Oscillations, Waves, and Interactions - GWDG

344 R. Pottel, J. Haller and U. Kaatze
Figure 9. Ultrasonic excess absorption spectrum for a solution of 0.1 mol/l MnSO4 in
water at 25 ◦ C. The data are taken from the literature [58,60,65], the line is the graph of a
superposition of two Debye type relaxation terms (Eq. (8)).
The former scheme (Eq. (9)) suggests another relaxation term to contribute to the
spectrum at frequencies above the measuring range, namely the term due to the
equilibrium between the completely dissociated ions and the outer-outer-sphere complexes.
The latter scheme (Eq. (10)) is based on the assumption of a negligibly small
concentration of outer-outer-sphere complexes.
In the early ultrasonic relaxation studies of ion complex formation [5–11,15] the
excess absorption of the electrolyte solutions has been calculated using the B value
of water in Eq. (6). The high frequency relaxation region was found to extend over a
broader frequency band than a single Debye term. For this reason the excess absorption
spectra were discussed in terms of three Debye-type relaxation processes which
were assigned to the three steps in the complete Eigen-Tamm scheme (Eq. (1)). This
assumption has been questioned [12,16,63] because of the unphysical volume change
for the formation of outer-sphere complexes from outer-outer-sphere complexes following
thereby. An unusually large change in volume results which is furthermore
negative. Since B depends on the shear viscosity ηS of the liquid and as ηS will
change on addition of salt, use of the B value of the solvent in the evaluation of the
electrolyte solution spectra is doubtless an approximation. Due to the dominance
of the background absorption at high frequencies, however, small errors in B may
virtually broaden the relaxation characteristics of that part of the ultrasonic spectra.
Such broadening of relaxation regions is illustrated in Fig. 10. Hence the assumption
of all three steps in the Eigen-Tamm scheme to show up in the ultrasonic spectra of
2:2 valent salt solutions seems to rely on a slightly incorrect background absorption.
Evidence for the existence of the outer-outer sphere complex may be obtained from
consistency of relaxation parameters, measured as a function of salt concentration,
with the kinetic relations [64].
Recently an alternative model for the description of ultrasonic spectra has been
proposed [63] in which the low frequency Debye-type relaxation in the spectra of 2:2
valent electrolyte solutions is furtheron assigned to the formation of inner-sphere