The mobility of electrons in simple insulating fluids as a percolation problem

The mobility of electrons injected into insulating fluids is extraordinarily sensitive to the density of the fluid. However, the process of understanding this fact is complicated by the availability of a large number of potentially important factors capable of influencing the electron; everything from single atom–electron scattering considerations to Anderson localization to polaron formation could all be relevant in principle. We show in this paper that the behavior of the mobility edge (the minimum electron energy needed for conduction) can be calculated within a reasonable accuracy, for the noble gas fluids, without invoking any mechanism beyond a kind of classical percolation. The model proposed is actually a semiclassical one that takes into account the local zero-point energy of the electron in the definition of an effective potential surface, but the mobility edge itself is simply identified as the height above the potential surface that permits a connected wave function to span the system—a purely geometrical calculation. The results so obtained are in good agreement with both electron-mobility experiments in He and with photoinjection experiments in Ar, Kr, and Xe. During the course of the development, we also arrive at some conclusions about the usefulness of the so-called Zallen filling fraction as a criterion for percolation in liquids.