Electrochemical Impedance at a Rotated Disk Electrode
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Whenever you read about Electrochemical Impedance, one of the first things they tell you is "The system must be stable and unchanging." Normally that means that should run the EIS experiment at the Open Circuit Potential, where the DC current is zero. Sometimes, though, you'd like to study the reaction when there IS a net current. A very relevant example is the study of catalysts for fuel cell electrodes. Often you'd like to study the catalyst under conditions very similar to that in an operating fuel cell, where the current density is large.
Rotated Disk TheoryFirst, a word or two about the Rotated Disk Electrode. A sketch of the working end of an RDE is shown at the
right. The disk electrode (blue) is embedded in a larger, non-conducting rod
or shroud. The entire assembly is rotated. Solution is drawn up
along the axis of rotation and past the electrode, so there is laminar
(i.e., smooth) flow past the electrode surface. However, the solution
at the surface is dragged along by the rotating disk, and there is a thin layer |
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With all of THAT out of the way, we can begin to talk about ... |
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Batteries | Fuel Cells | Corrosion | Paints & Coatings | Physical Electrochemistry
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Gamry
Instruments © 1997-2005
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The
( the
Nernst Diffusion Layer ) that is unstirred.
Within this layer, mass transport is by diffusion alone. The effective
thickness of this layer depends on the RPM of the rotator, the viscosity of
the solution, and the diffusion coefficient of the electroactive species. As
the rotation speed of the RDE is increased the Nernst Diffusion Layer
becomes thinner.
Another consequence of the NDL theory
is that the current-voltage curve is S-shaped at scan rates below about 100
mV/s. The limiting current is given by the Levich equation.
The
hydrodynamics described above fits the requisites for a 'Porous Bounded
Warburg': There is a thin layer of unstirred solution next to the electrode,
and large, stirred, homogeneous source of material outside that layer.
In between these regions there is a (virtual) membrane that is porous to the
diffusing molecule. Some people refer to this equivalent circuit
element as a Nernst circuit element because it fits the model of the
Nernst Diffusion Layer. The
porous bounded Warburg impedance is most easily recognized from its Nyquist
plot. At high frequency, this circuit element looks like a traditional
Warburg impedance and shows a 45° line on the Nyquist plot. At low
frequency, it looks like the semicircle of a Randles Cell. 
The Porous Bounded Warburg is characterized by two
parameters, YO and B. The equation for Z is shown here,
along with the gruesome definitions of YO and B. The
parameter B ( in sec1/2 ) is a measure of the time it takes for
the reactant to diffuse across the Nernst Diffusion Layer. What is
interesting is that B depends upon the NDL thickness, which in turn, depends
upon the rotation speed (r) of the electrode! 
