DIFFUSION REACTION IN RESTRICTED SPACES OF SPHERICAL-SYMMETRY - SURFACE QUENCHING OF LUMINESCENCE

The dynamics of bimolecular diffusion reaction in spherical microsystems is considered by solving Smoluchowski's equation. The results are presented in the format of luminescence quenching experiments. The model allows an inner reactant, a lumophore, to diffuse about inside the microsphere while an outer reactant, a quencher, is allowed only on the surface of the sphere where the reaction, not necessarily diffusion controlled, takes place. Two dimensionless variables describe the system's behavior completely. Simple analytical relations are derived for I0/I, the relative luminescence yield, and F(t), the luminescence intensity decay function. I0/I shows a simple dependence on the quencher concentration [Q], typically observed in systems where a certain fraction of lumophores are protected from quenching. F(t) shows multiexponential decay, which practically attains a single-exponential form [F(t) approximately exp(-t/tau(long))] when only less than 50% of the initial intensity has disappeared. An explicit expression for [Q] dependence of the long-time decay constant tau(long) shows the system has a finite lifetime even in the presence of an infinite quantity of quenchers. The experimentally observed behavior of luminescence quenching in surfactant micellar systems is contrasted with the theoretical results of this work, and the consequences of a Poissonian distribution of quenchers among micelles are discussed. Guidelines are presented for choosing the right lumophore in a given experimental system.