Determination of micellar aggregation numbers in dilute surfactant systems with the fluorescence quenching method.

This work addresses the problem of determining micellar aggregation numbers for dilute ionic surfactant systems by means of the time-resolved fluorescence quenching method. We argue that the use of quenchers that are themselves surfactants gives us two advantages. First, the altering of the micelles caused by the solubilization of quencher molecules is minimized. Second, the distribution of the quencher between the micelles and the aqueous subphase can be obtained. The latter point is particularly important for the case of dilute micellar systems and when the micelles are adsorbed at interfaces or associated with polymers. We describe a method to obtain the partitioning of the quencher for various surfactant/quencher combinations. The method is based on a detailed thermodynamic model of mixed micelles supported by Poisson-Boltzmann cell model calculations. It is shown that ideal mixing of surfactant and quencher in the micelles simplifies the analysis of effects related to polydispersity and probe distribution among the micelles. The method is applied to quaternary ammonium surfactants, both mono- and divalent, with various chain lengths, using the corresponding alkyl pyridinium ions as quenchers. Aggregation numbers at concentrations close to the critical micelle concentration (cmc) are presented and discussed.