Characterization of the Distribution of Pyrene Molecules in Confined Geometries with the Model Free Analysis.

Evidence is provided showing that global Model Free Analysis (MFA) of monomer and excimer fluorescence decays of pyrene dissolved in aqueous solutions of sodium dodecyl sulfate (SDS) provides the same structural and dynamic information on SDS micelles as the well-established Micelle Model (MM) does. Both MFA and MM were employed to characterize the quenching kinetics between dyes and quenchers located in surfactant micelles and the aggregation number of surfactant micelles. However, contrary to the MM, which assumes that dyes and quenchers distribute themselves among SDS micelles according to a Poisson distribution and react with a rate constant that is proportional to the number of reactants in a micelle, the MFA accomplishes this task without making any assumption about the process of pyrene excimer formation in SDS micelles. The ability of the MFA to retrieve accurately the molar fraction of pyrene molecules that are isolated in SDS micelles and do not form excimers was taken advantage of to establish that it equaled the Poisson probability of exciting micelles that contained a single pyrene. The molar fraction of isolated pyrenes could then be utilized to determine the aggregation number of the SDS micelles, and the rate constant of excimer formation between one excited- and one ground-state pyrene located inside a same micelle. Within experimental error, both the MFA and MM yielded the same micelle aggregation number and rate constant of excimer formation, with the MFA making no prior assumptions about the physical principles underlying the process of excimer formation contrary to the MM. The ability of the MFA to retrieve quantitative parameters providing structural and dynamic information about macromolecular systems with no prior knowledge about their architecture or labeling scheme implies that it can be applied to characterize a wide range of macromolecular architectures in solution.