Journal of Physical Chemistry B, Vol.101, No.39, 7766-7772, 1997
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 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.