Oscillations, Waves, and Interactions - GWDG

Multistep association of cations and anions 357
Figure 22. Ultrasonic excess absorption spectra for aqueous solutions of
ZnCl2(◦, 0.3mol/l; •, 0.8mol/l) at 25 ◦ C. The lines are graphs of the Dissado-Hill function
(Eq. (21)) with the parameter values given in Table 2.
tra [102,103]. Rewritten to apply to the sonic absorption per wavelength it reads
(αλ)exc
⎡
�
= ADHIm ⎣
1
1 + iωτDH
� 1−nDH
�
lim
ɛ→0
ɛ
1
t −nDH
�
1 −
t
1 − iωτDH
� −(1−mDH)
(21)
⎤
dt⎦
.
The parameter values of the zinc chloride solutions are collected in Table 2. Within
the framework of the Dissado-Hill model the ions are assumed to form clusters rather
than well-defined complexes. Relaxations within the clusters are characterized by
the principal relaxation time τDH. The parameter nDH (0≤ nDH ≤1) describes the
correlations within the clusters. The limiting values nDH = 0 and nDH = 1 represent
relaxation processes that are completely independent and strongly correlated,
C ADH τDH nDH mDH B
mol/l 10 −3
ns 10 −12 s
0.1 1.4 ± 0.1 4.5 ± 0.3 0 ± 0.02 0.88 ± 0.02 32.6 ± 0.1
0.2 5.1 ± 0.5 14.0 ± 0.7 0.34 ± 0.03 0.90 ± 0.02 32.7 ± 0.2
0.3 18.9 ± 0.3 14.5 ± 0.3 0.25 ± 0.01 0.87 ± 0.01 33.7 ± 0.1
0.35 22.8 ± 0.7 18.0 ± 0.6 0.31 ± 0.02 0.90 ± 0.02 33.4 ± 0.2
0.4 36.8 ± 0.6 16.0 ± 0.4 0.24 ± 0.01 0.89 ± 0.01 33.6 ± 0.2
0.5 56.5 ± 1.1 15.3 ± 0.6 0.23 ± 0.02 0.85 ± 0.02 34.1 ± 0.2
0.6 85.7 ± 1.1 14.7 ± 0.3 0.20 ± 0.01 0.90 ± 0.01 34.6 ± 0.1
0.8 119.1 ± 2.5 14.3 ± 0.6 0.23 ± 0.02 0.94 ± 0.02 34.7 ± 0.4
Table 2. Parameters of the Dissado-Hill spectral function (Eq. (21)) for aqueous solutions
of zinc(II) chloride at 25 ◦ C and salt concentration C [31].