Diffusion-reaction approach to electronic relaxation in solution. Exact solution for delta function sink models

Thermally-Activated, Delayed Fluorescence in O,B,O- and N,B,O-Strapped Boron Dipyrromethene Derivatives

A small series of boron dipyrromethene (BODIPY) dyes has been synthesized whereby the boron atom is constrained in a five-membered ring formed from either o-dihydroxypyridine or o-aminophenol. In the latter case, the amino group has been converted into the corresponding amide derivative so as to curtail the possibility for light-induced charge transfer from strap to BODIPY. These compounds are weakly emissive in fluid solution but cleavage of the strap, by treatment with a photoacid generator, restores strong fluorescence. Surprisingly, the same compounds remain weakly fluorescent in a rigid glass at 80 K where light-induced charge transfer is most unlikely. In fluid solution, the fluorescence quantum yield increases with increasing temperature due to a thermally activated step but does not correlate with the thermodynamics for intramolecular charge transfer. It is proposed that the strap causes rupture of the potential energy surface for the excited state, creating traps that provide new routes by which the wave packet can return to the ground state. Access to the trap from the excited state is reversible, leading to the delayed emission. Analysis of the temperature dependent emission intensities allows estimation of the kinetic parameters associated with entering and leaving the trap.

Lévy flights in the presence of a point sink of finite strength

In this paper, the absorption of a particle undergoing Lévy flight in the presence of a point sink of arbitrary strength and position is studied. The motion of such a particle is given by a modified Fokker-Planck equation whose exact solution in the Laplace domain can be described in terms of the Laplace transform of the unperturbed (absence of the sink) Green's function. This solution for the Green's function is a well-studied, generic result which applies to both fractional and usual Fokker-Planck equations alike. Using this result, the propagator and the absorption-time distribution are obtained for free Lévy flight and Lévy flight in linear and harmonic potentials in the presence of a delta function sink, and their dependence on the sink strength is analyzed. Analytical results are presented for the long-time behavior of the absorption-time distribution in all three above-mentioned potentials. Simulation results are found to corroborate closely with analytical results.