Flux-force formalism for charge transport dynamics in supramolecular structures. 2. Diffusivity and electroneutrality coupling effects

The conductance and transport number expressions are derived for the ion-involved electron-hopping (IIEH) mechanism taking into account the ion pairing between fixed redox ions and the mobile electroinactive counterions. Under the steady-state condition, the effects of ion pairing, the ratio of diffusivity associated with electron hopping and the mobile electroinactive counterion, and the applied potential are studied both in the presence and in the absence of supporting electrolyte. The main effect of ion pairing is to decrease the charge transport rate, and that of the diffusivity rake is to change the mechanism of the conductance process from ohmic (electronic) to redox (or nonohmic). This change in the conductance behavior from ohmic to nonohmic is shown to be due to the change in the rate-limiting process from electron transport to counterion movement. A direct correlation between the proposed theory and experimental results obtained earlier using poly(benzimidazobenzophenanthroline) and [Os(vbpy)3]2+/[Zn(vbpy)3]2+ copolymer coated electrodes is demonstrated.