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5.5 Ultrasonic spectrometry

Figure 5.13: Ultrasonic attenuation spectra for mixtures of critical composition. Left Figure (NE-3MP): (◦), T=304.20 K; (▲), T=303.34 K; (△), T=302.20 K; (▽), T=301.78 K; (▼), T=301.34 K; (•), T ≈299.68 K = Tc; Right Figure (n-PE-NM): (◦), T=307.86 K; (▽), T=305.93 K; (△), T=303.98 K; (♦), T=303.03 K; (♦), T=302.57 K; (▼), T=301.70 K; (▲), T=301.41 K; (■), T= 301.30 K; (□), T=301.22 K; (•), T ≈300.97 K = Tc.

Due to effects of critical slowing down near the consolute point (xc,Tc) as well as the dramatically increasing sound attenuation as shown in Fig.(5.13) in the case of the binary systems (n-PE-NM) and (NE-3MP), only the high-frequency part f > 180 kHz of critical contribution to the ultrasonic spectra is obtainable from ultrasonic spectrometry. Hence, the verification of the characteristic relaxation rate Γ from the ultrasonic measurement is quite difficult. In the Section ”Strategies of verifying scaling function” (Sec. 5.1) it has been argued that there is no difference between the characteristic relaxation rate ob- tained from the dynamic light scattering and from the ultrasonic spectroscopy Eq.(5.1). Therefore, the determination of the characteristic relaxation rate Γ0(ε) from dynamic light scattering allows the reduced frequency Ω= 2π/Γ0εZ0˜ν to be calculated and to be used in the calculations of the scaling function data.

5.5.1 Scaling functions

In a previous section it was supposed that the Bhattacharjee-Ferrell scaling function FBF(Ω) fits best to the experimental ultrasonic measurement. In fact, this conclusion can be drawn only, when the other theoretical scaling functions, which have been pro- posed by Onuki or Folk and Moser (Section 4.3) are also considered. For this reason the experimental data have been evaluated with the aid of the quasi-universal empirical scal- ing function Fx(Ω), Eq.(4.23). A graphical representation in addition to the experimental data points for the systems (n-PE-NM) and (NE-3MP) of the three scaling functions for

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