Analysis of charge hopping between redox center molecules in a polymer membrane based on percolation theory

Abstract

AbstractCharge propagation in a polymer membrane dispersing redox center molecules was studied using Monte‐Carlo simulation. The charge propagation was visualized using a uniform sphere sites model. The fraction of charge‐transported sites (R CT) increased above concentration called percolation threshold. The charge transfer in a Nafion® membrane confining [(bpy)2 (H2O)RuORu(H2O)(bpy)2]4+ (abbreviated to Nafion [Ru‐O‐Ru]) as well as in a polymer pendant $\hbox{Ru(bpy)}_{3}^{2+}$ membrane was investigated with a potential‐step chronoamperospectrometry (PSCAS), and the behavior was compared with the simulation The relationship between charge hopping distance and critical percolation concentration (c p) was obtained from the percolation theory and applied to the actual systems. The charge hopping distance between molecules was estimated as 2.04 nm for Nafion[Ru‐O‐Ru] system and 1.71 nm for polymer pendant $\hbox{\it Ru(bpy)}_{3}^{2+}$. When the charge propagation takes place by charge hopping mechanism, a slow diffusion of the redox centers increases R CT at the concentration below c p, but decreases at the concentration above c p. Although the c p becomes ambiguous with increasing diffusion coefficient (D phys), it was suggested that c p value doesn't change. Copyright © 2001 John Wiley & Sons, Ltd.