ELECTRON HOPPING IN IMMOBILIZED POLYVALENT AND OR MULTICOUPLE REDOX SYSTEMS

A general equation is derived which accounts for both diffusive and (electric) field-assisted electron hopping through a matrix comprising any number of simple or polyvalent redox couples (a simple redox couple has two valence states interconverted by the transfer of one electron; a polyvalent redox couple has three or more valence states with one-electron interconversions). The derivation evolves from a fundamental equation derived separately by Savéant and by Buck describing electron transport through a matrix comprising a single redox couple {A figure is presented}. Of particular interest is the trivalent system where the three valence states are related by A + e- ⇋ B and B + e- ⇋ C. Vectorial electron hopping can occur between appropriately positioned pairs of redox moieties: A-B ⇋ B-A; B-C ⇋ C-B; and A-C ⇋ B-B. Expressions for the electronic flux are discussed for four experimental cases: Case 1, the instantaneous electronic flux with a large excess of mobile counter ions; Case 2, the steady-state electronic flux with a large excess of mobile counterions; Case 3, the electronic flux with no counterions (i.e., the concentrations and charges of species A, B, and C sustain electroneutrality); Case 4, the electronic flux with immobile counterions. Only small (interfacial) perturbations and limiting (time independent) conditions are considered. A basis for the analysis of the electronic flux in a generalized system comprising immobilized polyvalent or multi-couple redox coupless is also presented. © 1990.