Flux-force formalism for charge transport dynamics in supramolecular structures. 1. Activity coefficient and interaction energy considerations

A comprehensive analysis starting from the formalism of irreversible thermodynamics, incorporating activity coefficients and interparticle interactions, is developed to derive expressions for mixed conductance, transport numbers, etc., for diffusive and electric field assisted electron hopping through polymer matrixes attached to electrode surfaces. The transport equation obtained is a combination of Dahms-Ruff diffusion and the Levich migration terms and includes short-range interparticle interactions under molecular field approximation as well as activity coefficient terms. The derived dynamical equation for electron flux follows a second-order law in species concentrations in contrast to the classical Nemst-Planck equation for ion migration. Applicable systems are thought to be organic pi-conjugated electroactive polymers, electronically conducting polymers with covalently linked redox groups, i.e., metal ion redox site membranes, and ion-exchange polymers. The concept of self and tracer diffusion coefficients is brought into the formalism of charge transport in supramolecular structures. Some new insights regarding the identification of Onsager's coefficient in diffusion through supramolecular structures are also provided.