Electron-transfer kinetics and electric double layer effects in nanometer-wide thin-layer cells.

Redox cycling in nanometer-wide thin-layer cells holds great promise in ultrasensitive voltammetric detection and in probing fast heterogeneous electron-transfer kinetics. Quantitative understanding of the influence of the nanometer gap distance on the redox processes in the thin-layer cells is of crucial importance for reliable data analysis. We present theoretical consideration on the voltammetric behaviors associated with redox cycling of electroactive molecules between two electrodes separated by nanometer widths. Emphasis is placed on the weakness of the commonly used Butler-Volmer theory and the classic Marcus-Hush theory in describing the electrochemical heterogeneous electron-transfer kinetics at potentials significantly removed from the formal potential of redox moieties and, in addition, the effect of the electric-double-layer on the electron-transfer kinetics and mass transport dynamics of charged redox species. The steady-state voltammetric responses, obtained by using the Butler-Volmer and Marcus-Hush models and that predicted by the more realistic electron-transfer kinetics formulism, which is based on the alignments of the density of states between the electrode continuum and the Gaussian distribution of redox agents, and by inclusion of the electric-double-layer effect, are compared through systematic finite element simulations. The effect of the gap width between the electrodes, the standard rate constant and reorganization energy for the electron-transfer reactions, and the charges of the redox moieties are considered. On the basis of the simulation results, the reliability of the conventional voltammetric analysis based on the Butler-Volmer kinetic model and diffusion transport equations is discussed for nanometer-wide thin-layer cells.