Classical Aspects of Energy Transfer in Molecular Systems

Abstract

The decay time of the luminescence of a molecule S in front of a metal mirror depends markedly on its distance from the mirror. This phenomenon is quantitatively explained by considering the radiation field of this dipole, given by Hertz classical equation. This field arrives at the molecule, after being reflected at the mirror, with a retardation of the order of 10⁻¹⁵ sec. The decay time of the luminescence depends on the phase shift produced by this retardation, and thus on the ratio of the distance of the oscillator from the mirror, and the wavelength of the emitted light. By measuring the distance dependence of the decay time of the luminescence this retardation effect can be studied. In quantum‐mechanical terms the phenomenon can be described as being due to a stimulation or inhibition of the emission of the light quantum. In contrast to the known cases of stimulated emission, the stimulating field is the radiation field of the emitter quantum itself. The energy transfer from an excited molecule S to an acceptor A can be treated in a similar manner by considering the phenomenon as a retardation effect. In classical terms the field of S induces A to oscillate, and the induced field of A arriving at S slows down this oscillator. Simple equations are given for the energy transfer from an excited dipole or quadrupole, and for a row of many dipoles, oscillating in phase, to a weakly absorbing acceptor layer. The latter case is considered as a model for a J‐aggregating dye and by comparison with experimental data conclusions concerning the size of a $J$ aggregate are drawn.