2004/06/16 by Kevin T. Chu, Martin Z. Bazant, Chu, Kevin T. +1 · 1 citation
Chemistry · Engineering · Physics and Astronomy · #Chemical Physics (physics.chem-ph) #Electrostatics and Colloid Interactions #FOS: Physical sciences #Nanopore and Nanochannel Transport Studies #Surface and Thin Film Phenomena #physics.chem-ph
paper · pdf · doi:10.48550/arxiv.physics/0406076
21 pages, 8 figures, 1 table
arxiv created 2004/06/16 · openalex publication_date 2004/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a model electrochemical thin film at dc currents exceeding the classical diffusion-limited value. The mathematical problem involves the steady Poisson-Nernst-Planck equations for a binary electrolyte with nonlinear boundary conditions for reaction kinetics and Stern-layer capacitance, as well as an integral constraint on the number of anions. At the limiting current, we find a nested boundary layer structure at the cathode, which is required by the reaction boundary condition. Above the limiting current, a depletion of anions generally characterizes the cathode side of the cell. In this regime, we derive leading-order asymptotic approximations for the (i) classical bulk space-charge layer and (ii) another, nested highly charged boundary layer at the cathode. The former involves an exact solution to the Nernst-Planck equations for a single, unscreened ionic species, which may apply more generally to Faradaic conduction through very thin insulating films. By matching expansions, we derive current-voltage relations well into the space-charge regime. Throughout our analysis, we emphasize the strong influence of the Stern-layer capacitance on cell behavior.