Oscillations, Waves, and Interactions - GWDG

Multistep association of cations and anions 337
Figure 2. Real part ɛ ′ (ν) and negative imaginary part ɛ ′′ (ν) of the complex dielectric
spectrum of water at 25 ◦ C [43]. Permittivity data from the literature [44,45] are presented.
Lines are graphs of Eq. (3) with parameter values from a regression analysis: ɛ (∞) =
5.2, ɛ (0) = 78.35, and τ = 8.27 ps [46].
A complementary situation exists in the ultrasonic spectrometry. Coupling of compressional
waves to shear motion and, to lower extent, to heat conduction results in
energy dissipation which manifests itself in the absorption coefficient by a contribution
proportional to ν 2 if the shear viscosity and thermal conductivity themselves
are independent of ν [49]. In the commonly used format, in which the absorptionper-wavelength,
αλ, is considered as a function of frequency, energy dissipation by
shear viscosity and thermal conductivity add an asymptotic high-frequency term Bν,
with B independent of ν. An example for an ultrasonic spectrum is given in Fig. 4,
where, along with the total absorption-per-wavelength, αλ, the excess absorption is
displayed,
(αλ)exc = αλ − Bν . (6)
The (αλ) exc data again follow a Debye-type relaxation function
(αλ)exc = Aωτ
1 + ω 2 τ 2
with discrete relaxation time τ and with amplitude A.
The background contribution restricts ultrasonic spectrometry at high frequencies.
Additionally, the wavelength λ of the sonic field becomes so small (λ=150 nm at
10 GHz, water, 25 ◦ C) that, at even higher frequencies, the use of continuum models
might be questioned.
(7)