Importance of stochastic limitations in electrochemistry at arrays of nanoelectrodes functionalized by redox self-assembled monolayers

In order to increase signal-to-noise (S/N) performances, the current trend in electro(bio)analytical chemistry consists in developing arrays whose electroactive components are considerably reduced in size and already approach the very nanoscale. A comparable situation involving nanoscale electroactive or electrocatalytic nanoparticles randomly dispersed on a flat non-electroactive surface is already extremely common. Similarly, insulating self-assembled monolayers (SAMs) are often modified by dispersed ‘molecular nanoelectrodes’ consisting of nanopatches of insulating tethers bearing redox-head groups exposed to the analyzed solution with the purpose of mediating/catalyzing electron transfer kinetics between a substrate and the electrode. Finally, most SAMs present randomly distributed nano-sized pinholes through which direct electron transfer from the underlying electrode and a dissolved substrate may occur. It is therefore clear that these continuous developments as well as the increasingly facile and low-cost access to nanofabrication techniques will soon let (bio)electroanalytical chemists to resort more and more often to arrays of functionalized nanoelectrodes or nanoparticles. However, the theoretical analyses and stochastic simulations reported in this work demonstrate that reaching the nanoscale implies a complete change of theoretical electrochemical paradigms. This is of extreme importance as soon as one wishes to rationalize quantitatively measurements involving nano-scaled electroactive components. Indeed, based on Brownian simulations, we established that beyond a dimension of a few tens of nanometers, stochastic effects strongly alter the meaning of the kinetic and thermodynamic measurements vs. those based on classical electrochemical models.