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 diffusion equations for excited and quencher molecules with appropriate initial and boundary conditions. The diffusion equations 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.

Fluorescence-quenching studies and temperature dependence of fluorescence quantum yield, decay time and intersystem crossing activation energy of TPB

“…(3) for all the solvents and the values are given in Table 3. The values of p are less than unity for all the solvents, indicating reaction of quenching that is not solely controlled by material diffusion and may depend on other processes [16]. This fact is also observed by Table 3 The values of inverse of viscosity (Z À1 ), slope (k q t o ), quenching rate parameter k q , and quenching probability per encounter 'p'.…”

“…The probability of quenching per encounter 'p' and frequency of encounter 'k d ' are given by given by [16] …”

Kinetics of Diffusion-Controlled Reaction between Chemically Asymmetric Molecules. I. General Theory

“…The same relation can be derived also from the discussions of one-dimensional random walks with partially absorbing walls given by Goodrich ll and Lehner. 12 By considering the balance between the diffusional flow of B*'s to a surface element and their reaction with A *, it can be shown that the boundary condition for our heterogeneous case is of the same form (2) where c is the density distribution function of B*, and the maximum value ~f k can be D/jJ., i.e., it may grow effectively to infinity. Rotational-diffusional flow does not make anv direct contribution to Eq.…”

“…As a simple example, the reaction of two types of molecules A and B has been considered for which the specific rate cons tan t k (fh, (2 ) can be expressed as a product of two functions…”

Diffusion-controlled reaction on a one dimensional lattice: Dependence on jump and reaction probabilities

“…As early as 1962 Burton and his coworkers [15,16] had constructed a pulsed radiolysis system which allowed diffusion-limited reactions to be followed on the nanosecond time scale. We suggest that, through pulsed radiolysis, it might be possible to generate reactive particles in situ in a pore or channel, and to follow their reactions.…”