Revisiting the Mechanisms of Charge Transport in Solutions of Redox-Active Molecules Using Computer Simulations: When and Why Do Analytical Theories Fail?

Understanding charge transport is essential for the development of energy-storage applications. This work introduces a new theoretical methodology to model diffusive charge transport in solutions of redox-active molecules by combining Langevin dynamics for the spatial degrees of freedom and a master-equation formalism to describe the electron-hopping events between redox molecules. The model is used to analyze the effects of the concentration of the redox molecules and the strength of the intermolecular interactions on the charge-transport mechanism. In the past, the rate of charge transport has been modeled with the analytical Dahms-Ruff equation; however, this is a mean-field equation, whose range of validity has not been tested with less approximate theories. We show that the Dahms-Ruff equation fails to quantitatively predict the diffusion coefficient for charge transport for large concentrations of the redox species and high bimolecular electron-transfer rates, i.e., the most relevant conditions for energy-storage applications. Under these conditions, the diffusion coefficient for charge transport obtained from simulations is larger than that predicted from the Dahm-Ruff equation because of the formation of transient clusters of redox molecules. Also, intermolecular interactions, which are not taken into account by the Dahms-Ruff equation, play a central role in the charge transport of redox species. We show that the apparent diffusion coefficient experiences a maximum with respect to the strength of the intermolecular attractions. This maximum is traced back to the formation of clusters and their two opposite effects on the diffusion coefficient: electron hopping is fast within a cluster but inefficient between neighboring clusters.