Discerning aggregation in homogeneous ensembles: A general description of photon counting spectroscopy in diffusing systems

In order to discern aggregation in solution, we present a quantum mechanical analog of the photon statistics from fluorescent molecules diffusing through a focused beam. A generating functional is developed to fully describe the experimental physical system as well as the statistics. Histograms of the measured time delay between photon counts are fit by an analytical solution describing the static as well as diffusing regimes. To determine empirical fitting parameters, fluorescence correlation spectroscopy is used in parallel to the photon counting. For expedient analysis, we find that the distribution’s deviation from a single Poisson shows a difference between two single fluor monomers or a double fluor aggregate of the same total intensities. Initial studies were performed on fixed-state aggregates limited to dimerization. However preliminary results on reactive species suggest that the method can be used to characterize any aggregating system.