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

Abstract

A comprehensive analysis of electron hopping between spatially separated redox centres pertaining to supramolecular structures is carried out by taking into account different mechanistic pathways. Spin exchange dynamics due to Kawasaki is invoked to study the transport phenomena for the more appropriate, thermodynamically favored ion pairing mechanism. The generalized master equation and its reduced form are presented and the dynamics of electron hopping is analyzed both under spin-1/2 and spin-1 Ising versions. Transition probabilities chosen for the present study satisfy the condition of detailed balancing and is a function of spin exchange jump frequencies and spin variables. Energetics of electron hopping process is obtained from the Ising Hamiltonian under molecular field approximation and incorporated into the spin exchange frequencies. The apparent diffusion coefficient that emerges along with the transport equation reflects the dynamics of electron propagation in the films. The importance of blocking factor and potential independent terms in the apparent diffusion coefficient expression overlooked in hitherto known phenomenological approaches is emphasized.

The influence of poly(2-methoxyaniline-5-sulfonic acid) on the electrochemical and photochemical properties of a highly luminescent ruthenium complex

“…Electron transport in redox polymers has been shown to occur via at least three mechanisms [34]. Where the backbone in nonconducting, outer-sphere electron exchange between redox sites provides the only significant contribution to electron transport [35,36].…”

Luminescent Metal Complexes within Polyelectrolyte Layers: Tuning Electron and Energy Transfer

“…This response is described by the Randles−Sevcik equation (eq ) i p = 2.69 × 10 5 ( n 3 / 2 A D c t 1 / 2 ν 1 / 2 C ) where n is the number of electrons involved, A is the area of the electrode, ν is the scan rate, and C is the concentration of electroactive sites within the film. There are three dominant mechanisms that contribute to charge transport in redox polymers, where the backbone in nonconducting, outer-sphere electron exchange between redox sites provides the only significant contribution to electron transport. , In highly conjugated systems, electron transport can also occur through the polymer backbone by mediated and/or superexchange mechanisms . These are distinguished by the availability of redox states within the polymer that have suitable energy to mediate electron transport.…”

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

“…We have excluded the effect of counterion displacement from our analysis assuming that it essentially influences charge transport by modifying the polymeric structure or by ion pairing . A detailed study incorporating counterion mobility into the flux equation may make the analysis more cumbersome, but will be a desirable pursuit.…”