Violation of the Exponential-Decay Law at Long Times

First-principles quantum mechanical calculations show that the exponential-decay law for any metastable state is only an approximation and predict an asymptotically algebraic contribution to the decay for sufficiently long times. In this Letter, we measure the luminescence decays of many dissolved organic materials after pulsed laser excitation over more than 20 lifetimes and obtain the first experimental proof of the turnover into the nonexponential decay regime. As theoretically expected, the strength of the nonexponential contributions scales with the energetic width of the excited state density distribution whereas the slope indicates the broadening mechanism.

Figure 1

Normalized prompt and delayed emission spectra as indicated after excitation at 3.5 eV, of polyfluorene and Rhodamine 6 G dissolved at ${10}^{-5}$ by weight in toluene and ethanol, respectively. The insets show the chemical structures with $R=2,6\mathrm{\text{−}}\mathrm{\text{ethylhexyl}}$.

Figure 2

Corresponding double logarithmic fluorescence decays of the emissions shown in Fig. 1. Exponential and power law regions are indicated by solid lines and the emission intensity at time zero has been normalized.