MSA treatment

The Born equation, proposed in 1920, has been modified in various ways in order to get a single equation that can express the experimental ionic solvation energies. In recent years, the so-called mean spherical approximation (MSA) has often been used in treating ion solvation. In the MSA treatment, the Gibbs energy of ion solvation is expressed by... 

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]. 

The so-called mean spherical approximation (MSA) treatment of the solvation energy should also be mentioned. Within the frame work of that model the electrostatic energy of ions is given by a Born-like expression [25], where the effective radius of the ion is considered to be the sum of the ionic radius and a correction term which depends not only on the solvent molecule diameter but also on the dielectric permittivity. Thus, the effective radius is a function of the frequency of the electromagnetic field. 

One should also mention the so-called mean spherical approximation (MSA) treatment of solvent reorganization [25]. McManis and Weaver [125] considered how the solvent radius and dielectric parameters affect the electron transfer within the frame of this theory. The frequency dependence of the effective radius should cause significant deviations from the Marcus expression for the activation energy of... 

At the end of the MSA treatment, the slurry was allowed to cool to room temperature and centrifuged to separate the solid residue, made of coated alumina. The residue was washed by redispersing it in distilled water and centrifuging. The cake was dried in vacuum at 110 °C for 12 h. 

There are two routes to derive the chemical (or mutual) diffusion coefficient. One has been taken for HNC calculations and the other for an MSA treatment. It should be noted that while the HNC calculation is generally regarded as more accurate, it does not lead to explicit analytical expressions, in contrast with the MSA which is simpler, but perhaps not as accurate, and leads to explicit formulas that are reasonably accurate when the energy route for the thermodynamic quantities is used. 

Guillot and Guissani [56] and Weiss and Schroer [221] went one step further. Guillot and Guissani considered the effect of unscreened DD interactions on the FL theory. They also performed an approximate treatment of unscreened DD interactions in the framework of the MSA. In contrast, Weiss and Schroer theory (WS) considers ionic screening of the DD interactions by the remainder of the fluid, the change of the dielectric permittivity caused by... 

What about the difficult problem of modeling electrolyte solutions at higher concentrations In the MSA approach, attempts were made to extend the treatment by allowing the ion size parameter to be a function of ionic strength. Unfortunately, such an approach became unrealistic because of the sharp reduction of effective cation size with increasing electrolyte concentration. 

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... 

All materials were prepared by alkali-free mixtures This method is usually adopted for MSA, ERS-8 and HMS preparations. Synthesis of MCM-41 is more usually performed in presence of alkali ions with a hydrothermal treatment at temperature higher than 70 °C. Nevertheless also alkali-free (10) and room temperature (11) synthesis are described. 

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. 

The DH and MSA theory, that are linear in charge can be considered in the framework of linearized Poisson-Boltzmann (PB) equation. The concept of ion association entails nonlinearity in the treatment of electrostatic interactions by the formulation of appropriate thermodynamic equilibrium constants between free ions and ion clusters [14], In general, this formulation can be considered as the division of ion-ion interaction potentials into an associative part responsible for the ion association, and nonassociative part which is more or less arbitrary. In order to optimize this division in the framework of associative hypernetted chain approximation (AHNC), the division of energy and distance were considered [17] with the parameters calculated from the condition of sta-... 

In this chapter some aspects of the present state of the concept of ion association in the theory of electrolyte solutions will be reviewed. For simplification our consideration will be restricted to a symmetrical electrolyte. It will be demonstrated that the concept of ion association is useful not only to describe such properties as osmotic and activity coefficients, electroconductivity and dielectric constant of nonaqueous electrolyte solutions, which traditionally are explained using the ion association ideas, but also for the treatment of electrolyte contributions to the intramolecular electron transfer in weakly polar solvents [21, 22] and for the interpretation of specific anomalous properties of electrical double layer in low temperature region [23, 24], The majority of these properties can be described within the McMillan-Mayer or ion approach when the solvent is considered as a dielectric continuum and only ions are treated explicitly. However, the description of dielectric properties also requires the solvent molecules being explicitly taken into account which can be done at the Born-Oppenheimer or ion-molecular approach. This approach also leads to the correct description of different solvation effects. We should also note that effects of ion association require a different treatment of the thermodynamic and electrical properties. For the thermodynamic properties such as the osmotic and activity coefficients or the adsorption coefficient of electrical double layer, the ion pairs give a direct contribution and these properties are described correctly in the framework of AMSA theory. Since the ion pairs have no free electric charges, they give polarization effects only for such electrical properties as electroconductivity, dielectric constant or capacitance of electrical double layer. Hence, to describe the electrical properties, it is more convenient to modify MSA-MAL approach by including the ion pairs as new polar entities. 

Modern theory of associative fluids is based on the combination of the activity and density expansions for the description of the equilibrium properties. The activity expansions are used to describe the clusterization effects caused by the strongly attractive part of the interparticle interactions. The density expansions are used to treat the contributions of the conventional nonassociative part of interactions. The diagram analysis of these expansions for pair distribution functions leads to the so-called multidensity integral equation approach in the theory of associative fluids. The AMSA theory represents the two-density version of the traditional MSA theory [4, 5] and will be used here for the treatment of ion association in the ionic fluids. 

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. 

In the treatment of ionic activity coefficients according to the MSA it was emphasized that the finite size of the ions is an important factor in estimating their Gibbs energy. Accordingly, the work done to introduce an additional ion to the solution... 

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. 

The bimetallic Pt-Mo(S)/MSA catalysts were prepared by deposition of Pt compounds on the Mo(S)/MSA, sulfided by 10 % H2S in H2 at 400°C/4 h. The deposited Pt compounds were transformed into active sulfide phase by successive sulfidation. The effect of the sulfidation temperature and composition of the sulfiding gas during this successive treatment was studied in the case of the sample F. It was found, that the lower sulfidation temperature 320 C instead of 400°C led to by 10 and 30 % higher values kpH and kpy, respectively, while the value kcs remained the same. This suggests that the activity of the R-Mo(S) system could be additionally improved by optimized activation conditions. 

Mutual solubility. Ideally the MSA and the bulk feed material would not be soluble in each other. Solubihty of MSA in the bulk feed material results in loss of MSA from the system and may present downstream compHcations since the MSA could be transferred to other process steps, to the products, or to the waste treatment facility. Solubility of the bulk feed material into the MSA may alter the selectivity, capacity, and physical stability of the MSA. 

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