Kinetics of Diffusion-Controlled Processes in Liquids. Theoretical Consideration of Luminescent Systems: Quenching and Excitation Transfer in Collision

Abstract

The over‐all behavior of reacting particles in solution is determined both by specific molecular properties and by probability of encounter. This paper presents an examination of the effect of the details of diffusion and locally inhomogeneous distributions on the over‐all behavior of a system of reacting particles both for steady‐state conditions and for the decay (or relaxation) phenomena subsequent to creation of an initial condition. The problem is formulated for the quenching of excited molecules in solution in terms of diffusionequations for excited and quencher molecules with appropriate initial and boundary conditions. The diffusionequations are solved for a completely determined, but otherwise arbitrary, initial distribution of quencher molecules around an excited molecule and two sets of boundary conditions: the so‐called Smoluchowski and ``radiation'' boundary conditions. The resultant equations give, in their turn, expressions for decay of excited molecules for initial random distributions following instantaneous excitation and, by the use of superposition integrals, for initial distributions following any form of excitation. Explicit expressions for the rise and fall of excited molecule concentrations result. The techniques are extendable in principle to a variety of essentially different processes.