Diffusion: Calculating D from a Warburg Impedance

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

and the Warburg coefficient, , is given by:

The equation for 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 C^b  denotes a bulk concentration. D is the diffusion coefficient of the species. 

The Warburg coefficient, , 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 . Yo is the magnitude of the admittance ( = 1/Z ) at =1 rad/s (~0.16 Hz).

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

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REFERENCES
(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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