Diffuse charge and Faradaic reactions in porous electrodes
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Bazant_Diffuse charge.pdf
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Author(s)
Biesheuvel, P. M.
Fu, Yeqing
Bazant, Martin Z.
Date Issued
June 2011
Journal
Physical Review E
Publisher
American Physical Society
Citation
Biesheuvel, P., Yeqing Fu, and Martin Bazant. “Diffuse Charge and Faradaic Reactions in Porous Electrodes.” Physical Review E 83.6 (2011) : 061507.
Version
Author's final manuscript
Abstract
Porous electrodes instead of flat electrodes are widely used in electrochemical systems to boost storage
capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates.
Existing porous electrode theories make a number of simplifying assumptions: (i) The charge-transfer rate is
assumed to depend only on the local electrostatic potential difference between the electrode matrix and the pore
solution, without considering the structure of the double layer (DL) formed in between; (ii) the charge-transfer
rate is generally equated with the salt-transfer rate not only at the nanoscale of the matrix-pore interface, but also
at the macroscopic scale of transport through the electrode pores. In this paper, we extend porous electrode theory
by including the generalized Frumkin-Butler-Volmer model of Faradaic reaction kinetics, which postulates charge
transfer across the molecular Stern layer located in between the electron-conducting matrix phase and the plane
of closest approach for the ions in the diffuse part of the DL. This is an elegant and purely local description of the
charge-transfer rate, which self-consistently determines the surface charge and does not require consideration of
reference electrodes or comparison with a global equilibrium. For the description of the DLs, we consider the
two natural limits: (i) the classical Gouy-Chapman-Stern model for thin DLs compared to the macroscopic pore
dimensions, e.g., for high-porosity metallic foams (macropores >50 nm) and (ii) a modified Donnan model for
strongly overlapping DLs, e.g., for porous activated carbon particles (micropores <2 nm). Our theory is valid
for electrolytes where both ions are mobile, and it accounts for voltage and concentration differences not only on
the macroscopic scale of the full electrode, but also on the local scale of the DL. The model is simple enough to
allow us to derive analytical approximations for the steady-state and early transients. We also present numerical
solutions to validate the analysis and to illustrate the evolution of ion densities, pore potential, surface charge,
and reaction rates in response to an applied voltage.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.83.061507
