Two-state model for sub-exponential fluorescence

We outline a theory of fluorescence in systems where the decay of the fluorescence takes place more slowly than exponential, a behavior we refer to as 'sub-exponential'. We develop a two-state model for the fluorescence where the two states are the trapped state and the fluorescing level. The sub-exponential behavior is associated with a distribution of detrapping rates. Asymptotic inverse power-law behavior of the fluorescence, i.e., t(-delta), arises from a distribution that varies near the origin as the delta - 2 power of the detrapping rate. Stretched exponential behavior, where the asymptotic time dependence of the fluorescence is dominated by the factor exp[ - (t/tau)(beta)], 0 < beta < 1, is associated with a steep but continuous decrease in the density of transition rates. A one-parameter thermal activation model is introduced in which the distribution of detrapping rates arises from a distribution of activation energies. Power-law behavior of the fluorescence is associated with an exponential decrease in the activation energy distribution at high energies, while stretched exponential dynamics reflects an even faster decrease. The thermal activation model is used to make predictions about the temperature dependence of the exponents characterizing the fluorescence decay. Possible experimental tests of the theory are discussed. (C) 2000 Elsevier Science B.V. All rights reserved.