Quasi-Three-Dimensional Diffusion in Membranes

The concept of quasi-three-dimensionil diffusion in membranes is illustrated by pyrene exclmer fonnation. Although excimer formation is not strictly quenching, the monomer emission is decreased by diffusive encounters of excited memomers with ground-atate monomers. Hence, the quenching of the monomer emission is described by Stem-Volmer kinetics. 

In these expiessioiis, [P] is the pyrene concentration. Cm and Ce are constants reflecting the senahvity of the instrument at each wawlengtfa. rjf and Fe are the radiative decay rates of the monomer and the excimer. respectively, and and are the nonradiative decay rates of the monomer 

If lifetime measurements are availaUe, it is not necessary to use the excimer-to-monomer ratios. TMs can be seen by considering the monoiner lifetime at low concentrations, where excimer formation does not occur (Tqm). and in the presence of excimer formation (Tm), 

the pyrene monomer lifetime is decreased accord, ing to the Stem-Volmer equation, where the quencher concentration is replaced by the ground-state pyrene monomer concentration. 

A disadvantage of the use of pyrene is that the extent of excimer formation depends on the bulk concentration of pyrene in the membranes. For this reason, several groups have synthesized covalently linked pyrenes or pyrene-amine conjugates. Examples of such molecules are 

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