Diffuse-charge effects on the transient response of electrochemical cells
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Soestbergen-2010-Diffuse charge effec.pdf
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Author(s)
van Soestbergen, M.
Biesheuvel, P. M.
Bazant, Martin Z.
Date Issued
February 2010
Journal
Physical Review E
Publisher
American Physical Society
Citation
van Soestbergen, M., P.M. Biescheuvel, and M.Z. Bazant. "Diffuse-charge effects on the transient response of electrochemical cells." Physical Review E 81.2 (2010): 021503. © 2010 The American Physical Society
Version
Final published version
Abstract
We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or “space charge”) near the electrodes on Faradaic reaction kinetics. The full model is based on the classical Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions to describe electron-transfer reactions across the Stern layer at the electrode surface. In practical situations, diffuse charge is confined to thin diffuse layers (DLs), which poses numerical difficulties for the full model but allows simplification by asymptotic analysis. For a thin quasi-equilibrium DL, we derive effective boundary conditions on the quasi-neutral bulk electrolyte at the diffusion time scale, valid up to the transition time, where the bulk concentration vanishes due to diffusion limitation. We integrate the thin-DL problem analytically to obtain a set of algebraic equations, whose (numerical) solution compares favorably to the full model. In the Gouy-Chapman and Helmholtz limits, where the Stern layer is thin or thick compared to the DL, respectively, we derive simple analytical formulas for the cell voltage versus time. The full model also describes the fast initial capacitive charging of the DLs and superlimiting currents beyond the transition time, where the DL expands to a transient non-equilibrium structure. We extend the well-known Sand equation for the transition time to include all values of the superlimiting current beyond the diffusion-limiting current.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.81.021503
