Electrochemistry at a Metal Nanoparticle on a Tunneling Film: A Steady-State Model of Current Densities at a Tunneling Ultramicroelectrode

Here, a new methodology is proposed for treating electrochemical current densities in metal-insulator-metal nanoparticle (M-I-MNP) systems. The described model provides broad, practical insights about MNP-mediated electron transfer to redox species in solution, where electron transfer from the underlying electrode to a MNP via tunneling and heterogeneous electron transfer from the MNP to redox species in solution are treated as sequential steps. Tunneling is treated through an adaptation of the Simmons model of tunneling in metal-insulator-metal structures, and explicit equations are provided for tunneling currents, which demonstrate the effect of various experimental parameters, such as insulator thickness and MNP size. Overall, a general approach is demonstrated for determining experimental conditions where tunneling will have a measurable impact on the electrochemistry of M-I-MNP systems.