Redox migration mechanism of charge transport in molecularly doped polymers

Abstract

Abstract A simple model of hopping transport in a molecularly doped polymer is described based on a small electric-field perturbation of diffusional (random walk) electron self-exchange reactions in the solid state. A master expression is derived which quantitatively accounts for the electrical field, temperature and concentration dependence of the hole mobility in the N,N′-diphenyl-N,N′-bis(3-methylphenyl)-[1,1′-biphenyl]-4,4′-diamine/polycarbonate system in terms of fundamental electron exchange parameters employed in modern (semi-classical) electron-transfer theory. Charge mobility which is simply related to electron hopping between neighbouring oxidized/reduced sites is assumed and shown to be normally thermally activated. The electric-field dependence of mobility is derived by modifying the zero-field Arrhenius rate expression for charge diffusion in a manner analogous to the derivation of the overpotential (electric field) dependence of charge transfer at an electrified interface. The intersite distance dependence of the mobility arises from the pre-exponential factor A′. Predictions of the model are an exponential field dependence of mobility at high fields, field-independent mobility at low fields, normal Arrhenius behaviour, decreasing activation enthalpy with increasing field, and an exponential decrease in mobility with increasing intersite distance. The free energy of activation for the elementary electron exchange reaction for this system at zero field is 0·3 eV while the inner (small molecule) and outer-sphere (medium) contributions to the overall free energy of activation are estimated, respectively, to be 0·19 and 0·13eV at 80wt%.