Hopping rate, self-exchange reaction

Most of the redox centers in a polymer film cannot rapidly come into direct contact with the electrode surface. The widely accepted mechanism proposed for electron transport is one in which the electroactive sites become oxidized or reduced by a succession of electron-transfer self-exchange reactions between neighboring redox sites [22]. However, control of the overall rate is a more complex problem. To maintain electroneutrality within the film, a flow of counterions and associated solvent is necessary during electron transport. There is also motion of the polymer chains and the attached redox centers which provides an additional diffusive process for transport. The rate-determining step in the electron site-site hopping is still in question and is likely to be different in different materials. 

At the microscopic level, polaron hopping can be viewed as a self-exchange electron-transfer reaction where a charge hops from an ionized oligomer or chain segment to an adjacent neutral unit. In the framework of semiclassical Marcus theory, the electron-transfer rate is written as... 

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