Semimicroscopic Theory for Underscreening-Induced Anomalous Migration–Diffusion Coupling

Abstract

We develop a novel theory for the impedance response of reversible electron transfer reactions under the influence of migration–diffusion coupling. Theory accounts for the influence of the supporting electrolyte, electroactive species, solvent, metal, and the interfacial electric field accounting underscreening. This semimicroscopic formalism is based on a modified electrode surface boundary constraint, which circumvents the essential nonlinearity in the Nernst–Planck equation. The interfacial electric field determines the kinetics of formation of compact electric double layer (C-EDL) embedded with electroactive species and influence the mass transport. This kinetics is governed by an intrinsic C-EDL formation resistance (RH), solution resistance (RΩ), and the extent of ion packing dependent on electrolyte composition. Theory unravels a characteristic ohmic-migration frequency, ω* = D/LMΩ2, a prerequisite for the outer sphere electron transfer step. A dimensionless migration–diffusion coupling number δM is unriddled, which quantifies the extent of migration contribution dependent on the potentials at IHP (ϕ1), OHP (ϕ2), diffuse layer (ϕDL), ion size-corrected screening length, charge on electroactive species, interfacial diffusivity, and RH. The magnitude of impedance (in low-frequency regime) evinces an anomalous nonmonotonic variation with ionic strength. Finally, theory accredits us to understand the underscreening-induced anomalies in migration–diffusion-controlled impedance response.