Diffusion: Calculating D from a Warburg Impedance


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The equations (Ref 1) which define a Warburg Impedance are

Z for Warburg

Warburg Z magnitude

and the Warburg coefficient, sigma, is given by:

Eqn for sigma

The equation for sigma applies to both reversible and quasi-reversible reactions for which both halves of the couple are soluble. The subscripts O and R represent the Oxidized and Reduced forms of the species, and Cb  denotes a bulk concentration. D is the diffusion coefficient of the species. 

The Warburg coefficient, sigma, can be determined from the slope of the Warburg plot, or by fitting to an equivalent circuit model which includes a Warburg impedance. However, most equivalent circuit modeling programs return "Yo" rather than sigmaYo is the magnitude of the admittance ( = 1/Z ) at omega=1 rad/s (~0.16 Hz).


The units of sigma are ohm·s-1/2 and the units of Yo are S·s1/2 (Ref 2).

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Impedance Plots for a Warburg
Equivalent Circuits for Diffusion

More about EISMore About EIS

(1) Bard and Faulkner, "Electrochemical Methods, Fundamentals and Applications", Wiley (2000).  See Sect. 10.3.
(2) S = siemens =ohm-1, s = second.

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