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

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^α-1, 0<α<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 α~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 α~0.1, providing fairly direct evidence that non-Gaussian diffusion of electrons from shallow to deep traps underlies the t^α-1 dependence.