Theoretical models for electron conduction in polymer systems—II. Tunnelling coupled with guided diffusion as a mechanism of electron transport in the conducting polymer systems

Abstract

A mechanism is proposed for electron transport in inhomogeneous systems in which the dimensionality of space where diffusion or hopping takes place can be reduced. Instead of bringing an electron to a small target (physical trap or a localized hole) by probing three-dimensional space the mechanism reduces the process to a sequence of fast processes in one- or two-dimensional subspaces. The model is applicable to the inhomogeneous media of fibre-like structures. We assume that the mobile charge carriers occupy the quasi one-dimensional, conducting polymers. The polymer fibres are separated by the non-conducting regions which are accessible for electrons only by quantum-mechanical tunnelling. The three-dimensional tunnelling of the electron to its target is thus reduced to the fast one-dimensional diffusion along the polymer chain coupled with the two-dimensional tunnelling from the polymer to the target. This mechanism was assumed as a basis for theoretical calculations in two cases. The first case corresponds to the electron reaction with homogeneously-distributed physical traps. The expressions for the trapping rate constant and the electron survival probability as functions of time were derived. The second application of the model provides the description of the electron-hole recombination in pulse-irradiated columnar aggregates of peripherally octa- n-alkoxy-substituted phthalocyanines. The charge recombination occurs via intercolumnar electron tunnelling through the hydrocarbon mantle coupled with free movement of charge carriers along the phthalocyanine cores of the columns. The carrier survival probability was calculated as a function of time.