Modeling Interfacial Electron Transfer in the Double Layer: The Interplay between Electrode Coupling and Electrostatic Driving

In this manuscript, we present a theoretical model for studying the population dynamics of electrochemical systems within the region of the electrical double layer. We formulate this model in a coordinate system that separately resolves both the transport of redox species in the direction perpendicular to the electrode surface and the thermal fluctuations of the solvent environment that drive electron transfer. This formulation enables us to explore how the observable characteristics of electrochemical systems are influenced by spatial variations in the electric fields and electronic couplings that are inherent to the double layer, especially under conditions of low ionic strength, where screening lengths are larger. We apply this model to highlight the fundamental interplay between two physical attributes of interfacial electrochemistry: electrode coupling and electrostatic driving. Using a simple model system designed to isolate this interplay, we demonstrate how variations in the location of electron transfer can lead to systematic changes to the electrochemical transfer coefficient. We also illustrate that for certain redox reactions, differences in electrostatic driving between products and reactants can lead to nonmonotonic current-voltage behavior.