Statistics of solubilizate distribution and its application to pyrene fluorescence in micellar systems. A concise kinetic model

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Abstract
A statistical model describing the distribution of solubilizate molecules in micellar systems is developed on the basis of their kinetic interaction with the host aggregates. The distribution function obtained corresponds to a Poisson law governing the occupancies of individual micelles by quest molecules. This model provides the basis for the development of a theory which treats the behavior of pyrene fluorescence emission in micellar systems. Solutions of this fluorophore in cetyltrioxyethylene sulfate micelles were examined experimentally both by steady‐state and time‐resolved fluorescence techniques. The results obtained are in excellent agreement with the predictions of the model. From this analysis the rate constant for the intramicellar encounter of two pyrene molecules was derived as ke=9×106 s−1. The aggregation number of CTOES was determined as 96 surfactant molecules/micelle.