The electrical properties of amorphous polymers described by a modified variable-range hopping model

The d.c. conductivity σ_dc and the thermopower S of a number of polyacene quinone radical polymers obey the relationship σ_dc = σ_o exp (-T_o/T) ^{1 3} and S/T = a+bT^{- 1 3}, typical for two-dimensional variable-range hopping. The results can be explained by Mott's model modified, however, by allowing for a linearly varying density of states near the Fermi level, and by taking into account the form of the wave function of the localized states. Special attention is paid to the prefactor σ_o which contains important hopping parameters, such as a frequency factor ν_o, usually assumed to be not higher than a typical phonon frequency (∼ 10¹³ s^-1). The original calculation of Miller and Abrahams (MA) of the hopping rate, however, gives ν_o values ranging from 10¹⁶ to 10²¹ s^-1. For the PAQR polymers reasonable estimates of the parameters are obtained when using MA expressions adapted for two-dimensional systems.