Title: Diffuse Charge and Limiting Current in Dilute, Binary
Electrochemical Cells
Speaker: Martin Z. Bazant
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA, USA
Date: June 18, 1999, 10:30am
Place: Centre de Recherche Paul Pascal
Pessac, France
Abstract:
The macroscopic theory of electrochemistry is founded on the
assumption of electroneutrality, which is an excellent approximation
on scales much larger than the Debye screening length. On scales below
Debye length, "diffuse charge" exists in boundary layers against
electrodes or charged surfaces, as described by the familiar
Gouy-Chapman theory. Roughly a century ago, Nernst and others
predicted that a neutral electrochemical cell possesses a "limiting
current" set by the maximum steady-state diffusive flux, which occurs
when the electrolyte concentration vanishes at the cathode. In the
1958, however, Levich realized that this classical picture contains an
inherent flaw: The (local) Debye screening length diverges as the
concentration goes to zero, and it can be shown that the
Nernst-Gouy-Chapman theory completely breaks down at the very same
limiting current it itself predicts. In 1967, Smyrl and Newman
brilliantly resolved this apparent paradox by showing that the
classical limiting current can be attained and exceeded as the diffuse
charge layer expands far beyond the Debye length. In 1990, Chazalviel
and others went on to propose the existence of macroscopic "space
charge" layer above the classical limiting current, but a careful,
mathematical analysis with more realistic boundary conditions is still
needed to unify and validate these theories.
In this work, the classical problem of uniform, steady conduction
through a dilute binary, electrolyte between parallel-plate electrodes
is revisited, using matched asymptotic expansions and direct numerical
simulations. It is shown that as the current nears and eventually
exceeds the classical limiting value, the diffuse charge arranges into
nested boundary layers with features of both the Smyrl-Newman and
Chazalviel theories. Understanding these non-classical effects is
increasingly important today, as microelectrode dimensions shrink
toward the scale of the Debye length. Moreover, the modified
double-layer structure strongly influences electrokinetic effects
during fast deposition, which implies that several recently
investigated theoretical problems, such as the stability of a flat
plate and electroconvection at dendrite tips, are still open.