Kinetic enhancement in nanoscale electrochemical systems caused by non-normal distributions of the electrode potential

We have recently shown Proc. Natl. Acad. Sci. U.S.A. 107, 4528 (2010)] that the discreteness and stochasticity of an electron transfer event on a resistively coupled nanoelectrode causes mesoscopic fluctuations in time of the electrode potential. These fluctuations give rise to a time-average faradaic current density substantially larger than in the macroscopic limit. The deviations result to a large extent from the potentiostatic control, which imposes a constraint on the evolution of the electrode potential that leads to non-normal distributions. The degree of freedom of the electrode potential requires a resistance between nanoelectrode and metallic support. In this article, we study the dependence of the mesoscopic stochastic dynamics on this resistance (assumed to be ohmic). We show that the enhancement of the reaction rate vanishes in both limits, zero and infinite resistance. The distribution of the electrode potential continuously transforms from a normal distribution at infinite resistance (the galvanostatic limit), through a more and more peaked distribution with increasingly important rare events to the deterministic behavior at zero resistance.