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Seminar on Industrial Problems

The Role of Charge Separation in the Response of Electrochemical Systems

The Role of Charge Separation in the Response of Electrochemical Systems

March 2, 1998

Electrodes of microscopic dimensions play an increasingly important
role in many electrochemical systems of industrial significance,
e.g., thin-film batteries (with electrodes and electrolyte layers
of micron dimensions), and microelectrodes (with micron or submicron
dimensions) used as sensors or tools for electroanalytical studies.
As the size of an electrode decreases, the thin charge layer
adjacent to its surface, often on the order of angstroms, exerts
an increasing influence on the current characteristics of the
electrode. A mathematical model is used to study the impact
of the charge layer on a microelectrode immersed in a dilute
concentration of binary electrolyte. The transport-limited current
density on the electrode depends on a dimensionless parameter
, corresponding
to the quotient of the Debye length by the electrode radius.
(The Debye length characterizes the charge-layer thickness.)
As becomes
small, the pde's describing charge transport become singularly
perturbed, and numerical solution of the equations becomes increasingly
difficult. Matched asymptotics were used to calculate the current
in the limit
< < *1*, and the results were compared with numerical solutions
for larger -values.
This talk will focus mostly on the matched asymptotic procedure,
with some discussion of how a knowledge of the boundary-layer
structure can be used to aid in the numerical solution of the
equations.

This is joint work with Mark W. Verbrugge.