Activity Mean Spherical Approximation

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. 

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... 

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... 

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. 

Corti HR (1987) Prediction of activity coefficients in aqueous electrolyte mixtures using the mean spherical approximation. J Phys Chem 91 686-689... 

Fawcett WR, Tikanen AC (1996) Role of solvent permittivity in estimation of electrolyte activity coefficients on the basis of the mean spherical approximation. J Phys Chem 100 4251-4255... 

Fawcett WR, TikanenAC. (1997) Application of the mean spherical approximation to the estimation of electrolyte activity coefficients in methanol solutions. JMolLiq 73-4 373-384. 

Most of the electrochemical promotion studies surveyed in this book have been carried out with active catalyst films deposited on solid electrolytes. These films, typically 1 to 10 pm in thickness, consist of catalyst grains (crystallites) typically 0.1 to 1 pm in diameter. Even a diameter of 0.1 pm corresponds to many (-300) atom diameters, assuming an atomic diameter of 3-10 10 m. This means that the active phase dispersion, Dc, as already discussed in Chapter 11, which expresses the fraction of the active phase atoms which are on the surface, and which for spherical particles can be approximated by ... 

It is interesting that the average heat of vaporization of a liquid is approximately three times the activation energy of viscosity. This means that three times as much energy is required to remove a surface molecule as to move a bulk molecule past a neighbor. The ratio n = E apfEvis was shown byEyring to be equal to the ratio of the size of a molecule to the size of a hole needed for viscous flow. It has been found that, since a hole of molecular dimensions is not required if, for example, two molecules rotate about their point of contact, the value of n is about 3 for a spherically symmetric nonpolar molecule and increases to 5 as the deviation from spherical symmetry increases. 

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