Oscillations, Waves, and Interactions - GWDG

396 U. Kaatze and R. Behrends
Figure 28. Broadband ultrasonic attenuation spectrum of the triethyleneglycol monoheptyl
ether-water mixture of critical composition (C7E3-H2O, Y = 0.1) at 15 ◦ C displayed in both
common formats. Full lines are graphs of the relaxation function representing the spectrum,
dashed lines represent the Bhattacharjee-Ferrell critical term. The dashed-dotted line shows
the high-frequency contribution to the α/ν 2 values and the dotted line indicates the Hill
type relaxation term reflecting the fast monomer exchange of the surfactant system.
spectra can be analyzed in terms of a linear superposition of both relaxation terms, a
coupling between the fluctuations in the local concentration and the kinetics of micelle
formation seems to exist. An indication for interferences of the critical dynamics with
the micelle kinetics is the small value ΩBF 1/2 = 1 for the half-attenuation frequency in
the scaling function, which deviates considerably from the value ΩBF 1/2 = 2.1 as characteristic
for simpler critical mixtures (Sect. 4.2). Such interferences are also revealed by
the remarkable correlation between the maximum attenuation-per-wavelength value
(αλ) max
exc in a series of CiEj/H2O mixtures and the critical micelle concentration of
that system (Fig. 29). This correlation, which exists for a broad range of cmc values,
has stimulated a fluctuation controlled monomer exchange model [15]. Apart
from a critical demixing point, no noticeable fluctuations in the local concentrations
of micelles and monomers exist. Hence the micelle kinetics is governed by the
monomer exchange as predicted by the Teubner-Kahlweit-Aniansson-Wall model or
its extended version described before (Sect. 3.2). Approaching the critical demixing
point, diffusion controlled local fluctuations in the spatial distribution of micelles,
accompanied by fluctuations in the distribution of monomers, act a noticeable effect
on the molecular dynamics. Due to the law of mass action the monomer exchange
kinetics, via the rate equations, is largely governed by the fluctuations in the local
concentration of micelles. The coupling between concentration fluctuations and the
micelle formation/decay process suggests the linear superposition of relaxation terms
in the ultrasonic spectra as a first approximation. Strictly the theoretical model of
sonic attenuation should combine both molecular mechanisms in a comprehensive
treatment.