Theoretical model of electron scavenging in irradiated glassy media based on a tunnelling mechanism

Abstract

A simple theory of electron tunnelling to scavenger sites in radiolysed glasses is developed. A time-dependent radial density function of scavengers around central electrons is derived and used to construct a time-dependent rate constant [k(t)]. Values of k(t) for typical parameters are calculated by numerical integration. By approximating the radial density function to a rectangular step function, an analytical expression for the rate constant is obtained which agrees well with the exact results for times greater than 10^–8 s. An analytical expression for the dependence of the electron concentration on time and on scavenger concentration is also derived. These equations are tested using available experimental data, and sensible values are found for the depth of the electron trap in methyltetrahydrofuran and 6 mol dm^–3 NaOH glasses. Scavenging by NO^–₃ in 6 mol dm^–3 NaOH presents difficulties, which possibly arise from the anisotropy of the nitrate ion.