On Interpreting Fluorescence Measurements: What Does Thermodynamics Have To Say about Change in Micellar Aggregation Number versus Change in Size Distribution Induced by Increasing Concentration of the Surfactant in Solution?

Fluorescence techniques have been widely used for the determination of micellar aggregation numbers.' However, the interpretation of the fluorescence data and the consequent estimates for the micellar aggregation numbers are not always unambiguous. The results usually depend on both the type of experiments performed and the micellar models invoked for the data analysis. In an interesting recent study, Reekmans et aL2 employed dynamic fluorescence quenching to examine whether an increase in the concentration of the surfactant in solution will cause a growth in the size of the micellar aggregates or only a change in the size distribution and polydispersity of the micelles. Fluorescence decay measurements were made on the cationic surfactant cetyltrimethylammonium chloride (CTAC) using 1-methylpyrene as the fluorescence probe and cetylpyridinium chloride (C(Pyr)C) as the quencher. Eight different decay curves were obtained corresponding to differing values of quencher concentration, and all the decay curves were simultaneously analyzed using modified versions of the Infelta-Tachia model. Reference 2 provides the details of the experimental measurements as well as the methods of data interpretation. In carrying out the analysis, two different descriptions of the micelles were employed. In the first case, the micellar solution was assumed to be made up of aggregates of a single size. In the second case, the micelles were assumed to be polydispersed. For a given total surfactant concentration, a global fitting of the eight decay curves (each corresponding to a different quencher concentration) yielded the aggregation numbers and indices of size polydispersity for the two micellar models considered. A part of the results, obtained at 20 "C (summarized in Table I1 of ref 2), is shown in Table 1. The tabulated data (see results for either sample I or 11) reveal that when a monodispersed micellar model was assumed, the fluorescence decay curves were consistent with the interpretation that an increasing concentration of the surfactant causes an increase in the aggregation number. By definition, the size dispersion index is 0 for this case. When a polydispersed micellar model was assumed, the fluorescence decay measurements were consistent with the interpretation than an increasing concentration of the surfactant causes a decrease in the size polydispersity index while the weight-average aggregation number of the micelle remains practically a constant. In this paper, we show that the above interpretations of experimental measurements are not consistent with the general thermodynamic principles of self-assembly for both nonionic and ionic surfactants. In particular, if the micelles are all of a single size, then their size cannot increase significantly with increasing surfactant concentration. On the other hand, if the micelles are polydispersed, then the