





Whenever you look at a ComplexPlane Impedance Plot ( Nyquist or ColeCole plot) and see a 45° line, or fit data to an equivalent circuit and find a Constant Phase Element (CPE) with an nvalue close to 0.5, you should consider diffusion as a possible explanation. Diffusion Circuit Elements  WarburgThe most common diffusion circuit is the socalled "Warburg" diffusion element, but it is not the only one! A Warburg impedance element can be used to model semiinfinite linear diffusion, that is, unrestricted diffusion to a large planar electrode. This is the simplest diffusion situation because it is only the linear distance from the electrode that matters. The Warburg impedance is an example of a constant phase element for which the phase angle is a constant 45° and independent of frequency. The magnitude of the Warburg impedance is inversely proportional to the square root of the frequency ( ) as you would expect for a CPE with an nvalue of 0.5. The Warburg is unique among CPE's because the real and imaginary components are equal at all frequencies and both depend upon . Warburg EquationsThe equation for a Warburg's impedance ( Z_{w}
) is a
simple one, but the equation for the Warburg constant (
) is a bit more complicated and will be discussed on another
page. 



Electrochemistry The Bookstore Tell Us ! 


A fairly readable derivation of these equations can be found in Bard's book
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