A New Approach to the Analysis of the Thermal Equilibration of Optically Excited States

Mechanisms and rates of relaxation of optically excited states are important in the study of almost every material. They often determine the efficiency of some desired photoeffect and usually carry interesting information about the excited states themselves. Many fluorescent systems have been analyzed on the basis of the "universal relationship" introduced by Kennard and by Stepanov (K-S). These analyses frequently claim experimental confirmation of the applicability of the fundamental K-S assumption, namely, that the manifold of states associated with an excited electronic state have reached thermal equilibrium by the time of emission. The K-S prediction is that a certain function F(v) will be linear in v with slope h/kBT, where T is the ambient temperature. A more precise look at the K-S function, reported here, reveals the possibility of extensive lack of excited-state thermal equilibration. The spectral K-S temperature T * (v) = (h /kB)/ (d~/dv) is introduced, and it is found to be seldom close to T in a sampling of spectral data from various systems. While T ( V ) does not necessarily represent an actual molecular temperature, its variation can be modeled in broadband systems by I assuming coupled emitting and absorbing submanifolds that 1 are demonstrably far from the equilibrium envisaged by KenI nard and Stepanov.