Calculations on ionic solvation. III. The electrostatic free energy of solvation of ions, using a multilayered continuum model

Abstract

For the calculation of the electrostatic free energy (and also the entropy) of solvation of an ion, a model is set up in which an ion of given crystallographic radius is surrounded by a series of concentric spherical layers, each with a different relative permittivity, immersed in the bulk liquid. A complete general solution is given for any number of such layers, both for the electrostatic free energy of solvation and the corresponding entropy term. The dielectric saturation effect is taken into account through the different relative permittivities of the layers. The first layer, next to the ion, is considered to have a special role and to have a relative permittivity ε=n2, independent of the dielectric saturation effect of the ion.

Clusters: A bridge across the disciplines of physics and chemistry

“…The Born relationship often yields an overestimation of the heat of solvation when typical values of crystalline radii are used for the ion size. This failure has led to proposed modifications based on structural considerations as well as other attempts to employ detailed ion-dipole, ion-quadrupole, and higher-order interactions (106)(107)(108)(109). The general success of the model in relating clustering data to the condensed phase can be seen from data plotted in Fig.…”

A revisit to the non-Bornian theory of the Gibbs energy of ion transfer between two immiscible liquids

“…However, the defects of the simple Born model have been known, and some attempts [3][4][5][6][7] to improve the model have been made mainly by considering the dielectric saturation (i.e., the lowering of the permittivity of solvents adjacent to an ion due to the high electric field). In 1998, Osakai (one of the present authors) and Ebina [8] proposed a non-Bornian theory for DG ;W!O tr , which was quite different from conventional Born-type electrostatic theories.…”

“…This is because DG ;W!O tr is fundamentally important for understanding ion-transfer processes in various two-phase systems, which include ion-transfer voltammetry, solvent extraction, phase-transfer catalysis, ionselective electrodes, emulsions, micelles, and possibly biomembranes. So far, theoretical studies have been performed to estimate DG ;W!O tr for ions, mostly based on electrostatic models [2][3][4][5][6][7]. In the classical Born model [2], the ion is considered as a hard sphere of a given radius r immersed in a continuous medium of constant permittivity; the transfer or resolvation energy of the ion is obtained as a difference between electrostatic energies for charging the ion up to ze (e the elementary charge) in O and W:…”

Ion-induced nucleation in polar one-component fluids

“…This quantity is negative and grows strongly as r approaches R i , leading to accumulation of the fluid particles around the ion. Here we are neglecting the nonlinear electric field effect near the ion 7,15,16 , for which see a discussion in the summary. The effect arising from the complex molecular structure of solvent molecules is also beyond the scope of this work, which leads to the dependence of the nucleation rate on the sign of the charge of ions 7 .…”

“…This has been the approach in the previous continuum theories 2,10 , but it is not well justified. In particular, we should examine the effect of nonlinear dielectric saturation in solvation, which gives rise to a decrease in the effective dielectric constant close to the ion 15,16 . (iii) The difference ∆ sol of the solvation free energies in Eq.…”