Interplay of electron hopping and bounded diffusion during charge transport in redox polymer electrodes

Redox polymer electrodes (RPEs) have been prepared both by attachment of random copolymers of hydroxybutyl methacrylate and vinylferrocene (poly(HBMA-co-VF)) to carbon substrates by grafting either "to" or "from" the substrate surfaces, and by impregnation of porous carbon substrates with redox polymer gels of similar composition. An observed linear dependence of peak current on the square root of the applied voltage scan rate in cyclic voltammetry (CV) led to the conclusion that the rate controlling step in the redox process was the diffusive transfer of electrons through the redox polymer layer. The variation in the peak current with increasing concentration of the redox species in the polymer indicated that the electron transport transitioned from bounded diffusion to electron hopping. A modified form of the Blauch-Saveant equation for apparent diffusivity of electrons through a polymer film indicated that bounded diffusion was the dominant mechanism of electron transport in RPEs with un-cross-linked polymer chains at low concentrations of the redox species, but, as the concentration of the redox species increased, electron hopping became more dominant, and was the primary mode of electron diffusion above a certain concentration level of redox species. In the cross-linked polymer gels, bounded diffusion was limited because of the restricted mobility of the polymer chains. Electron hopping was the primary mode of electron diffusion in such systems at all concentrations of the redox species.