Theory for Diffusion: Migration Coupling-Induced Cathodic and Anodic Current Anomaly

We developed a novel semimicroscopic theory for diffusion and migration-controlled oxidative and reductive charge transfer for fully and partially supported systems under single-potential-step perturbation on a planar electrode. The electric field-induced asymmetrical migration contribution of oxidized and reduced species in the electric double layer (EDL) region is accounted for using our jellium-dipole-underscreened-diffuse-layer model for the electric double layer. The essential nonlinearity that appears in the Nernst–Planck equation is circumvented through a novel approach by projecting migration contributions to modified Nernstian boundary constraint. Our formulation also accounts for the ionic strength-dependent anomalies in the interfacial electric field due to ionic underscreening, electrostatic interaction on diffusivity, the ion size effect of supporting electrolyte, and the charge of electroactive species in the migration current. The formula is derived for the current transient, and it accounts for the influence of the supporting electrolyte, electroactive species, solvent, electrode through jellium, and applied potential. The extent of migration–diffusion coupling is characterized by a dimensionless coupling number δ M α (0 ≤ δ M α < 1). A smaller magnitude represents a weak coupling regime with a limiting ideal Cottrell behavior, and δ M α sim 0.5 represents a strong coupling regime. The theory elucidates that δ M α is dependent on the potential at IHP, OHP, diffuse electric double layer, ion size-corrected screening length, interfacial diffusivity, the charge on electroactive species, and the operative resistance from bulk to interface. Finally, we validate the theory with experiments and show that migration has a significant influence on the chronoamperometric response at all time scales.