At 25 °C the ultrasonic absorption spectra between 100 kHz and 2 GHz, the sound velocities, and the shear viscosities of aqueous solutions of n-heptylammonium chloride have been measured at the critical micelle concentration (cmc) and also at concentrations above the cmc. The term cmc denotes a concentration range rather than a well-defined value here. The absorption spectra reveal two relaxation regions, one at frequencies around a few megahertz and the other one at around 1 GHz. The low-frequency relaxation may be attributed to the exchange of surfactant monomers between the micelles and the suspending phase. In contrast to the theoretical predictions from the accepted models of the kinetics of micelle formation, however, the low-frequency process is subject to a relaxation time distribution. The width of the distribution function is particularly large near the cmc. Close to the cmc, in addition, the relaxation time and relaxation amplitude do not follow the theoretically predicted dependences upon concentration. In conformity with previous findings, the high-frequency relaxation seems to be partly due to the mechanism of chain isomerization in the micellar cores. However, estimations show that the process of rotational isomerization cannot fully account for the measured facts. It is assumed that, at least at solute concentrations in the cmc region and slightly above the cmc, a variety of geometrically less defined supramolecular structures exist in the solutions of amphiphiles rather than globular micelles that follow a comparatively narrow size distribution. This idea is supported by the shear viscosity data.

The Teubner−Kahlweit theory, which, based on the Aniansson−Wall model of micelle formation, relates the kinetics of stepwise association to the ultrasonic absorption spectrum, has been extended in order to better apply to solutions of short-chain surfactants. In doing so the size distribution of micellar aggregates has been obtained from reasonable assumptions on the forward and backward rate constants of the reaction scheme representing the series of chemical equilibria in the system under consideration. In conformity with experimental spectra, it is found that an ultrafast relaxation process exists that reflects the exchange of monomers between oligomers and the suspending phase. Also in agreement with the characteristics of measured spectra, the slow relaxation process found with long-chain surfactant systems is missing. This turns out to result from the comparatively high oligomer concentration in short-chain surfactant solutions. The fast process of the original model of micelle formation is found to be subject to a relaxation time distribution. Particularly in the cmc range, however, the width of the predicted ultrasonic spectra is nevertheless distinctly smaller than measured. It is suggested that this still remaining discrepancy results from the assumption of discrete rate constants, which may be inappropriate with micelles of rather small size.

Ultrasonic resonator cells for liquid attenuation and velocity measurements below 1 MHz with one planar and one concave piezoelectric transducer are described. Such cells with a limited sample volume are needed for broad band ultrasonic relaxation spectrometry and for studies in chemical reaction kinetics, particularly for frequencies below 200 kHz. Measurement and evaluation procedures are described and an example of a broad band spectrum is shown.

Ultrasonic attenuation spectra between 100 kHz and 500 MHz, mutual diffusion coefficients and shear viscosities of the triethylamine/water mixture of critical composition have been measured at various temperatures near the critical one. The broadband ultrasonic spectra reveal two relaxation terms with discrete relaxation time and a term that is subject to a broad relaxation time distribution. The former have been discussed to be due to a protolysis reaction and a structural isomerization. The latter term has been evaluated in the light of the Bhattacharjee–Ferrell dynamic scaling theory, relating the sonic spectrum to fluctuations in the local mixture concentrations. The relaxation rate of the Bhattacharjee–Ferrell term follows power law behavior. However, its amplitude (Γ0=45×109 s−1) is considerably smaller than that derived from the dynamic light scattering and shear viscosity measurements (Γ0=96×109 s−1). This result is assumed to be due to a shear viscosity relaxation. Using density and heat capacity measurements from the literature, the adiabatic coupling constant g of the triethylamine/water system has been derived from the amplitude of the Bhattacharjee–Ferrell term in the ultrasonic spectra and from a thermodynamic relation as well. Again, a discrepancy is found. The ultrasonic spectra yield g=0.19, whereas g=0.98 follows otherwise. This difference in the g values is taken as an indication of the limitations of the Bhattacharjee–Ferrell model. It had been derived assuming a small amplitude in the singular part of the heat capacity, a precondition which is clearly not fulfilled with the triethylamine/water system.

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.