Distribution of surfactants in a nonideal mixed micellar system. Effect of a surfactant quencher on the fluorescence decay of solubilized pyrene

We calculate a distribution of the surfactants in nonideal mixed micelles of equal size, which is consistent with the regular solution expressions for the concentrations of the free surfactants in equilibrium with the micellar pseudophase. The distribution gives in particular the fraction of micelles, at given mean composition, which contains only the nonquenching surfactant. This is a quantity that is measured in fluorescence quenching experiments, using a surfactant quencher such as alkylpyridinium chloride, at low concentration, mixed with the main surfactant. In the time-resolved fluorescence quenching method, it is assumed that the distribution is Poissonian, and an apparent aggregation number is determined. The deviation of the apparent aggregation number from the true one is shown to increase linearly with the quencher concentration, at low concentrations, with the slope related to the interaction parameter from the regular solution theory. Experimental results from measurements with a nonionic surfactant and the cationic quencher are reported and compared with the predictions.