Oscillations, Waves, and Interactions - GWDG

Multistep association of cations and anions 349
broadband relaxation contributions from the different ion complex species [20]. Dielectric
spectroscopy thus yields direct evidence for the existence of ion pairs with
life times exceeding the reorientation times, respectively, but a deconvolution of the
experimental spectra is normally only possible when reasonable assumptions on the
underlying molecular processes are made.
4 Electrolyte solutions of monovalent anions
4.1 Evidence from the solvent contribution to the static permittivity
As revealed by the dielectric spectrum of the aluminium sulfate solution displayed
in Fig. 12 the solvent contribution ɛ1 to the extrapolated static permittivity may fall
significantly below the solvent permittivity ɛv (0) (= ɛw (0)). The reduction in ɛ1
is partly due to the dilution of the dipolar solvent by the solute. This part in the
polarization deficiency can be considered by a suitable mixture relation, e.g. the
Bruggeman formula [71]
� �1/3 ɛv(0)
= (1 − v)
ɛ(0)
ɛv(0) − ɛu
ɛ(0) − ɛu
for the resulting permittivity ɛ (0) of a solution of spherical particles with volume
fraction v and frequency independent permittivity ɛu in solvent with permittivity
ɛv (0). In addition, two other effects may contribute to the reduction in ɛ1. One
effect is suggested by extrapolated static permittivity data as shown in Fig. 14.
The dielectric spectra of the bromide salt solutions for which the ɛ (0) data are
presented, within the frequency range of measurements, do not indicate contributions
from ion complexes, thus ɛ1 = ɛ (0) with these systems. For the bromides of large
organic cations the ɛ (0) values slightly exceed the predictions of the Bruggeman
mixture relation (Eq. (16)). This tendency in the extrapolated static permittivity
seems to be characteristic to aqueous solutions of organic solutes and is assumed to
be due to hydrophobic interaction effects [74–76]. The ɛ (0) value of the alkali halide
solutions are smaller than predicted by Eq. (16) and, furtheron, the deviation from
the mixture relation increases with decreasing cation radius. This feature points at an
interaction between the dipole moment of the solvent molecules and the electric field
of the small cations. The preferential orientation of the dipole moments within the
Coulombic fields (Fig. 15) leads to a reduced orientation polarizability of the solvent,
usually named “dielectric saturation” [72,77]. We shall get back to saturation effects
later.
The other effect that leads to a reduction in the extrapolated static permittivity of
electrolyte solutions is featured by the ɛ (0) data for solutions of lithium chloride in
two different solvents, given in Fig. 16. For methanol solutions the reduction in the
permittivity ratio ɛ (0) /ɛv (0) is considerably larger than for aqueous solutions. These
findings reflect a feature of the kinetic polarization deficiency [80–84] resulting from
a coupling of dielectric properties to the hydrodynamics of the conducting liquids.
An ion moving in a liquid, that is exposed to an external electric field, sets up
a nonuniform flow in its ambient solvent [85]. The dipole moments of the solvent
(16)