Fluctuations Near the Critical Micelle Concentration. II. Ultrasonic Attenuation Spectra and Scaling

Abstract

Based on a thermodynamic model of amphiphile solutions derived in the first part of the paper, the ultrasonic attenuation of such systems has been considered theoretically, including fluctuations of local concentrations and micelle sizes. At amphiphile concentrations smaller than the critical micelle concentration (cmc), scaling behavior in terms of the concentration distance to the cmc is predicted by theory, in fair agreement with experimental evidence. The scaling function in the sound attenuation below the cmc reveals the unsymmetric broadening in the spectra that clearly emerges from measurements when approaching the cmc. The shape of the scaling function corresponds to the experimental spectra of solutions with comparatively large cmc as well as with the relaxation spectral function of the unifying model of non-critical concentration fluctuations. Above the cmc, an additional relaxation term is predicted in correspondence with the Landau-Khalatnikov term in the sound attenuation of superfluid helium. This term is difficult to verify by measurements because, in the relevant frequency range, other processes may also contribute the ultrasonic attenuation spectra.