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.

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.