Oscillations, Waves, and Interactions - GWDG

Multistep association of cations and anions 339
Figure 4. Spectra of the total ultrasonic absorption per wavelength (points), the asymptotic
high frequency background contribution (dashed curve), and the excess absorption per
wavelength (circles) for a 0.5 mol/l CuCl2 solution in water at 25 ◦ C [50,51]. Lines are graphs
of the analytical forms of αλ and (αλ)exc, using the relaxation spectral function defined by
Eq.(7) and parameter values as following from a regression analysis of the experimental
data: A = 7.6 · 10 −3 , τ = 0.35 ns, B = 33.95 ps [50].
coaxial-line components or waveguide devices. The central part is accentuated in
grey. This part establishes a microwave bridge of which one branch contains the
sample cell (6, Fig. 5), basically a circular waveguide or coaxial line, holding the
liquid. Another waveguide or coaxial line (8) is immersed in the liquid. It can
be precisely shifted along the direction z of wave propagation. The other branch
is made of an attenuator (4) and a phase shifter (14) which, at a certain sample
thickness z0 can be adjusted to yield zero signal Uout at the interferometer output.
Varying the position z of the probing waveguide or coaxial line and measuring Uout
as the interferometer goes off-balance, along with the input signal Uin, yields the
interferometer transfer function T (z) = Uout (z) /Uin. Fitting the theoretical T (z)
relation to the experimental data yields the propagation constant and thus the desired
sample permittivity ɛ (ν).
The corresponding set-up for the ultrasonic spectrometry is sketched in Fig. 6.
Pulse-modulated waves are applied in order to allow for the separation of the measurement
signal from electrical crosstalk and also from waveforms resulting from multiple
reflections [53,54]. Therefore, instead of an interferometer, a comparator set-up
is employed, in which coaxial switches (5, Fig. 6) allow the measurement branch,
containing the sample cell (8), to be replaced by a high presicion piston attenuator
(13), featuring a calculable signal vernier [55]. The scalar transfer function T (z) of
the sample cell at varying sample thickness z allows for a straightforward evaluation
in terms of the absorption coefficient of the liquid. From a standing-wave pattern in