Kinetics of electron trapping reactions in amorphous solids; a non-Gaussian diffusion model

Abstract

Decay patterns of trapped electrons in aqueous glasses have been analyzed over the time span of more than eight decades in terms of a time-dependent "rate constant" of the form ${t}^{\ensuremath{\alpha}\ensuremath{-}1}$, $0<\ensuremath{\alpha}<1$, which can be derived from the long-tail hopping-time distribution of Scher and Montroll. The curve fitting of experiments in our model is quite satisfactory with $\ensuremath{\alpha}\ensuremath{\sim}0.1$ and with another adjustable parameter which depends on the trapping species and varies within one order of magnitude from one system to another. The time-dependent spectral shift for the absorption spectrum of trapped electrons can also be fitted by $\ensuremath{\alpha}\ensuremath{\sim}0.1$, providing fairly direct evidence that non-Gaussian diffusion of electrons from shallow to deep traps underlies the ${t}^{\ensuremath{\alpha}\ensuremath{-}1}$ dependence.