Charge transfer in paraffinic hydrocarbons under the influence of external electric fields

Abstract

Two papers treating electrical conductivity in organic solids, by McCubbin and Eley and Willis, are discussed and the approaches there in modified and combined in a first-order time-independent perturbation treatment of electrical conductivity in the paraffinic hydrocarbon octacosane (C₂₈H₅₈). Extrinsic conductivity is assumed, electrons moving within one-dimensional wells of width comparable to the length of the molecule, and of depth slightly less than its ionization potential. The electrons tunnel through potential barriers between neighbouring molecules. Electron mobilities in the range 50–100 cm²/V s are deduced for paraffins containing twenty or more carbon atoms and for polymers such as polyethylene. This result agrees with an estimate of hole mobility in polyethylene published by McCubbin and Gurney using conventional band theory. Since tunnelling and hopping models of conduction are generally considered to apply when carrier mobilities do not exceed approximately 1 cm²/V s, it would therefore appear that, in the absence of reliable experimental mobility data for polymers, the charge transfer properties of such materials are more properly described in terms of the familiar energy-band formation concepts.