Oscillations, Waves, and Interactions - GWDG

392 U. Kaatze and R. Behrends
Figure 23. Graphs of the scaling functions (Eq. (61)) of the Bhattacharjee-Ferrell (BF),
Folk-Moser (FM), and Onuki (On) theory. Arrows indicate the half-attenuation frequencies
[107].
the scaling function at its half-attenuation frequency. Graphs of the scaling functions
from the three theoretical models are shown in Fig. 23. The corresponding parameter
values are ΩBF 1/2 = 2.1, ΩFM
1/2 = 3.1, and ΩOn
1/2 = 6.2, as well as nBF = nOn = 0.5 and
nFM = 0.635 [107].
Recently a variety of binary mixtures has been studied in order to find out which of
the theoretical scaling functions fits best to the experimental findings. For these investigations
systems with an as simple as possible background part in the attenuationper-wavelength
spectra have been chosen because interferences of the critical dynamics
with noncritical processes are largely avoided thereby [108–114]. The scaling function
has been directly calculated from the experimental data using the relation [99]
F (Ω) = α c λ(ν, T )/α c λ(ν, Tc) . (62)
The relaxation rate Γ, required for the determination of F (Ω), has been obtained
from dynamic light scattering experiments, yielding the mutual diffusion coefficient,
and shear viscosity measurements. Considering effects of the crossover from Ising
to mean field behaviour the shear viscosity ηs has been evaluated in terms of the
dynamic scaling theory [115], which predicts
ηs(ɛ) = ηb(ɛ) exp(ZηH) , (63)
with the universal critical exponent Zη of the shear viscosity (Zη = 0.065 [116,117]),
with the background viscosity
� �
Bη
ηb(ɛ) = Aη exp , (64)
T − Tη
and with the crossover function H = H(ξ, qc, qD), depending upon the fluctuation
correlation length ξ and on two cutoff wave numbers qc and qD. The analytical form