PHOTOCHEMICAL-REACTIONS ON THE SURFACE OF A CIRCULAR DISK - A THEORETICAL APPROACH TO KINETICS IN RESTRICTED 2-DIMENSIONAL SPACE

Kinetics of decay of excited donor molecules B by static and diffusio n-induced electron and energy transfer to accepters (A) in restricted two-dimensional space, as described by the surface of a circular disk (circle), have been examined. In the first instance, an analytical sol ution is given to outline the decay of B by a static distance-depende nt electron and energy transfer process to some random accepters. Resu lts show that luminescence decay of B on a restricted two-dimensional surface is slower than a similar decay on an infinite surface, with t he difference between the kinetics in restricted space and infinite sp ace increasing with increasing observation time. The decay of B molec ules on diffusion approach of reagents along the two-dimensional disk surface is exponential at sufficiently long times, a kinetic behavior that contrasts with the long-time behavior of diffusion-limited decay processes taking place on an infinite surface where the rate constant does not achieve an asymptotic value even for long times, Decay proces ses of excited triplet molecules of B by triplet-triplet (T-T) annihi lation on the restricted circle were also examined. These differ princ ipally from those of luminescence quenching by the fact that the conce ntrations of surface-reacting species are equal. An approximate soluti on to T-T annihilation by static interactions is described on the basi s of the average reagent concentration approximation and with the assu mption that, in the course of the annihilation process, the triplet mo lecules are always randomly distributed at the prevalent mean surface concentration. The decay kinetics described by the analytical expressi ons derived agree fairly well with the results from Monte Carlo simula tions. Kinetic expressions for diffusion-induced annihilation on the t wo-dimensional restricted surface are also described using an infinite space approximation for the rate constant; Monte Carlo simulations in dicate that the resulting kinetic solution is useful to analyse the de cay process on the circular disk provided that the effective radius of the annihilation event does not exceed one tenth the disk radius.