Electrolyte Mean Spherical Approximation

Recent developments of the chemical model of electrolyte solutions permit the extension of the validity range of transport equations up to high concentrations (c 1 mol L"1) and permit the representation of the conductivity maximum Knm in the framework of the mean spherical approximation (MSA) theory with the help of association constant KA and ionic distance parameter a, see Ref. [87] and the literature quoted there in. 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

The long-range electrostatic term is expressed by mean spherical approximations which is a very promising method for describing the thermodynamic properties of electrolyte solutions [192,193] ... 

The concept of mean spherical approximation (MSA, 3) in Chapter 2) has also been used to reproduce the conductivity data of electrolytes of fairly high concentration [23]. The MSA method applies to both associated and non-associated electrolytes and can give the values of association constant, KA. Although not described here,... 

From the various possible closures, the mean spherical approximation (MSA) [189] has found particularly wide attention in phase equilibrium calculations of ionic fluids. The Percus-Yevick (PY) closure is unsatisfactory for long-range potentials [173, 187, 190]. The hypemetted chain approximation (HNC), widely used in electrolyte thermodynamics [168, 173], leads to an increasing instability of the numerical algorithm as the phase boundary is approached [191]. There seems to be no decisive relation between the location of this numerical instability and phase transition lines [192-194]. Attempts were made to extrapolate phase transition lines from results far away, where the HNC is soluble [81, 194]. 

In the mean spherical approximation (MSA) treatment of the ion association in aqueous solutions, the linearity of the relative permittivity and of the hydrated cation diameters with the electrolyte concentration was taken into account and a good fit of the experimental activity and osmotic coefficient was obtained [72-75]. The MSA model was elaborated on the basis of cluster expansion considerations involving the direct correlation function the treatment can deal with the many-body interaction term and with a screening parameter and proved expedient for the interpretation of experimental results concerning inorganic electrolyte solutions [67,75-77]. 

Simonin, J.P., Bernard, O., and Blum, L. Real ionic solutions in the mean spherical approximation 3 osmotic and activity coefficients for associating electrolytes in the primitive model. 7. Phys. Chem.B. 1998, 102,4411 417. 

HOW FAR HAS THE MEAN SPHERICAL APPROXIMATION GONE IN THE DEVELOPMENT OF ESTIMATION OF PROPERTIES FOR ELECTROLYTE SOLUTIONS ... 

The latest models propose to represent electrolyte solutions as a collections of hard spheres of equal size, ions, immersed in a dielectric continuum, the solvent. For such a system, what is called the Mean Spherical Approximation, MSA, has been successful in estimating osmotic and mean activity coefficients for aqueous 1 1 electrolyte solutions, and has provided a reasonable fit to experimental data for dilute solutions of concentrations up to -0.3 mol dm". The advantage in this approach is that only one... 

Another approach to the conductance of electrolytes, which is less complex than that of Lee and Wheaton, is due to Blum and his co-workers. This theory goes back to the original Debye-Hiickel-Onsager concepts, for it does not embrace the ideas of Lee and Wheaton about the detailed structure around the ion. Instead, it uses the concept of mean spherical approximation of statistical mechanics. This is the rather portentous phrase used for a simple idea, which was fully described in Section 3.12. It is easy to see that this is an approximation because in reality an ionic collision with another ion will be softer than the brick-wall sort of idea used in an MSA approach. However, using MSA, the resulting mathematical treatment turns out to be relatively simple. The principal equation from the theory of Blumet al. is correspondingly simple and can be quoted. It runs... 

In addition to the short-range interactions between species in all solutions, long-range electrostatic interactions are found in electrolyte solutions. The deviation from ideal solution behavior caused by these electrostatic forces is usually calculated by some variation of the Debye-Huckel theory or the mean spherical approximation (MSA). These theories do not include terms for the short-range attractive and repulsive forces in the mixtures and are therefore usually combined with activity coefficient models or equations of state in order to describe the properties of electrolyte solutions. 

Abstract Analytical solution of the associative mean spherical approximation (AMSA) and the modified version of the mean spherical approximation - the mass action law (MSA-MAL) approach for ion and ion-dipole models are used to revise the concept of ion association in the theory of electrolyte solutions. In the considered approach in contrast to the traditional one both free and associated ion electrostatic contributions are taken into account and therefore the revised version of ion association concept is correct for weak and strong regimes of ion association. It is shown that AMSA theory is more preferable for the description of thermodynamic properties while the modified version of the MSA-MAL theory is more useful for the description of electrical properties. The capabilities of the developed approaches are illustrated by the description of thermodynamic and transport properties of electrolyte solutions in weakly polar solvents. The proposed theory is applied to explain the anomalous properties of electrical double layer in a low temperature region and for the treatment of the effect of electrolyte on the rate of intramolecular electron transfer. The revised concept of ion association is also used to describe the concentration dependence of dielectric constant in electrolyte solutions. 

Keywords Electrolyte solutions, ion association, associative mean spherical approximation,... 

Protsykevytch, I.A., Kalyuzhnyi, Yu.V., Holovko, M.F., and Blum, L. Solution of the polymer mean spherical approximation for the totally flexible sticky two-point electrolyte model. Journal of Molecular Physics, 1997, 73, No. 4, p. 1-20. 

Harvey, A.H., Copeman, T.W., and Prausnitz, J.M. Explicit approximations to the mean spherical approximation for electrolyte systems with unequal ion sizes. Journal of Physical Chemistry, 1988, 92, No. 22, p. 6432-6436. 

L. Blum, Solution of a model for the solvent-electrolyte interactions in the mean spherical approximation, J. Chem. Phys. 61, 2129 (1974). 

G. Stell and S. F. Sun, Generalized mean spherical approximation for charged hard spheres. The electrolyte regime. J. Chem. Miys. 63,5333 (1975). 

During the last decade, the statistical thermodynamics of electrolytes have been continuously developed. The MSA theory (Mean Spherical Approximation) can yield analytical expressions for parameters which have a certain physical meaning (e.g., ionic diameter). To maintain the advantages of the NRTL electrolyte model and overcome its difficulties, the MSA theory has been successfully combined with the NRTL equation by Kunz and his co-workers (25). 

Blum, L. (1980). Primitive electrolytes in the mean spherical approximation. In Theoretical Chemistry Advances and Perspectives, pp. 1-66, Academic Press, New York. 

Simonin JP, Bernard O, Blum L (1999) Ionic solutions in the binding mean spherical approximation thermodynamic properties of mixtures of associating electrolytes. J Phys Chem B 103 699-704... 

Description of vapor-liquid equilibria for CO2 in electrolyte solutions using the mean spherical approximation. J Phys Chem B 107 5948-5957... 

Barthel J, Krienke H, Holovko M, Kapko VI, Protsykevich I (2000) The application of the associative mean spherical approximation in the theory of nonaqueous electrolyte solutions. Cond Mat Phys 3(23) 657... 

Numerous models are available in the literature for the description of the thermodynamic properties of ionic solutions [1—8]. In this entry, we focus on two particular models the mean spherical approximation (MSA) and the electrolyte ncmrandom two Uquid model (NRTL). 

H0ye JS, Lomba E (1988) Mean spherical approximation (MSA) for a simple model of electrolytes. I. Theoretical foundations and thermodynamics. J Chem Phys 88 5790-5797... 

Triolo R, Blum L, Floriano MA (1976) Simple electrolytes in the mean spherical approximation. 2. Study of a refined model. J Phys Chem 82 1368-1370... 

Sun T, Lenard JL, Teja AS (1994) A simplified mean spherical approximation for the prediction of the osmotic coefficient of aqueous electrolyte solutions. J Phys Chem 98 6870-6875... 

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