Oscillations, Waves, and Interactions - GWDG

348 R. Pottel, J. Haller and U. Kaatze
sented assuming a sum of Cole-Cole terms [66]
ɛ(ν) = ɛ(∞) +
ɛ1 − ɛ(∞)
+
(1−h1)
1 + (iωτ1)
ɛ(0) − ɛ1
. (15)
(1−h2)
1 + (iωτ2)
These terms reflect a relaxation time distribution function G (τ) which, when τG (τ)
is plotted versus ln(τ/τi), i = 1, 2, is symmetrically bell shaped around τ/τi = 1.
Here τ1 and τ2 denote the principal relaxation times and parameters h1 and h2,
0 ≤ h1, h2 < 1 measure the width of the distribution function.
Despite of the clear indications of ion complex structures by the low-frequency
relaxation term in the dielectric spectra the finding of only one relaxation regime
for the ion processes is, on a first glance, a surprising result. It is common to all
dielectric studies of ion complex formation [18–29,67–70]. Absence of distinct relaxation
terms for the different ion species in the dielectric spectra becomes particularly
evident when comparison to the corresponding ultrasonic spectra is made (Fig. 13).
Interesting, the relaxation frequency (2πτ2) −1 in the dielectric spectrum shown in
Fig. 13 is larger than the largest relaxation frequency in the ultrasonic excess absorption
spectrum. Obviously, in the dielectric spectra of the electrolyte solutions
the complex formation/decay processes are short-circuited by the faster reoriental
motions.
Based on the Debye model of rotational diffusion [41] reorientation times for the
outer-outer-sphere, the outer-sphere, as well as the inner-sphere complexes have been
estimated which are too close to each other to allow for a clear separation of the
Figure 13. Ultrasonic excess absorption (◦) and dielectric loss spectrum (•) for the solution
of 0.1 mol/l Sc2(SO4)3 in water at 25 ◦ C [20].