Flux−Force Formalism for Charge Transport Dynamics in Supramolecular Structures. 2. Diffusivity and Electroneutrality Coupling Effects

Abstract

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.

Electron Self-Exchange in Redox Polymers. 1. Mechanistic Analysis and Statistical Mechanical Considerations

“…33,35 In comparison, the present kinetic Ising model formalism does not require this improvization because the spatiotemporal equation is independent of the value of the symmetry coefficient. An identical conclusion emerged from our earlier analysis 52,53 of transport equations using nonequilibrium thermodynamics as well.…”

“…and, (iii) to compare the microscopic framework provided by kinetic Ising model formalism with other phenomenological approaches. For example, we have recently demonstrated the applicablity of the concepts of irreversible thermodynamics , for electron hopping, and this provides scope for comparing nonequilibrium thermodynamics formalism with kinetic Ising model versions. The hitherto unknown connectivity between Onsager's phenomenological coefficients and microscopic transition probabilities seems therefore possible.…”

Charge Transport through Chemically Modified Electrodes: a General Analysis for Ion Exchange and Covalently Attached Redox Polymers

“…Figure 4) (ii) conductivitysolvents with low dielectric constants non-ohmic conductivity non-ohmic conductivity (cf. Figure 6b) solvents with high dielectric constants ohmic conductivity of lower magnitude, provided D c is not affected by solvent ohmic conductivity of higher magnitude (cf. Figure 6a) (C) transport number t e (transport of number of electron) can vary between 0 and 1 when physical diffusion of the redox species is neglected t redox cannot approach unity since D c is normally greater than D phys (cf.…”

Electron Self-Exchange in Redox Polymers. 2. A Study of Ion Aggregation and Intermolecular Interactions

“…Ion pair formation involving electroactive species and counterions is now a well-known phenomena in a large class of ionomeric systems. [1][2][3][4][5][6][7][8][9] The influence of ion pair formation and intermolecular interactions between the electroactive species has not yet been simultaneously analyzed in detail in chemically modified electrodes. However, few isolated investigations exist in the context of charge transport in redox polymers for studying conductance, redox capacity, and diffusion coefficient variation with interaction energy and no systematic study starting from the diffusion-migration equation, relating the observable current responses to the interaction energy and ion pairing, is available.…”

“…One of the earliest methods of calculating current when interaction effects are present is due to Laviron et al 10 wherein current is explicitly reported in terms of potential and interaction coefficients using an approach analogous to Frumkin isotherm for adsorption of species. We have recently employed 8,[11][12][13] kinetic Ising model and irreversible thermodyanmics versions to derive transport equations, assuming all the redox species present are electron transfer active (i.e., for systems without ion pairing). When ion pairing is present, not all the redox species present in the lattice are electron transfer active but only those which exist as ions (whose concentration is governed by the ion association equilibrium constant) can transport charge.…”