ON THE KINETICS OF THE FORMATION OF SMALL MICELLES .2. EXTENSION OF THE MODEL OF STEPWISE ASSOCIATION

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 bett er 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 reactio n scheme representing the series of chemical equilibria in the system under consideration. In conformity with experimental spectra, it is fo und that an ultrafast relaxation process exists that reflects the exch ange of monomers between oligomers and the suspending phase. Also in a greement with the characteristics of measured spectra, the slow relaxa tion process found with long-chain surfactant systems is missing. This turns out to result from the comparatively high oligomer concentratio n in short-chain surfactant solutions. The fast process of the origina l model of micelle formation is found to be subject to a relaxation ti me distribution. Particularly in the cmc range, however, the width of the predicted ultrasonic spectra is nevertheless distinctly smaller th an measured. It is suggested that this still remaining discrepancy res ults from the assumption of discrete rate constants, which may be inap propriate with micelles of rather small size.