Electron self-exchange in redox polymers. 1. Mechanistic analysis and statistical mechanical considerations

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.