Theory for Heterogeneous Electron Transfer Kinetics on Nanocorrugated Atomic Stepped Metal Electrodes

Abstract

We develop a novel mean-field theoretical approach for the outer-sphere heterogeneous electron transfer (OS-HET) rate constant at an atomically stepped nanocorrugated metal surface. Theory accounts for the contributions from the nature of the metal, local curvature of the nanocorrugated atomic step, the density of atomic steps and kinks, dipolar solvents, and the frontier molecular orbital of electroactive molecules. Our theoretical approach develops a novel model for the free energy of activation obtained using the alignment of the Fermi energy level in the metal with one of the frontier molecular orbitals of the electroactive species. The activation free energy is obtained as a product of a modified work function (WF) and the fractional electronic charge of activation for the alignment of levels. Metal surface local curvatures at atomic steps are modeled as a hyperbolic tangent functional with a random nanocorrugated step edge. The influence of step density and edge fluctuations (or kinks) on the activation free energy is included through the surface average mean curvature and the mean-square gradient dependent modified WF. The theoretical results highlight the step density-dependent nonmonotonic variation in WF, fractional electronic charge, and activation free energy. The increase in step density shifts the Fermi energy level toward LUMO and away from HOMO energy levels. This causes the reduced (for the LUMO) and enhanced (for the HOMO) activation free energy for ET kinetics compared to the basal plane. The dichotomy in the OS-HET kinetics at the atomically stepped metal results in anomalous enhancement and suppression for the LUMO and HOMO, respectively. The strong influence of kinks along the step edge on the HET rate constant is predicted up to 6 decades (compared to the basal surface of Pt metal). Finally, theory shows agreement with the reported experimental data of WF and exchange current density for single crystal Pt electrodes.