Theory for Anion Bridge-Assisted Heterogeneous Electron Transfer on an Atomically Stepped Metal

A semimicroscopic theory for anion bridge-assisted heterogeneous electron transfer (HET), based on the hypothesis that the transition state formed through the matching of the fluctuating quasi-Fermi level of a metal with the fluctuating frontier molecular orbital (FMO) of electroactive species, is developed. The extent of energy fluctuations required to form a desired quasi-Fermi state for ET over a metal originates from solvent reorganization, anion adsorption, and random nanocorrugated atomic steps. Theory accounts for the effect of anion adsorption on the electrochemical work function (EWF), the related quantity of the potential of zero charge (PZC) and the electron affinity ratio, and the standard rate constant for HET. Ion adsorption is governed by the partial coverage (θa) and the partial charge of adsorption (δa). δa is a function of the electronegativity of the ion (χa), chemical hardness of the ion (ηa), and the metal. θa is obtained from the Flory–Huggins adsorption isotherm and is contrived with the microscopic formulation of the excess free energy of adsorption. Further, the free energy of activation for the HET kinetics (ΔG≠) via a bridging ligand complex is formulated as the product of the electron affinity ratio of the electrode interface and the energy gap between the electrode and the electroactive species, moderated through solvent reorganization. The chemisorption of anions on the metal shifts the PZC to more cathodic values. The enhancement in the kinetics in the presence of adsorbing anions is due to a lowering of the activation barrier through the affinity ratio. Theory accounts for the influence of atomic steps and halide ions on ORR kinetics. Finally, theoretical predictions for different concentrations of adsorbing anions on PZC and HET kinetics of complex ions, viz., [Cr(H2O)6]2+/3+, [V(H2O)6]2+/3+, and [Cd(H2O)6]0/2+, show good agreement with the extensive experimental data for mercury and solid metal electrodes.