Simulated concentration profiles of redox centers in thin polymer films: Oxidation-state dependence of diffusion and partitioning between film and solu

Abstract

Charge and mass transport in polymer films containing electrostatically bound redox centers are complicated by several factors: (1) the partitioning of the redox centers out of the film and into the adjacent solution, (2) the diffusion of redox centers within the film and in solution, and (3) the state of oxidation of the film, which affects the diffusivities locally. In this paper, digital simulations are used to analyze the effects of these factors separately on concentration profiles established laterally in a film between parallel cathodic and anodic band electrodes. The simulations are based on explicit finite difference methods and include partitioning of redox molecules between film and solution. The partitioning is governed by capacity factors for oxidized, A, and reduced, B, species, analogous to those defined in separation science, where solutes partition between stationary and mobile phases. Linear concentration profiles are obtained for cases where diffusion is (1) limited to the film without leaching of redox centers into the solution, and (2) limited to the solution, but with a partitioning equilibrium between the film and solution. The ratio of the slopes of the concentration profiles for B and A depends on the ratio of diffusion coefficients D A / D B and on the ratio of capacity factors k′ B′/ k′ A. Non-linear concentration profiles are established when transport depends on the state of oxidation of the film.