Identifying a Warburg Impedance

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 Recognizing a Warburg Impedance
A Warburg impedance element can be difficult to recognize because it is nearly always associated with a charge-transfer resistance and a double layer capacitance. These may hide the attributes of the Warburg Impedance.


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Warburg Bode Plot and a Diffusion-specific Plot

The Bode plot for a Warburg impedance ( W ) in series with a charge transfer resistance ( RCT ) is shown on the right.  At the lower frequencies where the impedance of the Warburg dominates, the slope of the |Z| Bode plot is minus 1/2. ( Not the familiar -1 slope associated with a simple RC circuit! ) In this region, the phase angle is 45. At the higher frequencies, the charge transfer resistance dominates and the phase angle becomes 0.

Bode | Z | plot for a Warburg Impedance
A Bode Magnitude Plot for a Warburg
 
Straight line plot for a Warburg
A  unique plot for a Warburg.

The plot shown to the left, is unique to the Warburg impedance. Both the real and imaginary parts of Z are plotted vs. 1/sqrt(omega). The lines should be straight and parallel: The slope of both lines should be equal tosigma,  the Warburg constant. The line for the imaginary component (shown in red) should intersect the Z axis at zero, while the intercept for the real component (shown in green) is RCT.

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