Handbook of Solvents - George Wypych - ChemTech - Ventech!

13.1 Solvent effects on chemical reactivity 769
most famous model in this respect is that of Born, originally proposed in 1920, 168 representing
the simplest continuum theory of ionic solvation. For a spherical ion, the Born excess
free energy ΔG B of solvation was derived by considering the free energy change resulting
from the transfer of an ion from vacuum to solvent. The equation has a very simple dependence
on the ionic charge z, the radius r B, and the solvent dielectric constant ε (for the prime
see eq. [13.1.16]):
* −ez
ΔGB
=
2r
2 2
B
⎛ ⎞
⎜1−⎟
⎝ ⎠
1
ε
[13.1.29]
While Born assumes that the dielectric response of the solvent is linear, nonlinear effects
such as dielectric saturation and electrostriction should occur due to the high electric
field near the ion. 169 Dielectric saturation is the effect that the dipoles are completely aligned
in the direction of the field so that any further increase in the field cannot change the degree
of alignment. Electrostriction, on the other hand, is defined as the volume change or compression
of the solvent caused by an electric field, which tends to concentrate dipoles in the
first solvation shell of an ion. Dielectric saturation is calculated to occur at field intensities
exceeding 10 4 V/cm while the actual fields around monovalent ions are on the order of 10 8
V/cm. 170
In the following we concentrate on ionic hydration that is generally the focus of attention.
Unaware of nonlinear effects, Latimer et al. 171 showed that the experimental hydration
free energies of alkali cations and halide anions were consistent with the simple Born equation
when using the Pauling crystal radii r P increased by an empirical constant Δ equal to
0.85 Å for the cations and 0.1 Å to the anions. In fact three years earlier a similar relationship
was described by Voet. 172 The distance r P + Δwas interpreted as the radius of the cavity
formed by the water dipoles around the ion. For cations, it is the ion-oxygen distance while
for anions it is the ion-hydrogen distance of the neighboring water molecules. From those
days onwards, the microscopic interpretation of the parameters of the Born equation has
continued to be a corundum because of the ambiguity of using either an effective radius
(that is a modification of the crystal radii) or an effective dielectric constant.
Indeed, the number of modifications of the Born equation is hardly countable. Rashin
and Honig, 173 as example, used the covalent radii for cations and the crystal radii for anions
as the cavity radii, on the basis of electron density distributions in ionic crystals. On the
other hand, Stokes 174 put forward that the ion’s radius in the gas-phase might be appreciably
larger than that in solution (or in a crystal lattice of the salt of the ion). Therefore, the loss in
self-energy of the ion in the gas-phase should be the dominant contributor. He could show
indeed that the Born equation works well if the vdW radius of the ion is used, as calculated
by a quantum mechanical scaling principle applied to an isoelectronic series centering
around the crystal radii of the noble gases. More recent accounts of the subject are available.
175,176
Irrespective of these ambiguities, the desired scheme of relating the Born radius with
some other radius is facing an awkward situation: Any ionic radius depends on arbitrary divisions
of the lattice spacings into anion and cation components, on the one hand, and on the
other, the properties of individual ions in condensed matter are derived by means of some
extra-thermodynamic principle. In other words, both properties, values of r and ΔG*, to be
compared with one another, involve uncertain apportionments of observed quantities. Con-