Diffusion-Controlled Quenching at Higher Quencher Concentrations

Abstract

A variational procedure is employed to establish rigorous upper and lower bounds on the rate of a diffusion‐controlled reaction, in which an excited species B^* is generated at a constant and uniform rate throughout a solution containing a quencher species A. De‐excitation is assumed to occur instantaneously whenever a B^* molecule has diffused to within a critical distance a of a quencher particle; the Brownian motion of the quencher itself is neglected. Results are obtained in terms of various statistical characterizations of the distribution of A particles in the solution. Explicit calculations have been carried out for the case where the quencher molecules exert no forces upon one another or upon the B^* species.