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Scanning Electrochemical Microscopy: Diffusion on a Microdisk Electrode

Scanning Electrochemical Microscopy (SECM) uses a microelectrode tip to image the microscopic domain. Because of the very small size of the microelectrode (of the order of micrometers) the mass transport in a disk-shaped microelectrode can be considered to occur in a semi-infinite region. This Demonstration shows the concentration profile of electroactive space during diffusion in and out of the surface of the microdisk electrode.

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Semi-infinite mass transport occurs to a disk-shaped electrode in which the following electrochemical reaction takes place:
.
The mass transport to the electrode can be modelled by the cylindrical diffusion equation
, where is the concentration of oxidant () and , represent the spatial coordinates.
In this Demonstration, the radius of the microelectrode is taken as on the axis. The boundary conditions are
at the surface of microelectrode,
: ,
: ;
and above the surface of the microelectrode, where ,
: ,
: .
The exact solution was given in [1] and can also be calculated with Mathematica's built-in function NDSolve.
[1] J. Crank and R. M. Furzeland, "The Treatment of Boundary Singularities in Axially Symmetric Problems Containing Discs," Journal of the Institute of Mathematics and Its Applications, 20(3), 1977 pp. 355–370.
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