MSA model

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). 

The Born term is no more necessary, as the reference state for the ions is not the pure aqueous solution but the infinite dilution of ions in the solvent mixture. Thus, the MSA-NRTL has only two terms  

The exact calculation equations are given in [25], where it has also been proved that the Gibbs-Duhem equation is fulfilled. As well, NRTL parameters have been fitted up to molalities of 30mol/kg for a number of systems. Together with the ionic diameters, they are listed in [25]. Osmotic and mean ionic activity coefficients could be reproduced in an excellent way for a number of systems. Furthermore, the parameters fitted to binary systems have been successfully applied to ternary systems, that is, one salt in a binary solvent mixture, which always causes problems with the Electrolyte NRTL model [25]. 

---

The integral equation approach has also been explored in detail for electrolyte solutions, with the PY equation proving less usefiil than the HNC equation. This is partly because the latter model reduces cleanly to the MSA model for small h 2) since... 

Our group is involved since several years in ESA s studies of the NIRSPEC instrument. We have focused our work on three main topics MMA and MSA modeling, characterization of the MMA and MSA, and optical design for the MOS (Zamkotsian et al., 1999 Zamkotsian et al., 2000a). 

An important advance in the understanding of microscopic solvation and Onsager s snowball picture has recently been made through the introduction of the linearized mean spherical approximation (MSA) model for the solvation dynamics around ionic and dipolar solutes. The first model of this type was introduced by Wolynes who extended the equilibrium linearized microscopic theory of solvation to handle dynamic solvation [38]. Wolynes further demonstrated that approximate solutions to the new dynamic MSA model were in accord with Onsager s predictions. Subsequently, Rips, Klafter, and Jortner published an exact solution for the solvation dynamics within the framework of the MSA [43], For an ionic solute, the exact results from these author s calculations are in agreement with Onsager s inverted snowball model and the previous numerical calculations of Calef and Wolynes [37]. Recently, the MSA model has been extended by Nichols and Calef and Rips et al. [39-43] to solvation of a dipolar solute. 

Recent work on the theory of solvation dynamics has attempted to go beyond the linearized MSA model of Wolynes, which considers the rotational dynamics of the solvent as the only relaxation mechanism. Certain translational and hydrodynamic-like motions of the solvent are neglected. 

TABLE 3 Comparison of Calculated Average Solvation Times from Dielectric Continuum and MSA Models with Experimental Results... 

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]. 

Extended and more precise elaborations of the MSA model have been published [27]. 

Tlie main assumption of this approach is that the shape of the molecule is closely related to the shape of the - binding site cavity and, as a consequence, to the biological activity. Therefore, a shape reference compound is chosen which represents the binding site cavity, and the similarity (or commonality) measured between the reference shape and the shape of other compounds is used to determine the biological activity of these compounds. As well as the shape similarity measures, other molecular descriptors such as those in - Hansch analysis can be used to evaluate the biological response. The MSA model is thus defined as ... 

Acetonitrile is a polar solvent with a relative permittivity of 35.9. It may be represented as a hard sphere with a diameter of 427 pm. Estimate the Gibbs energy of solvation of Na in acetonitrile according to the Born and MSA models. Compare the theoretical estimates with the experimental estimate given that the Gibbs energy of transfer for Na" " from water to acetonitrile is 15.1 kJmoP ... 

The fit of the MSA model with varying solvent permittivity is shown in fig. 3.9. These results demonstrate the importanee of eonsidering the true solvent permit-... 

Inclusion of the change in solvent permittivity in the MSA description is an effective way of dealing with the change of solvent properties which accompany the addition of an electrolyte to a polar solvent. Since permittivity data are now available for a large number of electrolyte solutions in water [23], the MSA model can be applied to a wide variety of systems. However, there is one feature of electrolyte solutions which has been neglected in the treatments presented up to this point, namely, the existence of ion aggregates. This feature of electrolyte solutions is discussed in the following sections of this chapter. 

Fig. 3.12 Plots of yip, y , and oq on a logarithmic scale for the MgS04 system according to the modified MSA model at 25°C against electrolyte concentration in water.

In summary, the models discussed in this chapter focus on the physical aspects of electrolyte solutions but they ignore the chemical aspects. This is especially apparent in the treatment of ion solvation where an empirical correction to the MSA model was applied to treat the differences in behavior seen for cations and anions in water. The same problem arises in using classical electrostatics to describe ion pairing. In spite of the fact that the Bjerrum and Fuoss models give a good qualitative description of an ion association, this phenomenon can only be understood in detail by using quantum-mechanical methods. Needless to say, such calculations in condensed media are much more difficult to carry out. 

Values of Xs and have been estimated for the polar solvents considered in this chapter and are summarized in table 4.4. Also included in this table are values of the Kirkwood correlation parameter g. It is defined in the MSA model as... 

One may also use the MSA model to describe the permittivity of the system at optical frequencies. Under these circumstances the system responds to the electrical field only through electronic polarization, the orientational component being frozen. The directional stickiness of the dipoles is then unimportant so that to is effectively zero at very high frequencies. Under these circumstances, the polarization parameter is given by... 

Estimate the Kirkwood polarization parameter for dimethylsulfoxide using the MSA model described in section 4.4. Your result should agree with that given in table 4.4. 

Salimi HR, Taghikhani V, Ghotbi C (2005) Application of the GV-MSA model to the electrolyte solutions containing mixed salts and mixed solvents. Fluid Phase Equlllb 231 67-76... 

It is possible to take into account the short range ion-ion interaction effect on the volumetric properties of electrolytes by resorting to integral equation theories, as the mean spherical approximation (MSA). The MSA model renders an analytical solution (Blum, 1975) for the umestricted primitive model of electrolytes (ions of different sizes immersed in a continuous solvent). Thus, the excess volume can be described in terms of an electrostatic contribution given by the MSA expression (Corti, 1997) and a hard sphere contribution obtained form the excess pressure of a hard sphere mixture (Mansoori et al, 1971). The only parameters of the model are the ionic diameters and numerical densities. 

Even when the MSA model has not been extensively used for fitting volumetric properties of electrolyte aqueous solutions it is an interesting alternative to the ion-interaction model for predictive purpose because it renders reasonable values of the excess volume using the crystallographic values of ionic diameters (Corti, 1997). 

Sedlbauer and Wood (2004) used the MSA model to describe the tiiermodynamics properties of NaCl near the critical point. In this case the crystallographic diameters of the ions were used along with a model (Sedlbauer et al, 2000) for the standard state term. The MSA model without adjustable parameters provides a better fit of the partial molar volume than the Pitzer model. 

The first three terms pertain to the ideal-, reference-, and chain-contributions of the SAFT model and the fourth to the electrostatic interactions from the MSA model. The cations have m+ segments and the anions have only one, m = segment. The ideal term is ... 

Papaiconomou et al combined the NRTL model with the semi-restricted version of the MSA model adapted to the Gibbs energy formalism. Simonin ct applied the MSA-NRTL to strong electrolytes... 

---