Oscillations, Waves, and Interactions - GWDG

374 U. Kaatze and R. Behrends
Figure 5. Sonic excess attenuation spectra for aqueous solutions of D-fructose at 25 ◦ C [44].
The saccharide concentrations are △, 0.5 mol/l; �, 0.7 mol/l; ◦, 1 mol/l; ⋄, 1.5 mol/l. The
lines represent a relaxation spectral function with three Debye-type relaxation terms and
with parameter values from a nonlinear fitting procedure.
Basically ourdays principles of measurement are the same as in early acoustical relaxation
studies [43]. More sophisticated liquid spectrometry is enabled by a higher
precision of the cell constructions, by advanced electronics, and by computer controlled
measuring routines. Mechanical stability offers a 10 nm resolution in the cell
length, which is mandatory for measurements in the GHz region where the wavelength
is on the order of 300 nm and where the extraordinary large attenuation coefficient
allows for small variations in the sample length only [42]. Modern electronics enable
progressive measurement routines, scanning the complete transfer function of resonators
to properly consider effects from higher order modes and running routinely
calibrations in the variable-path-length method. Automatic measuring procedures
finally facilitate multiple measurements for the reduction of statistical errors. Examples
of broadband attenuation spectra are shown in Fig. 5.
2.3 Sound velocity dispersion
According to the Kramers-Kronig relations acoustical attenuation originating from
relaxation processes is associated with a dispersion in the sound velocity c, which
could be also utilized for liquid spectrometry. Normally, however, the dispersion in
c is small and it is notoriously difficult to reach, in a significant frequency range, a
sufficiently high accuracy in the sound velocity measurements. But since the sound
velocity follows as a byproduct from the attenuation coefficient spectrometry, it can
be used to consider the dispersion corresponding with large sonic absorption. Figure 6
shows the dispersion in c that is related to the formation of ion complexes in an
aqueous solution of zinc chloride [45]. The total dispersion step of that system
amounts to c(∞) − c(0) = 0.01 · c(0) which should not be neglected in the evaluation
procedures.