Dynamic scaling of the critical ultrasonic attenuation in binary liquids: Evidence from broadband spectrometry

Abstract

Between 200 kHz and 500 MHz, the ultrasonic attenuation spectrum of the ethanol/dodecane mixture of critical composition has been measured at various temperatures near the critical one. The measured broadband spectra are evaluated in light of the Ferrell-Bhattacharjee dynamic scaling theory. The experimental findings largely fit the theoretical spectral function if suitable crossover corrections are made using dynamic light-scattering data. The measured scaling function follows the predictions of the recent Folk-Moser renormalization-group theory even better. Combining our ultrasonic attenuation coefficient data with density data from the literature, the asymptotic critical behavior of the thermal expansion coefficient and of the specific heat has been determined and found consistent with the two-scale factor universality. The sonic attenuation data have also been evaluated to yield the adiabatic coupling constant g of the dynamic scaling theory. The unusually small absolute value |g|=0.1 resulted, in fairly good agreement with |g|=0.13 as following from thermodynamic data.

Monomer Exchange and Concentration Fluctuations of Micelles. Broad-Band Ultrasonic Spectrometry of the System Triethylene Glycol Monohexyl Ether/Water

“…With the C 6 E 3 /water system, however, even the Hill relaxation spectral function (eq 14) cannot adequately account for the high-frequency wing in the excess absorption spectrum at c > cmc (Figure ). In addition to the contribution that is due to the kinetics of micelle formation and decay, there seems to exist a broad-band background contribution as characteristic for critical systems. ,− …”

“…During the past years, the Bhattacharjee-Ferrell model, ,,, which is based on the dynamic scaling hypothesis, , has proven a satisfactory description of the sonic excess absorption of various binary liquids with miscibility gap . The Bhattacharjee−Ferrell spectral function R BF may be expressed as where the amplitude A BF is given by …”

“…Ultrasonic spectrometry has proven a powerful tool for the study of the kinetics of micelle formation. − In conformity with theoretical predictions, , Debye-type relaxation spectra are found for proper micelle systems. In contrast, ultrasonic spectra resulting from concentration fluctuations in critical binary mixtures exhibit a characteristic shape, − reflecting a broad continuous distribution of relaxation times. Broad-band ultrasonic spectrometry is thus a suitable method for the investigation of the micelle kinetics and of the fluctuations in the local micelle concentration of nonionic surfactant solutions.…”

Model of Noncritical Concentration Fluctuations in Binary Liquids. Verification by Ultrasonic Spectrometry of Aqueous Systems and Evidence of Hydrophobic Effects

“…Only recently the cross-over region between critical and noncritical systems has been considered both theoretically and experimentally. 1,2 (ii) Ultrasonic attenuation spectra of critical mixtures of associating liquids always show contributions with relaxation characteristics, in excess of the contribution predicted by existing theories of concentration fluctuations. 3,4 (iii) Rather unexpectedly, a multitude of binary aqueous systems exhibit a microinhomogeneous structure and display features of noncritical concentration fluctuations.…”

“…(i) Theoretical treatments of the dynamic behavior of critical systems is restricted to the close vicinity of a critical point. Only recently the cross-over region between critical and noncritical systems has been considered both theoretically and experimentally. , (ii) Ultrasonic attenuation spectra of critical mixtures of associating liquids always show contributions with relaxation characteristics, in excess of the contribution predicted by existing theories of concentration fluctuations. , (iii) Rather unexpectedly, a multitude of binary aqueous systems exhibit a microinhomogeneous structure and display features of noncritical concentration fluctuations. Among these systems are mixtures of water with monohydric alcohols, poly(ethylene glycol)monoalkyl ethers C i E j , tetraalkylammonium bromides, triethylenediamine, and derivatives of urea .…”