Dielectric solvation energy

This fomuila does not include the charge-dipole interaction between reactants A and B. The correlation between measured rate constants in different solvents and their dielectric parameters in general is of a similar quality as illustrated for neutral reactants. This is not, however, due to the approximate nature of the Bom model itself which, in spite of its simplicity, leads to remarkably accurate values of ion solvation energies, if the ionic radii can be reliably estimated [15],... 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

Similar observations hold for solubility. Predominandy ionic halides tend to dissolve in polar, coordinating solvents of high dielectric constant, the precise solubility being dictated by the balance between lattice energies and solvation energies of the ions, on the one hand, and on entropy changes involved in dissolution of the crystal lattice, solvation of the ions and modification of the solvent structure, on the other [AG(cryst->-saturated soln) = 0 = A/7 -TA5]. For a given cation (e.g. K, Ca +) solubility in water typically follows the sequence... 

Although the LD model is clearly a rough approximation, it seems to capture the main physics of polar solvents. This model overcomes the key problems associated with the macroscopic model of eq. (2.18), eliminating the dependence of the results on an ill-defined cavity radius and the need to use a dielectric constant which is not defined properly at a short distance from the solute. The LD model provides an effective estimate of solvation energies of the ionic states and allows one to explore the energetics of chemical reactions in polar solvents. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

Dissolution of an ionic salt is essentially a separation process carried out by the interaction of the salt with water molecules. The separation is relatively easy in water because of its high dielectric constant. Comparison of the energies needed to separate ions of NaCl from 0-2 nm to infinity shows that it takes 692-89 kJ mol" in vacuum, but only 8-82 kJ moF in aqueous solution (Moore, 1972). Similar arguments have been used to try to estimate solvation energies of ions in aqueous solution, but there are difficulties caused by the variations in dielectric constant in the immediate vicinity of individual ions. 

The modification by method 2 is more acceptable. Although several types of modifications have been reported, Abraham and Liszi [15] proposed one of the simplest and well-known modifications. Figure 2(b) shows the proposed one-layer model. In this model, an ion of radius r and charge ze is surrounded by a local solvent layer of thickness b — r) and dielectric constant ej, immersed in the bulk solvent of dielectric constant ),. The thickness (b — r) of the solvent layer is taken as the solvent radius, and its dielectric constant ej is supposed to become considerably lower than that of the bulk solvent owing to dielectric saturation. The electrostatic term of the ion solvation energy is then given by... 

On the assumption that = 2, the theoretical values of the ion solvation energy were shown to agree well with the experimental values for univalent cations and anions in various solvents (e.g., 1,1- and 1,2-dichloroethane, tetrahydrofuran, 1,2-dimethoxyethane, ammonia, acetone, acetonitrile, nitromethane, 1-propanol, ethanol, methanol, and water). Abraham et al. [16,17] proposed an extended model in which the local solvent layer was further divided into two layers of different dielectric constants. The nonlocal electrostatic theory [9,11,12] was also presented, in which the permittivity of a medium was assumed to change continuously with the electric field around an ion. Combined with the above-mentioned Uhlig formula, it was successfully employed to elucidate the ion transfer energy at the nitrobenzene-water and 1,2-dichloroethane-water interfaces. 

Since the reverse of the reaction Nl is the ionisation of the ester, the equilibrium position for any one system depends critically on the nature, especially the polarity, of the solvent, which determines the AHS terms. The accumulation of the necessary thermochemical data is essential to a rationalisation of the relation between cationic and pseudocationic polymerisations but the prevalence of the former at low temperatures and of the latter at high temperatures is surely related to the fact that the dielectric constant, and with it solvation energies, increases as the temperature of a polar solvent is reduced, so that decreasing temperature favours ionisation. 

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... 

The simplest approach to describing the interactions of metal cations dissolved in water with solvent molecules is the Born electrostatic model, which expresses solvation energy as a function of the dielectric constant of the solvent and, through transformation constants, of the ratio between the squared charge of the metal cation and its effective radius. This ratio, which is called the polarizing power of the cation (cf Millero, 1977), defines the strength of the electrostatic interaction in a solvation-hydrolysis process of the type... 

Systems of ionic radii have also been used to discuss the solvation-energies of ionic crystals. Fifty years ago Born 42) deduced for the free energy AG of transfer of an ion of valency Z from vacuum to a medium of dielectric constant C ... 

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