Continuum Modeling of Ion Transport in Nano-electrochemical Systems
APS March Meeting, Montreal, Canada, March 25, 2004
Traditional models of macroscopic electrochemical systems are based on two fundamental assumptions: (i) electroneutrality of the bulk solution and (ii) Boltzmann equilibrium of diffuse charge in the interfacial double layers. In nanostructures, these assumptions break down as the distinction between ``bulk'' and ``interface'' becomes blurred. Moreover, at the nanoscale, tiny voltages can lead to enormous electric fields, which can drastically alter diffuse-charge distributions and current-voltage relations. Although quantum mechanical descriptions are important the atomic scale, continuum models may still provide valuable analytical insights at the nanoscale (as in the classical theory of the double layer), albeit in a different limit from macroscopic electrochemistry. Here, we study the classical Poisson-Nernst-Planck equations in nano-electrochemical systems (near the scale of the screening length), including the boundary conditions for Faradaic reactions and surface capacitance. For binary electrolytes, our analysis reveals new non-equilibrium double-layer structures near and above the classical diffusion-limited current and polarographic (V vs. I) curves that are very sensitive to interfacial properties. We also consider the exotic case of a single unscreened charge carrier to model lithium diffusion in SiO2 nano-thin films, which has recently been demonstrated in on-chip micro-batteries.