Born theory of solvation

Suppose we have a spherical conductor of radius R in a vacuum and we bring up a total charge q from infinite distance, in infinitesimal increments dq. The work Wq done in charging the sphere against the charge itself, as it builds up, will be 

Relative Permittivities (Dielectric Constants) D and Normal Liquid Ranges of Common Solvents 

Consequently, if we transfer the charged sphere from a vacuum to the solvent, its electrostatic self-energy is lowered by an amount AW  

Born pointed out that a mole of gaseous ions of radius r and charge ze would be similarly stabilized on transfer to the solvent, the work difference being — Strictly speaking, the foregoing argument is not really 

For polar solvents like water, DMSO, or 100% sulfuric acid, D is quite small compared to unity (Table 13.1) so the electrostatic self-energy of a gaseous ion is almost entirely eliminated on transferring the ion to a polar solvent. For an ionic compound to be freely soluble in a given solvent, the solvation energies of its anions and cations must outweigh the lattice energy sufficiently, otherwise an ionic solid results instead. Ionic solids are therefore not usually very soluble in solvents of low D. 

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The upshot is that the Born theory of solvation fails because it regards the solvent as a continuous dielectric, whereas in fact solute ions (especially metal cations with z > 1) often interact in a specific manner with solvent molecules. In any event the molecular dielectric is obviously very lumpy on the scale of the ions themselves. The Born theory and other continuous dielectric models work reasonably well when metal ion solute species are treated as solvent complexes such as Cr(OH2)63+ rather than naked ions such as Cr3+, but the emerging approach to solvation phenomena is to simulate solvation dynamically at the molecular level using computer methods. 

So, Born s equation remains a controversial part of the theory of solvation although there have been many recent attempts striving to justify it. The difficulty resides in the avoidance of molecular-level arguments and in applying continuum electrostatics, which clearly involves fundamental limitations when it comes to atomic... 

Data such as those in Fig. 4.20 can be compared directly with Born s theory of solvation (Makov et al., 1988). The ionization energy is taken to be the difference in solvation energies of a charge e in an infinite dielectric and in a sphere of the same dielectric constant ... 

Thus, with the help of Marcus equation, we can obtain some useful estimates and predictions. The quantitative accuracy of this theory, however, should not be overstated. It was shown above that this theory is based on the same physical model as the Born theory of ion solvation and hence suffers from the same drawbacks. We do not know whether any attempts have been made to take into account the effect of dielectric saturation of the medium in the vicinity of ions in kinetics. An attempt to take into account the spatial dipole correlation while considering the redox reaction MnOi+ /MnO was made by Dolin et al,[237]. As mentioned in section 3.2, the correlation in dipole orientation leads, as it were, to an increase in the effective ionic radius. Consequently, it should somewhat decrease the activation energy. According to estimates in [237], this effect is not strong, but it must increase with decreasing ionic radius. 

Although the Born equation is a rough approximation, it is often used for comparison of the solvation effects of various solvents. The simplification involved in the Born theory is based primarily on the assumption that the permittivity of the solvent is the same in the immediate vicinity of the ion as in the pure solvent, and the work required to compress the solvent around the ion is neglected. 

The Born solvation equation is based on the difference in the energy needed to charge a sphere of radius r,- in a solvent of dielectric constant e, and in vacuum having a dielectric constant of unity. Thae are basic flaws in the concept of the Born solvation equation (5) on which the continuum theory of ET reactions is based. First, Bom Eq. (5) does not take into account the interaction of ions with a water solvent that has a dielectric constant of approximately 80 at room temperature. Hence, the Born solvation energy will have negligible contribution from solvents with high dielectric constants. Consequently, for solvents of high dielectric constant, Eq. (5) can be written as... 

These points indicate that the continuum theory expression of the free energy of activation, which is based on the Born solvation equation, has no relevance to the process of activation of ions in solution. The activation of ions in solution should involve the interaction energy with the solvent molecules, which depends on the structure of the ions, the solvent, and their orientation, and not on the Born charging energy in solvents of high dielectric constant (e.g., water). Consequently, the continuum theory of activation, which depends on the Born equation,fails to correlate (see Fig. 1) with experimental results. Inverse correlations were also found between the experimental values of the rate constant for an ET reaction in solvents having different dielectric constants with those computed from the continuum theory expression. Continuum theory also fails to explain the well-known Tafel linearity of current density at a metal electrode. ... 

Assuming that the electrostatic contributions are given by Born theory and that the solvated ions, irrespective of the composition of the solvation shell, have the same radii, then Equation 19, utilizing the assumptions embodied in Equations 25, 26, and 27, simplifies to... 

Specifically, in the Born theory model of solvation, the intermolecular relaxation energy is (21)... 

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. 

In the present chapter, the properties of electrolyte solutions in water are discussed in detail. Initially the solvation of ions in infinitely dilute solutions is considered on the basis of the Born theory. Then, the Debye-Hiickel model for... 

Over 100 years have passed since Arrhenius published his Dissociation Theory of Electrolytes in 1887. Prior to this it was believed that electrolytes did not dissociate into ions in water until current was passed, and Arrhenius work was not well received. It was some decades after this that Born s theory of ionic solvation, and then, Debye and Huckel s theory of ionic activities in... 

The central difficulty of acceptance of the expression for the free energy of activation in the continuum theory (cf. Marcus ) is that it takes into consideration only the Born part of the many-component solvation energy. 

Using the fundamental continuum theories (of Born, Onsager, Kirkwood), a direct calculation is in fact made not of the solvation energy but rather of the free solvation energy. Since, however, in most publications on this theme the calculated free solvation energy is stubbornly called the solvation energy, we shall retain this customary term. 

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