Relating Electrical Properties of Highly Disordered Insulating Materials via the Dispersion Parameter*

Relations between electrical properties, critical transitions (CT), and the dispersion parameter α for highly disordered insulating materials (HDIM) are presented. The dispersion parameter is often defined as the thermal energy (low field regime) or field energy (high field regime) scaled by a material-dependent characteristic energy (energetic width of DOS within mobility gap). For dispersive transport, 0<α<1; α=1 defines a CT in both temperature (T) and electric field. A kink is observed in double logarithmic current-time plots measured at constant voltage, similar to Scher-Montroll curves for pulsed photoconductivity. Dark conductivity measurements transition from T^-1 to T^-1/4 dependence on a double logarithmic current-T plot at the temperature CT, indicative of a transition from multiple trapping to variable range hopping dominated transport. A field CT is apparent in pulsed electroacoustic measurements of charge distributions where normal transport is observed at high fields, corresponding to the onset of normal transport and electrostatic breakdown. As an example of a prototypical HDIM, various measurements are presented for low-density polyethylene.