Estimation of activity coefficients at different temperatures by using the mean spherical approximation

A method of estimating activity coefficients for a variety of electrolytes at different temperatures is presented. The MSA approximation is used to calculate the activity coefficients from experimental data available in the literature. This strategy provides suitable results within a wide range of temperatures, electrolyte stoichiometries and concentrations of investigated solutions.     

Relaxation effect on the Onsager coefficients of mixed strong electrolytes in the mean spherical approximation

The Fuoss-Onsager continuity equations are solved by using the equilibrium pair distribution functions of the mean spherical approximation in the case of equal diameters. An analytical expression is obtained for the relaxation effect on the Onsager coefficients of mixed strong electrolytes. This work also extends the existing expressions for the conductivity of binary and ternary electrolytes to any number of ions.     

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.     

Phase coexistence in polydisperse charged hard-sphere fluids: mean spherical approximation

Taking advantage of the availability of the analytic solution of the mean spherical approximation for a mixture of charged hard spheres with an arbitrary number of components we show that the polydisperse fluid mixture of charged hard spheres belongs to the class of truncatable free energy models, i.e., to those systems where the thermodynamic properties can be represented by a finite number of (generalized) moments of the distribution function that characterizes the mixture. Thus, the formally infinitely many equations that determine the parameters of the two coexisting phases can be mapped onto a system of coupled nonlinear equations in these moments. We present the formalism and demonstrate the power of this approach for two systems; we calculate the full phase diagram in terms of cloud and shadow curves as well as binodals and discuss the distribution functions of the coexisting daughter phases and their charge distributions.     

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).     

Analytic solution of the mean spherical approximation for a multi-component plasma

The mean spherical approximation for a mixture of charged hard spheres in a uniform neutralizing background is solved analytically. The factor correlation functions and the excess thermodynamic properties are explicitly expressed through a single parameter, which can be obtained by solving an algebraic equation.     

Isopiestic determination of osmotic coefficients and evaluation of vapor pressures for electrolyte solutions of some lithium salts in ethanol

The osmotic coefficients of lithium chloride, lithium bromide and lithium nitrate in ethanol have been measured by the isopiestic method at the temperature 298 K. Sodium iodide served as isopiestic standard for the calculation of osmotic coefficients. The molality range covered in this study correspond to about 0.1–2 mol kg⁻¹. The system of equations developed by Chen, Haghtalab–Vera and Pitzer were used to fit each set of osmotic coefficients. The parameters from the fit were used to calculate the vapor pressures. The osmotic coefficient data are successfully correlated with these models, and the models provide reliable predictions of vapor pressures.     

On the mean spherical approximation for the Lennard–Jones fluid

Subtle details on the mean spherical approximation (MSA) theory for the Lennard–Jones potential [Fluid Phase Equilib. 134 (1997) 21] are presented. In order to enhance the appreciation of the theory, the accuracy of the mapping method and the contact approximation used in the theory are demonstrated by comparing with the exact results at certain extreme conditions. Technical derivation of internal energy of the MSA is also fully displayed. In addition, the typographic errors appeared in [Fluid Phase Equilib. 134 (1997) 21] are also corrected in this work.     

Toward making the mean spherical approximation of primitive model electrolytes analytic: an analytic approximation of the MSA screening parameter

The mean spherical approximation (MSA) for the primitive model of electrolytes provides reasonable estimates of thermodynamic quantities such as the excess chemical potential and screening length. It is especially widely used because of its explicit formulas so that numerically solving equations is minimized. As originally formulated, the MSA screening parameter Γ (akin to the reciprocal of the Debye screening length) does not have an explicit analytic formula; an equation for Γ must be solved numerically. Here, an analytic approximation for Γ is presented whose relative error is generally ?10(-5). If more accuracy is desired, one step of an iterative procedure (which also produces an explicit formula for Γ) is shown to give relative errors within machine precision in many cases. Even when ion diameter ratios are ～10 and ion valences are ～10, the relative error for the analytic approximation is still ?10(-3) and for the single iterative substitution it is ?10(-9).     

The osmotic and activity coefficients of some guanidinium salts at 298.15 K

Osmotic and activity coefficients are reported for aqueous solutions of six guanidinium salts at (298.15 ± 0.01) K, and these coefficients are compared with those of other uni-univalent electrolytes. The results are consistent with previously reported spectral results that indicated hydrogen bonding of guanidinium ion with chloride ion in aqueous solutions.     

Phase coexistence in a polydisperse charged hard-sphere fluid: polymer mean spherical approximation

We have reconsidered the phase behavior of a polydisperse mixture of charged hard spheres (CHSs) introducing the concept of minimal size neutral clusters. We thus take into account ionic association effects observed in charged systems close to the phase boundary where the properties of the system are dominated by the presence of neutral clusters while the amount of free ions or charged clusters is negligible. With this concept we clearly pass beyond the simple level of the mean spherical approximation (MSA) that we have presented in our recent study of a polydisperse mixture of CHS [Yu. V. Kalyuzhnyi, G. Kahl, and P. T. Cummings, J. Chem. Phys. 120, 10133 (2004)]. Restricting ourselves to a 1:1 and possibly size-asymmetric model we treat the resulting polydisperse mixture of neutral, polar dimers within the framework of the polymer MSA, i.e., a concept that--similar as the MSA--readily can be generalized from the case of a mixture with a finite number of components to the polydisperse case: again, the model belongs to the class of truncatable free-energy models so that we can map the formally infinitely many coexistence equations onto a finite set of coupled, nonlinear equations in the generalized moments of the distribution function that characterizes the system. This allows us to determine the full phase diagram (in terms of binodals as well as cloud and shadow curves), we can study fractionation effects on the level of the distribution functions of the coexisting daughter phases, and we propose estimates on how the location of the critical point might vary in a polydisperse mixture with an increasing size asymmetry and polydispersity.     

Field induced anisotropy of charged magnetic colloids: a rescaled mean spherical approximation study

The liquidlike structure of colloidal suspensions with both electrostatic and magnetic interactions is investigated by means of small angle x-ray scattering (SAXS) dependent on an external magnetic field. For weak magnetic interactions, without external field, the magnetic dipoles are randomly oriented. Under this condition, isotropic structures are observed. In an external field, however, the magnetic momenta arrange parallel to the external field and induce anisotropic liquidlike structures. For weak magnetic interactions, the structure factor can be described within the framework of the rescaled mean spherical approximation. Due to the high experimental accuracy of synchrotron SAXS, from the anisotropic distortion of liquidlike structures, interparticle forces smaller than 10(-15) N can easily be detected.     

Equation of state for aqueous electrolyte systems based on the semirestricted non-primitive mean spherical approximation

The semirestricted non-primitive mean spherical approximation (npmsa) is used in combination with the PC-SAFT equation of state to model completely dissociating aqueous alkali halide systems. The salts are described using ion-specific parameters from tables and correlations. Upon analyzing aqueous electrolyte systems at infinite dilution of the salt it was concluded that for the arithmetic mean ion diameter of anion and cation, the semirestricted npmsa contribution gives no reliable results. Therefore, this parameter is adjusted in this work. The model was applied to aqueous alkali halide systems up to the solubility limit at T = 298.15 K. Mean ionic activity coefficients and osmotic coefficients were correlated with good results. The model was subsequently applied to temperatures up to T = 373.15 K and compared to liquid densities and to system pressures up to the solubility limit of the salts in water. The agreement between experimental data and the proposed equation of state is satisfactory for the liquid densities and excellent in case of the system pressures.     

Two-parameter debye-hückel approximation for the evaluation of mean activity coefficients of 109 electrolytes

Among the published formulae for the calculation of mean activity coefficients, the most trustworthy and comprehensive are those recently recommended by the National Bureau of Standards. In many applications, the ionic strength does not exceed ca. 1 M, and the NBS functions can then be approximated by a two-parameter Debye-Hückel model. The limits of applicability (e.g., 1% deviation from the corresponding NBS model) are listed. The procedure makes efficient use of calculator memory.