Smoluchowski equation description of solute diffusion dynamics and time-dependent fluorescence in nanoconfined solvents

The diffusion dynamics and time-dependent fluorescence of a model dye molecule dissolved in CH3I, CH3-CN, and CH3OH solvents confined in nanoscale cavities and pores of 20-30 angstrom diameter have been modeled using a Smoluchowski equation approach. The effects of the confining framework geometry (spherical or cylindrical) and size have been investigated. The two-degree-of-freedom free-energy surfaces for the dye molecule ground and excited states are constructed from one-dimensional free-energy curves in the solute position and model force constants for a collective solvent coordinate. Multiple time scales are found in the solute diffusion after excitation and in the time-dependent fluorescence. The origins of these time scales can be understood in terms of solvent reorganization and dye molecule diffusion. The results indicate that the Smoluchowski equation approach has promise for describing time-dependent fluorescence dynamics, and ultimately reaction dynamics, in a wide variety of confined solvent systems.