. Spectroscopic Study of Hydrogen Peroxide in Concentrated Sodium Hydroxide Solutions

The ultraviolet-visible (UV-vis) spectroscopy of hydrogen peroxide in concentrated sodium hydroxide solutions was studied. The peroxide band in the UV range shifts from approximately 214 nm to approximately 236 nm as the NaOH concentration increases from 0.338 mol dm-3 to 13.1 mol dm-3. The band originates from an intramolecular electronic transition of the hydroperoxide anion HO2-, as indicated by the negligible temperature effect on the band position and confirmed by ab initio quantum mechanical calculations. It is postulated that the bathochromic shift of the peroxide band that accompanies the increase in NaOH concentration originates from the formation of the ion pair (Na+HO2-). The equilibrium constant for the ion association reaction (0.048 mol-1 dm3) and the characteristics of the individual absorption bands of the hydroperoxide anion and its associate with Na+ were determined from the numerical modeling of the absorbance data, using the binding mean spherical approximation (BIMSA).

Experimental and Molecular Dynamics Studies of Dysprosium(III) Salt Solutions for a Better Representation of the Microscopic Features Used within the Binding Mean Spherical Approximation Theory

This work is aimed at a predictive description of the thermodynamic properties of actinide(III) salt solutions at high concentration and 25 degrees C. A new solution of the binding mean spherical approximation (BIMSA) theory, based on the Wertheim formalism, for taking into account 1:1 and also 1:2 complex formation, is used to reproduce, from a simple procedure, experimental osmotic coefficient variation with concentration for three binary salt solutions of the same lanthanide(III) cation: dysprosium(III) perchlorate, nitrate, and chloride. The relevance of the fitted parameters is discussed, and their values are compared with available literature values. UV-vis/near-IR, time-resolved laser-induced fluorescence spectroscopy experiments, and molecular dynamics (MD) calculations were conducted for dilute to concentrated solutions (ca. 3 mol.kg-1) for a study of the microscopic behavior of DyCl3 binary solutions. Coupling MD calculations and extended X-ray absorption fine structure led to the determination of reliable distances. The MD results were used for a discussion of the parameters used in the BIMSA.