Analytical and Computational Scaling Relationships for the Coupled Phenomena that Control Local Bipolar Electrochemical Behavior

Abstract

Bipolar electrochemistry involves intricate coupling of ionic migration in the electrolyte, charge transfer kinetics of the equal and opposite oxidation and reduction chemistries, and the thermodynamic relationship of the bipolar couple. Finite element method simulations are used to explore these coupled phenomena in the scanning bipolar cell (SBC), an experimental system we recently introduced. We generalize simulation results through the development of scaling relationships based on a linearized equivalent circuit model comprised of resistors and a transistor. Accurate analytical expressions are presented for the SBC electrolyte ohmic resistance. Secondary current distribution simulations for two thermodynamically distinct bipolar couples identify the most appropriate linearizations for the charge transfer resistance. In our model, the bipolar redox couple can have a thermodynamic barrier that serves as a gate voltage for switching the transistor that enables or blocks bipolar current flow through the substrate. The resulting resistor-transistor network provides an analytical expression for the bipolar current efficiency, the fraction of applied current participating in bipolar electrochemistry. Simplification of coupled (nonlinear) phenomenon into circuit elements has inevitable inaccuracies, and we explore the origins and size of these systematic errors. The implications of the scaling ideas presented here are generalizable for other purpose-driven bipolar electrochemical systems.