Mechanisms of Diffusive Charge Transport in Redox-Active Polymer Solutions

Redox-active polymers (RAPs) are a promising material for energy storage in flow batteries due their large size preventing detrimental redox material crossover and adjustable molecular chemistry and architecture for optimized performance. There has been a recent effort to understand the physics governing charge diffusion in RAPs. We use simulations and theory to show how a variety of molecular charge transport mechanisms affect diffusive motion in RAP solutions. Our coarse-grained model of RAP solutions employs Brownian dynamics for polymer motion and a kinetic Monte Carlo update step for the charge hopping dynamics. We perform these simulations for both an isolated and interacting case for single chains and multi-chain systems where we show how a various transport mechanisms interplay, including the intra-polymer transport of charge via self-exchange and polymer segmental motions, as well as hopping due to inter-polymer collisions and translational diffusion of the chains. We provide theoretical arguments to describe the diffusive motion of charge via these mechanisms, which match well with simulations. Our predictions suggest the existence of three charge transport regimes, which distinguish between inter- and intra-molecular processes and dilute and semi-dilute solutions.