Relation Between Fluorescence Decays and Temporal Evolution of Excited States

A differential equation system describing the temporal evolution of excited substates and fluorescence emission were tested using a DOPRI algorithm. The numerical solutions show that there is significant difference in the measurable parameters according to the type of connectivity among the excited substates. In the globally connected case, the fluorescence emission exhibits a double exponential behavior, and the first moment of the emitted spectrum decays with stretched exponential characterized by β < 1. In the diffusive case the fluorescence emission cannot be always fitted with double exponential, and the first moment of the emitted spectrum may decay with stretched exponential characterized by β> 1. Details of modeling and the possibilities of drawing conclusions are also presented. KEY WORDS: fluorescence decay; excited state relaxation; stretched exponential; numerical solution