Modeling of Ion Transport in Micro- and Nano-Electrochemical Systems
CSGF Annual Conference, Washington, D.C., July 21, 2004
Motivated by the recent interest in small-scale electrochemical devices, we revisit the classical analysis of electrochemical systems paying close attention to the assumptions underlying the model.
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. At nano-scales, these assumptions break down as the distinction between "bulk" and "interface" becomes blurred. Moreover, tiny voltages can lead to enormous electric fields, which can drastically alter diffuse-charge distributions and current-voltage relations. These conclusions (while physically intuitive) arise from an examination of solutions (asymptotic and numerical) to the steady, 1D Poisson-Nernst-Planck equations in nano-electrochemical systems, 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 are also exploring 2D systems at the micro-scale (where local electroneutrality is valid) using a recent result in conformal mapping theory which shows that the steady Nernst-Planck equations are conformally invariant in the electroneutral limit even though the solutions are non-harmonic functions . Thus, the problem of ion transport in an arbitrary geometry is always equivalent, via conformal mapping, to ion transport in a simple geometry (e.g. a rectangle). As examples, we show calculations for ion transport in polygonal geometries that are being considered in microfluidics devices.
In these studies, we use Chebyshev pseudospectral methods to obtain accurate solutions in a highly time and space efficient manner. Most results were obtained in only a few minutes on a workstation.
- M. Z. Bazant, Conformal mapping of some non-harmonic functions in transport theory, Proc. Roy. Soc. A. 460, 1433 (2004).