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 $t^{\alpha -1\mathrm{}}$, $0<\mathrm{}\alpha <1\mathrm{}$, 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 $\alpha \sim 0.1$ 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 $\alpha \sim 0.1$, providing fairly direct evidence that non-Gaussian diffusion of electrons from shallow to deep traps underlies the $t^{\alpha -1\mathrm{}}$ dependence.