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 resistortransistor 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.

Exploring the Kinetic and Thermodynamic Relationship of Charge Transfer Reactions Used in Localized Electrodeposition and Patterning in a Scanning Bipolar Cell

“…The ohmic resistance beneath the nozzle ( R ionic ) and near-field charge transfer resistance ( R CT,near ) depicted in Figure 1C dictate current flow in the SBC. Prior simulations (Braun and Schwartz, 2016a) of the primary current distribution in the SBC show that R- ionic is related to the electrolyte conductivity (κ) and nozzle geometry by…”

“…When the potential drop exceeds E gate ( on ), current may flow through the electronic branch of the parallel circuit at a rate regulated by the relationship between ohmic and kinetic resistances. Previous studies described R ionic − using primary current simulations and explored the relationship between ohmic and kinetic resistance ( R CT,near ) for a reversible bipolar couple (i.e., Δ E BC = 0) and for a thermodynamically uphill bipolar couple (Δ E BC < 0) (Braun and Schwartz, 2016a). In those simulations the kinetic resistances of the far-field reactions were negligible, arising from the experimental far-field region having a much larger surface area than the near-field region and thus lower current densities.…”

“…Rather than rely on metal dissolution as the bipolar counter reaction, an electrolyte-born redox couple was used to generalize electrodeposition in the SBC for a diverse range of metals (Braun and Schwartz, 2016c). Computational methods validated analytical scaling relationships approximating current flow and coupling between thermodynamics, kinetics, and transport in the SBC (Braun and Schwartz, 2016a).…”

“…Previous work by our group demonstrated that a rastering microjet nozzle can be employed for localized bipolar electrodeposition and patterning on an electrically floating substrate, a system we called a scanning bipolar cell (SBC) (Braun and Schwartz, 2015, 2016a,b,c). Initial applications of the SBC on a copper bipolar electrode involved copper electrodeposition in the region beneath the nozzle (near-field) and copper dissolution of the substrate material in the region surrounding the nozzle (far-field) (Braun and Schwartz, 2015).…”

Generator-Sensor Impedance at Double Channel Electrodes

“…These effects are estimated on the assumption that the SE does not interact with the concentration field generated by the WE or the electric field generated by the WE and CE. Other more subtle effects dependent on coupling between migration, diffusion and reaction are possible, such as local faradaic currents induced at the SE by the bipolar effect [31], or significant current carried by the reactants or products. These effects, including extension to 3-D modelling.…”