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

Charge propagation in a polymer membrane dispersing redox center molecules was studied using Monte-Carlo simulation. The charge propagation was visual ized using a uniform sphere sites model. The fraction of charge-transported sites (R-CT) increased above concentration called percolation threshold. T he charge transfer in a Nafion(R) membrane confining [(bpy)(2) (H2O)RuORu(H 2O) (bpy)(2)](4+) (abbreviated to Nafion [Ru-O-Ru]) as well as in a polymer pendant Ru(bpy)(3)(2+) membrane was investigated with a potential-step chr onoamperospectrometry (PSCAS), and the behavior was compared with the simul ation The relationship between charge hopping distance and critical percola tion concentration (c(p)) was obtained from the percolation theory and appl ied to the actual systems. The charge hopping distance between molecules wa s estimated as 2.04 nm for Nafion[Ru-O-Ru] system and 1.71 nm for polymer p endant Ru(bpy)(3)(2+). When the charge propagation takes place by uge hoppi ng mechanism, a slow diffusion of the redox centers increases R-CT at the c oncentration below c(p), but decreases at the concentration above c(p). Alt hough the cp becomes ambiguous with increasing diffusion coefficient (D-phy s), it was suggested that c(p) value doesn't change. Copyright (C) 2001 Joh n Wiley & Sons, Ltd.