Identifying a Warburg Impedance

The Bode plot for a Warburg impedance ( W ) in series with a charge transfer resistance ( R_CT ) 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°.

The plot shown to the left, is unique to the Warburg impedance. Both the real and imaginary parts of Z are plotted vs. 1/. The lines should be straight and parallel: The slope of both lines should be equal to,  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 R_CT.