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5 Experimental Verification of Dynamic Scaling Theories and Discussions

5.5 Ultrasonic spectrometry

At frequencies f between 180 kHz and 500 MHz broad-band ultrasonic spectra of binary mixtures have been measured to verify non-existence of additional relaxation terms in the measuring range as well as to determine the background contribution (α/ f 2)bg. At three temperatures the ultrasonic absorption spectrum of the (NE-CH) mixture of critical com- position is shown in the homogenous phase in Fig.(5.11). In order to accentuate the low frequency part of the spectra, data are shown in the frequency normalized format

In this format the data approach asymptotically the frequency independent value (data extrapolated to frequencies far above the frequency range of measurements):

The constant frequency-independent contribution which is indicated in Fig.(5.11) has to be taken into account in the description of the ultrasonic spectra. Assuming, that the crit- ical fluctuations contribute additively to the ultrasonic spectrum, the spectral description of measured data can be displayed as a sum of the critical contribution Rc(f) = (αλ)c Eq.(4.16), governed by the dynamic scaling theory, and the background contribution (αλ)bg:

In Fig.(5.12) the broad band spectra of the critical mixture (n-PE-NM) at three temper- atures are shown. The strong increase of (α/f 2) data with decreasing frequency and approaching of the critical temperature, indicates the critical contribution to the spectra. Obviously the critical fluctuations contribute extensively to the sound attenuation spectra in the low frequency range. Therefore, for the purpose of verifying the dynamic scaling model, the low frequency behavior between 180 kHz and 1.8 MHz has been studied with more details. For measurements at those frequencies a plano-concave resonator method has been employed which enables α to be determined as a function of frequency and tem- perature with a minimum risk of effects from mechanical stress of the cell as T is varied. Examples of cavity resonator measurements are displayed in Fig.(5.13) for the systems (NE-3MP) and (n-PE-NM). The low frequency spectra demonstrate a non-linear increase of the sound attenuation coefficient α with decreasing f, caused by critical contributions. Unfortunately, due to this behavior the number of measurable data points decreases as Tc is approached, especially in the case of (n-PE-NM), for which the sound attenuation is

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